id	sid	tid	token	lemma	pos
ap-7723	1	1	acta	acta	PROPN
ap-7723	1	2	polytechnica	polytechnica	PROPN
ap-7723	1	3	https://doi.org/10.14311/ap.2022.62.0008	https://doi.org/10.14311/ap.2022.62.0008	PROPN
ap-7723	1	4	acta	acta	PROPN
ap-7723	1	5	polytechnica	polytechnica	PROPN
ap-7723	1	6	62(1):8–15	62(1):8–15	PROPN
ap-7723	1	7	,	,	PUNCT
ap-7723	1	8	2022	2022	NUM
ap-7723	1	9	©	©	ADP
ap-7723	1	10	2022	2022	NUM
ap-7723	1	11	the	the	DET
ap-7723	1	12	author(s	author(s	NOUN
ap-7723	1	13	)	)	PUNCT
ap-7723	1	14	.	.	PUNCT
ap-7723	2	1	licensed	license	VERB
ap-7723	2	2	under	under	ADP
ap-7723	2	3	a	a	DET
ap-7723	2	4	cc	cc	NOUN
ap-7723	2	5	-	-	PUNCT
ap-7723	2	6	by	by	ADP
ap-7723	2	7	4.0	4.0	NUM
ap-7723	2	8	licence	licence	NOUN
ap-7723	2	9	published	publish	VERB
ap-7723	2	10	by	by	ADP
ap-7723	2	11	the	the	DET
ap-7723	2	12	czech	czech	PROPN
ap-7723	2	13	technical	technical	PROPN
ap-7723	2	14	university	university	PROPN
ap-7723	2	15	in	in	ADP
ap-7723	2	16	prague	prague	NOUN
ap-7723	2	17	quantum	quantum	ADJ
ap-7723	2	18	description	description	NOUN
ap-7723	2	19	of	of	ADP
ap-7723	2	20	angles	angle	NOUN
ap-7723	2	21	in	in	ADP
ap-7723	2	22	the	the	DET
ap-7723	2	23	plane	plane	NOUN
ap-7723	2	24	roberto	roberto	AUX
ap-7723	2	25	beneducia	beneducia	PROPN
ap-7723	2	26	,	,	PUNCT
ap-7723	2	27	emmanuel	emmanuel	PROPN
ap-7723	2	28	frionb	frionb	PROPN
ap-7723	2	29	,	,	PUNCT
ap-7723	2	30	jean	jean	PROPN
ap-7723	2	31	-	-	PUNCT
ap-7723	2	32	pierre	pierre	PROPN
ap-7723	2	33	gazeauc,∗	gazeauc,∗	PROPN
ap-7723	2	34	a	a	DET
ap-7723	2	35	università	università	PROPN
ap-7723	2	36	della	della	PROPN
ap-7723	2	37	calabria	calabria	PROPN
ap-7723	2	38	and	and	CCONJ
ap-7723	2	39	istituto	istituto	PROPN
ap-7723	2	40	nazionale	nazionale	PROPN
ap-7723	2	41	di	di	PROPN
ap-7723	2	42	fisica	fisica	PROPN
ap-7723	2	43	nucleare	nucleare	PROPN
ap-7723	2	44	,	,	PUNCT
ap-7723	2	45	gruppo	gruppo	PROPN
ap-7723	2	46	c.	c.	PROPN
ap-7723	2	47	cosenza	cosenza	PROPN
ap-7723	2	48	,	,	PUNCT
ap-7723	2	49	87036	87036	NUM
ap-7723	2	50	arcavacata	arcavacata	PROPN
ap-7723	2	51	di	di	X
ap-7723	2	52	rende	rende	X
ap-7723	2	53	(	(	PUNCT
ap-7723	2	54	cs	cs	PROPN
ap-7723	2	55	)	)	PUNCT
ap-7723	2	56	,	,	PUNCT
ap-7723	2	57	italy	italy	PROPN
ap-7723	2	58	b	b	PROPN
ap-7723	2	59	university	university	PROPN
ap-7723	2	60	of	of	ADP
ap-7723	2	61	helsinki	helsinki	PROPN
ap-7723	2	62	,	,	PUNCT
ap-7723	2	63	helsinki	helsinki	PROPN
ap-7723	2	64	institute	institute	PROPN
ap-7723	2	65	of	of	ADP
ap-7723	2	66	physics	physics	PROPN
ap-7723	2	67	,	,	PUNCT
ap-7723	2	68	p.	p.	PROPN
ap-7723	2	69	o.	o.	PROPN
ap-7723	2	70	box	box	PROPN
ap-7723	2	71	64	64	NUM
ap-7723	2	72	,	,	PUNCT
ap-7723	2	73	fin-00014	fin-00014	PROPN
ap-7723	2	74	helsinki	helsinki	PROPN
ap-7723	2	75	,	,	PUNCT
ap-7723	2	76	finland	finland	PROPN
ap-7723	2	77	c	c	PROPN
ap-7723	2	78	université	université	PROPN
ap-7723	2	79	de	de	PROPN
ap-7723	2	80	paris	paris	PROPN
ap-7723	2	81	,	,	PUNCT
ap-7723	2	82	cnrs	cnrs	NOUN
ap-7723	2	83	,	,	PUNCT
ap-7723	2	84	astroparticule	astroparticule	NOUN
ap-7723	2	85	et	et	PROPN
ap-7723	2	86	cosmologie	cosmologie	PROPN
ap-7723	2	87	,	,	PUNCT
ap-7723	2	88	75013	75013	NUM
ap-7723	2	89	paris	paris	PROPN
ap-7723	2	90	,	,	PUNCT
ap-7723	2	91	france	france	PROPN
ap-7723	2	92	∗	∗	NOUN
ap-7723	2	93	corresponding	correspond	VERB
ap-7723	2	94	author	author	NOUN
ap-7723	2	95	:	:	PUNCT
ap-7723	2	96	gazeau@apc.in2p3.fr	gazeau@apc.in2p3.fr	PROPN
ap-7723	2	97	abstract	abstract	NOUN
ap-7723	2	98	.	.	PUNCT
ap-7723	3	1	the	the	DET
ap-7723	3	2	real	real	ADJ
ap-7723	3	3	plane	plane	NOUN
ap-7723	3	4	with	with	ADP
ap-7723	3	5	its	its	PRON
ap-7723	3	6	set	set	NOUN
ap-7723	3	7	of	of	ADP
ap-7723	3	8	orientations	orientation	NOUN
ap-7723	3	9	or	or	CCONJ
ap-7723	3	10	angles	angle	NOUN
ap-7723	3	11	in	in	ADP
ap-7723	3	12	[	[	X
ap-7723	3	13	0	0	NUM
ap-7723	3	14	,	,	PUNCT
ap-7723	3	15	π	π	NOUN
ap-7723	3	16	)	)	PUNCT
ap-7723	3	17	is	be	AUX
ap-7723	3	18	the	the	DET
ap-7723	3	19	simplest	simple	ADJ
ap-7723	3	20	non	non	ADJ
ap-7723	3	21	trivial	trivial	ADJ
ap-7723	3	22	example	example	NOUN
ap-7723	3	23	of	of	ADP
ap-7723	3	24	a	a	DET
ap-7723	3	25	(	(	PUNCT
ap-7723	3	26	projective	projective	ADJ
ap-7723	3	27	)	)	PUNCT
ap-7723	3	28	hilbert	hilbert	NOUN
ap-7723	3	29	space	space	NOUN
ap-7723	3	30	and	and	CCONJ
ap-7723	3	31	provides	provide	VERB
ap-7723	3	32	nice	nice	ADJ
ap-7723	3	33	illustrations	illustration	NOUN
ap-7723	3	34	of	of	ADP
ap-7723	3	35	quantum	quantum	ADJ
ap-7723	3	36	formalism	formalism	NOUN
ap-7723	3	37	.	.	PUNCT
ap-7723	4	1	we	we	PRON
ap-7723	4	2	present	present	VERB
ap-7723	4	3	some	some	PRON
ap-7723	4	4	of	of	ADP
ap-7723	4	5	them	they	PRON
ap-7723	4	6	,	,	PUNCT
ap-7723	4	7	namely	namely	ADV
ap-7723	4	8	covariant	covariant	ADJ
ap-7723	4	9	integral	integral	ADJ
ap-7723	4	10	quantization	quantization	NOUN
ap-7723	4	11	,	,	PUNCT
ap-7723	4	12	linear	linear	ADJ
ap-7723	4	13	polarisation	polarisation	NOUN
ap-7723	4	14	of	of	ADP
ap-7723	4	15	light	light	NOUN
ap-7723	4	16	as	as	ADP
ap-7723	4	17	a	a	DET
ap-7723	4	18	quantum	quantum	ADJ
ap-7723	4	19	measurement	measurement	NOUN
ap-7723	4	20	,	,	PUNCT
ap-7723	4	21	interpretation	interpretation	NOUN
ap-7723	4	22	of	of	ADP
ap-7723	4	23	entanglement	entanglement	NOUN
ap-7723	4	24	leading	lead	VERB
ap-7723	4	25	to	to	ADP
ap-7723	4	26	the	the	DET
ap-7723	4	27	violation	violation	NOUN
ap-7723	4	28	of	of	ADP
ap-7723	4	29	bell	bell	NOUN
ap-7723	4	30	inequalities	inequality	NOUN
ap-7723	4	31	,	,	PUNCT
ap-7723	4	32	and	and	CCONJ
ap-7723	4	33	spin	spin	VERB
ap-7723	4	34	one	one	NUM
ap-7723	4	35	-	-	PUNCT
ap-7723	4	36	half	half	NOUN
ap-7723	4	37	coherent	coherent	ADJ
ap-7723	4	38	states	state	NOUN
ap-7723	4	39	viewed	view	VERB
ap-7723	4	40	as	as	ADP
ap-7723	4	41	two	two	NUM
ap-7723	4	42	entangled	entangled	ADJ
ap-7723	4	43	angles	angle	NOUN
ap-7723	4	44	.	.	PUNCT
ap-7723	5	1	keywords	keyword	NOUN
ap-7723	5	2	:	:	PUNCT
ap-7723	5	3	integral	integral	ADJ
ap-7723	5	4	quantization	quantization	NOUN
ap-7723	5	5	,	,	PUNCT
ap-7723	5	6	real	real	ADJ
ap-7723	5	7	hilbert	hilbert	NOUN
ap-7723	5	8	spaces	space	NOUN
ap-7723	5	9	,	,	PUNCT
ap-7723	5	10	quantum	quantum	ADJ
ap-7723	5	11	entanglement	entanglement	NOUN
ap-7723	5	12	.	.	PUNCT
ap-7723	6	1	1	1	X
ap-7723	6	2	.	.	X
ap-7723	6	3	introduction	introduction	NOUN
ap-7723	6	4	the	the	DET
ap-7723	6	5	formulation	formulation	NOUN
ap-7723	6	6	of	of	ADP
ap-7723	6	7	quantum	quantum	ADJ
ap-7723	6	8	mechanics	mechanic	NOUN
ap-7723	6	9	in	in	ADP
ap-7723	6	10	a	a	DET
ap-7723	6	11	real	real	ADJ
ap-7723	6	12	hilbert	hilbert	NOUN
ap-7723	6	13	space	space	NOUN
ap-7723	6	14	has	have	AUX
ap-7723	6	15	been	be	AUX
ap-7723	6	16	analyzed	analyze	VERB
ap-7723	6	17	by	by	ADP
ap-7723	6	18	stueckelberg	stueckelberg	NOUN
ap-7723	6	19	in	in	ADP
ap-7723	6	20	1960	1960	NUM
ap-7723	7	1	[	[	X
ap-7723	7	2	1	1	X
ap-7723	7	3	]	]	PUNCT
ap-7723	7	4	in	in	ADP
ap-7723	7	5	order	order	NOUN
ap-7723	7	6	to	to	PART
ap-7723	7	7	show	show	VERB
ap-7723	7	8	that	that	SCONJ
ap-7723	7	9	the	the	DET
ap-7723	7	10	need	need	NOUN
ap-7723	7	11	for	for	ADP
ap-7723	7	12	a	a	DET
ap-7723	7	13	complex	complex	ADJ
ap-7723	7	14	hilbert	hilbert	NOUN
ap-7723	7	15	space	space	NOUN
ap-7723	7	16	is	be	AUX
ap-7723	7	17	connected	connect	VERB
ap-7723	7	18	to	to	ADP
ap-7723	7	19	the	the	DET
ap-7723	7	20	uncertainty	uncertainty	NOUN
ap-7723	7	21	principle	principle	NOUN
ap-7723	7	22	.	.	PUNCT
ap-7723	8	1	later	later	ADV
ap-7723	8	2	,	,	PUNCT
ap-7723	8	3	solèr	solèr	VERB
ap-7723	8	4	[	[	X
ap-7723	8	5	2	2	NUM
ap-7723	8	6	]	]	PUNCT
ap-7723	8	7	showed	show	VERB
ap-7723	8	8	that	that	SCONJ
ap-7723	8	9	the	the	DET
ap-7723	8	10	lattice	lattice	NOUN
ap-7723	8	11	of	of	ADP
ap-7723	8	12	elementary	elementary	ADJ
ap-7723	8	13	propositions	proposition	NOUN
ap-7723	8	14	is	be	AUX
ap-7723	8	15	isomorphic	isomorphic	ADJ
ap-7723	8	16	to	to	ADP
ap-7723	8	17	the	the	DET
ap-7723	8	18	lattice	lattice	NOUN
ap-7723	8	19	of	of	ADP
ap-7723	8	20	closed	closed	ADJ
ap-7723	8	21	subspaces	subspace	NOUN
ap-7723	8	22	of	of	ADP
ap-7723	8	23	a	a	DET
ap-7723	8	24	separable	separable	ADJ
ap-7723	8	25	hilbert	hilbert	NOUN
ap-7723	8	26	space	space	NOUN
ap-7723	8	27	(	(	PUNCT
ap-7723	8	28	over	over	ADP
ap-7723	8	29	the	the	DET
ap-7723	8	30	reals	real	NOUN
ap-7723	8	31	,	,	PUNCT
ap-7723	8	32	the	the	DET
ap-7723	8	33	complex	complex	ADJ
ap-7723	8	34	numbers	number	NOUN
ap-7723	8	35	or	or	CCONJ
ap-7723	8	36	the	the	DET
ap-7723	8	37	quaternions	quaternion	NOUN
ap-7723	8	38	)	)	PUNCT
ap-7723	8	39	.	.	PUNCT
ap-7723	9	1	in	in	ADP
ap-7723	9	2	other	other	ADJ
ap-7723	9	3	words	word	NOUN
ap-7723	9	4	,	,	PUNCT
ap-7723	9	5	the	the	DET
ap-7723	9	6	lattice	lattice	NOUN
ap-7723	9	7	structure	structure	NOUN
ap-7723	9	8	of	of	ADP
ap-7723	9	9	propositions	proposition	NOUN
ap-7723	9	10	in	in	ADP
ap-7723	9	11	quantum	quantum	ADJ
ap-7723	9	12	physics	physics	NOUN
ap-7723	9	13	does	do	AUX
ap-7723	9	14	not	not	PART
ap-7723	9	15	suggest	suggest	VERB
ap-7723	9	16	the	the	DET
ap-7723	9	17	hilbert	hilbert	NOUN
ap-7723	9	18	space	space	NOUN
ap-7723	9	19	to	to	PART
ap-7723	9	20	be	be	AUX
ap-7723	9	21	complex	complex	ADJ
ap-7723	9	22	.	.	PUNCT
ap-7723	10	1	more	more	ADV
ap-7723	10	2	recently	recently	ADV
ap-7723	10	3	,	,	PUNCT
ap-7723	10	4	moretti	moretti	PROPN
ap-7723	10	5	and	and	CCONJ
ap-7723	10	6	oppio	oppio	PROPN
ap-7723	11	1	[	[	X
ap-7723	11	2	3	3	NUM
ap-7723	11	3	]	]	PUNCT
ap-7723	11	4	gave	give	VERB
ap-7723	11	5	stronger	strong	ADJ
ap-7723	11	6	motivation	motivation	NOUN
ap-7723	11	7	for	for	SCONJ
ap-7723	11	8	the	the	DET
ap-7723	11	9	hilbert	hilbert	PROPN
ap-7723	11	10	space	space	NOUN
ap-7723	11	11	to	to	PART
ap-7723	11	12	be	be	AUX
ap-7723	11	13	complex	complex	ADJ
ap-7723	11	14	which	which	PRON
ap-7723	11	15	rests	rest	VERB
ap-7723	11	16	on	on	ADP
ap-7723	11	17	the	the	DET
ap-7723	11	18	symmetries	symmetry	NOUN
ap-7723	11	19	of	of	ADP
ap-7723	11	20	elementary	elementary	ADJ
ap-7723	11	21	relativistic	relativistic	ADJ
ap-7723	11	22	systems	system	NOUN
ap-7723	11	23	.	.	PUNCT
ap-7723	12	1	in	in	ADP
ap-7723	12	2	this	this	DET
ap-7723	12	3	contribution	contribution	NOUN
ap-7723	12	4	,	,	PUNCT
ap-7723	12	5	we	we	PRON
ap-7723	12	6	do	do	AUX
ap-7723	12	7	not	not	PART
ap-7723	12	8	address	address	VERB
ap-7723	12	9	the	the	DET
ap-7723	12	10	question	question	NOUN
ap-7723	12	11	of	of	ADP
ap-7723	12	12	the	the	DET
ap-7723	12	13	physical	physical	ADJ
ap-7723	12	14	validity	validity	NOUN
ap-7723	12	15	of	of	ADP
ap-7723	12	16	the	the	DET
ap-7723	12	17	real	real	ADJ
ap-7723	12	18	hilbert	hilbert	NOUN
ap-7723	12	19	space	space	NOUN
ap-7723	12	20	formulation	formulation	NOUN
ap-7723	12	21	of	of	ADP
ap-7723	12	22	quantum	quantum	ADJ
ap-7723	12	23	mechanics	mechanic	NOUN
ap-7723	12	24	but	but	CCONJ
ap-7723	12	25	limit	limit	VERB
ap-7723	12	26	ourselves	ourselves	PRON
ap-7723	12	27	to	to	PART
ap-7723	12	28	use	use	VERB
ap-7723	12	29	the	the	DET
ap-7723	12	30	real	real	ADJ
ap-7723	12	31	2	2	NUM
ap-7723	12	32	-	-	PUNCT
ap-7723	12	33	dimensional	dimensional	ADJ
ap-7723	12	34	case	case	NOUN
ap-7723	12	35	,	,	PUNCT
ap-7723	12	36	i.e.	i.e.	X
ap-7723	12	37	the	the	DET
ap-7723	12	38	euclidean	euclidean	ADJ
ap-7723	12	39	plane	plane	NOUN
ap-7723	12	40	,	,	PUNCT
ap-7723	12	41	as	as	ADP
ap-7723	12	42	a	a	DET
ap-7723	12	43	toy	toy	NOUN
ap-7723	12	44	model	model	NOUN
ap-7723	12	45	for	for	ADP
ap-7723	12	46	illustrating	illustrate	VERB
ap-7723	12	47	some	some	DET
ap-7723	12	48	aspects	aspect	NOUN
ap-7723	12	49	of	of	ADP
ap-7723	12	50	the	the	DET
ap-7723	12	51	quantum	quantum	ADJ
ap-7723	12	52	formalism	formalism	NOUN
ap-7723	12	53	,	,	PUNCT
ap-7723	12	54	as	as	ADP
ap-7723	12	55	quantization	quantization	NOUN
ap-7723	12	56	,	,	PUNCT
ap-7723	12	57	entanglement	entanglement	NOUN
ap-7723	12	58	and	and	CCONJ
ap-7723	12	59	quantum	quantum	NOUN
ap-7723	12	60	measurement	measurement	NOUN
ap-7723	12	61	.	.	PUNCT
ap-7723	13	1	the	the	DET
ap-7723	13	2	latter	latter	ADJ
ap-7723	13	3	is	be	AUX
ap-7723	13	4	nicely	nicely	ADV
ap-7723	13	5	represented	represent	VERB
ap-7723	13	6	by	by	ADP
ap-7723	13	7	the	the	DET
ap-7723	13	8	linear	linear	ADJ
ap-7723	13	9	polarization	polarization	NOUN
ap-7723	13	10	of	of	ADP
ap-7723	13	11	light	light	NOUN
ap-7723	13	12	.	.	PUNCT
ap-7723	14	1	this	this	DET
ap-7723	14	2	real	real	ADJ
ap-7723	14	3	2	2	NUM
ap-7723	14	4	-	-	PUNCT
ap-7723	14	5	dimensional	dimensional	ADJ
ap-7723	14	6	case	case	NOUN
ap-7723	14	7	relies	rely	VERB
ap-7723	14	8	on	on	ADP
ap-7723	14	9	the	the	DET
ap-7723	14	10	manipulation	manipulation	NOUN
ap-7723	14	11	of	of	ADP
ap-7723	14	12	the	the	DET
ap-7723	14	13	two	two	NUM
ap-7723	14	14	real	real	ADJ
ap-7723	14	15	pauli	pauli	PROPN
ap-7723	14	16	matrices	matrice	VERB
ap-7723	14	17	σ1	σ1	NOUN
ap-7723	14	18	=	=	PUNCT
ap-7723	14	19	(	(	PUNCT
ap-7723	14	20	0	0	NUM
ap-7723	14	21	1	1	NUM
ap-7723	14	22	1	1	NUM
ap-7723	14	23	0	0	NUM
ap-7723	14	24	)	)	PUNCT
ap-7723	14	25	,	,	PUNCT
ap-7723	14	26	σ3	σ3	NOUN
ap-7723	14	27	=	=	PUNCT
ap-7723	14	28	(	(	PUNCT
ap-7723	14	29	1	1	NUM
ap-7723	14	30	0	0	NUM
ap-7723	14	31	0	0	NUM
ap-7723	14	32	−1	−1	NOUN
ap-7723	14	33	)	)	PUNCT
ap-7723	14	34	,	,	PUNCT
ap-7723	14	35	(	(	PUNCT
ap-7723	14	36	1	1	X
ap-7723	14	37	)	)	PUNCT
ap-7723	14	38	and	and	CCONJ
ap-7723	14	39	their	their	PRON
ap-7723	14	40	tensor	tensor	NOUN
ap-7723	14	41	products	product	NOUN
ap-7723	14	42	,	,	PUNCT
ap-7723	14	43	with	with	ADP
ap-7723	14	44	no	no	DET
ap-7723	14	45	mention	mention	NOUN
ap-7723	14	46	of	of	ADP
ap-7723	14	47	the	the	DET
ap-7723	14	48	third	third	ADJ
ap-7723	14	49	,	,	PUNCT
ap-7723	14	50	complex	complex	ADJ
ap-7723	14	51	matrix	matrix	NOUN
ap-7723	14	52	σ2	σ2	NOUN
ap-7723	14	53	=	=	SYM
ap-7723	14	54	(	(	PUNCT
ap-7723	14	55	0	0	NUM
ap-7723	14	56	−i	−i	NOUN
ap-7723	14	57	i	i	PRON
ap-7723	14	58	0	0	NUM
ap-7723	14	59	)	)	PUNCT
ap-7723	14	60	.	.	PUNCT
ap-7723	15	1	as	as	ADP
ap-7723	15	2	a	a	DET
ap-7723	15	3	matter	matter	NOUN
ap-7723	15	4	of	of	ADP
ap-7723	15	5	fact	fact	NOUN
ap-7723	15	6	,	,	PUNCT
ap-7723	15	7	many	many	ADJ
ap-7723	15	8	examples	example	NOUN
ap-7723	15	9	aimed	aim	VERB
ap-7723	15	10	to	to	PART
ap-7723	15	11	illustrate	illustrate	VERB
ap-7723	15	12	tools	tool	NOUN
ap-7723	15	13	and	and	CCONJ
ap-7723	15	14	concepts	concept	NOUN
ap-7723	15	15	of	of	ADP
ap-7723	15	16	quantum	quantum	ADJ
ap-7723	15	17	information	information	NOUN
ap-7723	15	18	,	,	PUNCT
ap-7723	15	19	quantum	quantum	NOUN
ap-7723	15	20	measurement	measurement	NOUN
ap-7723	15	21	,	,	PUNCT
ap-7723	15	22	quantum	quantum	NOUN
ap-7723	15	23	foundations	foundation	NOUN
ap-7723	15	24	,	,	PUNCT
ap-7723	15	25	...	...	PUNCT
ap-7723	15	26	(	(	PUNCT
ap-7723	15	27	e.g.	e.g.	ADV
ap-7723	15	28	,	,	PUNCT
ap-7723	15	29	peres	pere	NOUN
ap-7723	16	1	[	[	X
ap-7723	16	2	4	4	NUM
ap-7723	16	3	]	]	PUNCT
ap-7723	16	4	)	)	PUNCT
ap-7723	16	5	are	be	AUX
ap-7723	16	6	illustrated	illustrate	VERB
ap-7723	16	7	with	with	ADP
ap-7723	16	8	manipulations	manipulation	NOUN
ap-7723	16	9	of	of	ADP
ap-7723	16	10	these	these	DET
ap-7723	16	11	matrices	matrix	NOUN
ap-7723	16	12	.	.	PUNCT
ap-7723	17	1	in	in	ADP
ap-7723	17	2	[	[	X
ap-7723	17	3	5	5	NUM
ap-7723	17	4	]	]	PUNCT
ap-7723	17	5	,	,	PUNCT
ap-7723	17	6	it	it	PRON
ap-7723	17	7	was	be	AUX
ap-7723	17	8	shown	show	VERB
ap-7723	17	9	that	that	SCONJ
ap-7723	17	10	the	the	DET
ap-7723	17	11	set	set	NOUN
ap-7723	17	12	of	of	ADP
ap-7723	17	13	pure	pure	ADJ
ap-7723	17	14	states	state	NOUN
ap-7723	17	15	in	in	ADP
ap-7723	17	16	the	the	DET
ap-7723	17	17	plane	plane	NOUN
ap-7723	17	18	is	be	AUX
ap-7723	17	19	represented	represent	VERB
ap-7723	17	20	by	by	ADP
ap-7723	17	21	half	half	NOUN
ap-7723	17	22	of	of	ADP
ap-7723	17	23	the	the	DET
ap-7723	17	24	unit	unit	NOUN
ap-7723	17	25	circle	circle	NOUN
ap-7723	17	26	and	and	CCONJ
ap-7723	17	27	the	the	DET
ap-7723	17	28	set	set	NOUN
ap-7723	17	29	of	of	ADP
ap-7723	17	30	mixed	mixed	ADJ
ap-7723	17	31	states	state	NOUN
ap-7723	17	32	by	by	ADP
ap-7723	17	33	half	half	DET
ap-7723	17	34	the	the	DET
ap-7723	17	35	unit	unit	NOUN
ap-7723	17	36	disk	disk	NOUN
ap-7723	17	37	,	,	PUNCT
ap-7723	17	38	and	and	CCONJ
ap-7723	17	39	also	also	ADV
ap-7723	17	40	that	that	SCONJ
ap-7723	17	41	rotations	rotation	NOUN
ap-7723	17	42	in	in	ADP
ap-7723	17	43	the	the	DET
ap-7723	17	44	plane	plane	NOUN
ap-7723	17	45	rule	rule	NOUN
ap-7723	17	46	time	time	NOUN
ap-7723	17	47	evolution	evolution	NOUN
ap-7723	17	48	through	through	ADP
ap-7723	17	49	majorana	majorana	PROPN
ap-7723	17	50	-	-	PUNCT
ap-7723	17	51	like	like	ADJ
ap-7723	17	52	equations	equation	NOUN
ap-7723	17	53	,	,	PUNCT
ap-7723	17	54	all	all	PRON
ap-7723	17	55	of	of	ADP
ap-7723	17	56	this	this	PRON
ap-7723	17	57	using	use	VERB
ap-7723	17	58	only	only	ADJ
ap-7723	17	59	real	real	ADJ
ap-7723	17	60	quantities	quantity	NOUN
ap-7723	17	61	for	for	ADP
ap-7723	17	62	both	both	CCONJ
ap-7723	17	63	closed	closed	ADJ
ap-7723	17	64	and	and	CCONJ
ap-7723	17	65	open	open	ADJ
ap-7723	17	66	systems	system	NOUN
ap-7723	17	67	.	.	PUNCT
ap-7723	18	1	this	this	DET
ap-7723	18	2	paper	paper	NOUN
ap-7723	18	3	is	be	AUX
ap-7723	18	4	a	a	DET
ap-7723	18	5	direct	direct	ADJ
ap-7723	18	6	extension	extension	NOUN
ap-7723	18	7	of	of	ADP
ap-7723	18	8	our	our	PRON
ap-7723	18	9	previous	previous	ADJ
ap-7723	18	10	paper	paper	NOUN
ap-7723	18	11	[	[	X
ap-7723	18	12	6	6	NUM
ap-7723	18	13	]	]	PUNCT
ap-7723	18	14	,	,	PUNCT
ap-7723	18	15	and	and	CCONJ
ap-7723	18	16	for	for	ADP
ap-7723	18	17	this	this	DET
ap-7723	18	18	reason	reason	NOUN
ap-7723	18	19	we	we	PRON
ap-7723	18	20	start	start	VERB
ap-7723	18	21	the	the	DET
ap-7723	18	22	discussion	discussion	NOUN
ap-7723	18	23	by	by	ADP
ap-7723	18	24	recalling	recall	VERB
ap-7723	18	25	some	some	DET
ap-7723	18	26	key	key	ADJ
ap-7723	18	27	elements	element	NOUN
ap-7723	18	28	of	of	ADP
ap-7723	18	29	the	the	DET
ap-7723	18	30	mathematical	mathematical	ADJ
ap-7723	18	31	formalism	formalism	NOUN
ap-7723	18	32	.	.	PUNCT
ap-7723	19	1	2	2	X
ap-7723	19	2	.	.	X
ap-7723	19	3	background	background	NOUN
ap-7723	19	4	2.1	2.1	NUM
ap-7723	19	5	.	.	PUNCT
ap-7723	20	1	definition	definition	NOUN
ap-7723	20	2	of	of	ADP
ap-7723	20	3	povms	povms	NOUN
ap-7723	20	4	we	we	PRON
ap-7723	20	5	start	start	VERB
ap-7723	20	6	with	with	ADP
ap-7723	20	7	the	the	DET
ap-7723	20	8	definition	definition	NOUN
ap-7723	20	9	of	of	ADP
ap-7723	20	10	a	a	DET
ap-7723	20	11	normalized	normalize	VERB
ap-7723	20	12	positiveoperator	positiveoperator	NOUN
ap-7723	20	13	valued	value	VERB
ap-7723	20	14	measure	measure	NOUN
ap-7723	20	15	(	(	PUNCT
ap-7723	20	16	povm	povm	NOUN
ap-7723	20	17	)	)	PUNCT
ap-7723	21	1	[	[	X
ap-7723	21	2	7	7	NUM
ap-7723	21	3	]	]	PUNCT
ap-7723	21	4	.	.	PUNCT
ap-7723	22	1	it	it	PRON
ap-7723	22	2	is	be	AUX
ap-7723	22	3	defined	define	VERB
ap-7723	22	4	as	as	ADP
ap-7723	22	5	a	a	DET
ap-7723	22	6	map	map	NOUN
ap-7723	22	7	f	f	X
ap-7723	22	8	:	:	PUNCT
ap-7723	22	9	b(ω	b(ω	X
ap-7723	22	10	)	)	PUNCT
ap-7723	22	11	→	→	PUNCT
ap-7723	22	12	l+	l+	X
ap-7723	22	13	s	s	X
ap-7723	22	14	(	(	PUNCT
ap-7723	22	15	h	h	NOUN
ap-7723	22	16	)	)	PUNCT
ap-7723	22	17	from	from	ADP
ap-7723	22	18	the	the	DET
ap-7723	22	19	borel	borel	PROPN
ap-7723	22	20	σ	σ	PROPN
ap-7723	22	21	-	-	PUNCT
ap-7723	22	22	algebra	algebra	NOUN
ap-7723	22	23	of	of	ADP
ap-7723	22	24	a	a	DET
ap-7723	22	25	topological	topological	ADJ
ap-7723	22	26	space	space	NOUN
ap-7723	22	27	ω	ω	NOUN
ap-7723	22	28	to	to	ADP
ap-7723	22	29	the	the	DET
ap-7723	22	30	space	space	NOUN
ap-7723	22	31	of	of	ADP
ap-7723	22	32	linear	linear	PROPN
ap-7723	22	33	positive	positive	ADJ
ap-7723	22	34	self	self	NOUN
ap-7723	22	35	-	-	PUNCT
ap-7723	22	36	adjoint	adjoint	NOUN
ap-7723	22	37	operators	operator	NOUN
ap-7723	22	38	on	on	ADP
ap-7723	22	39	a	a	DET
ap-7723	22	40	hilbert	hilbert	NOUN
ap-7723	22	41	space	space	NOUN
ap-7723	22	42	h	h	NOUN
ap-7723	22	43	such	such	ADJ
ap-7723	22	44	that	that	SCONJ
ap-7723	22	45	f	f	PROPN
ap-7723	22	46	(	(	PUNCT
ap-7723	22	47	∞⋃	∞⋃	PROPN
ap-7723	22	48	n=1	n=1	PROPN
ap-7723	22	49	∆n	∆n	PROPN
ap-7723	22	50	)	)	PUNCT
ap-7723	23	1	=	=	PUNCT
ap-7723	24	1	∞∑	∞∑	NUM
ap-7723	24	2	n=1	n=1	PROPN
ap-7723	24	3	f	f	PROPN
ap-7723	24	4	(	(	PUNCT
ap-7723	24	5	∆n	∆n	PROPN
ap-7723	24	6	)	)	PUNCT
ap-7723	24	7	f	f	PROPN
ap-7723	24	8	(	(	PUNCT
ap-7723	24	9	ω	ω	NOUN
ap-7723	24	10	)	)	PUNCT
ap-7723	24	11	=	=	SYM
ap-7723	24	12	1	1	X
ap-7723	24	13	.	.	PUNCT
ap-7723	24	14	(	(	PUNCT
ap-7723	24	15	2	2	X
ap-7723	24	16	)	)	PUNCT
ap-7723	24	17	in	in	ADP
ap-7723	24	18	this	this	DET
ap-7723	24	19	definition	definition	NOUN
ap-7723	24	20	,	,	PUNCT
ap-7723	24	21	{	{	PUNCT
ap-7723	24	22	∆n	∆n	NOUN
ap-7723	24	23	}	}	PUNCT
ap-7723	24	24	is	be	AUX
ap-7723	24	25	a	a	DET
ap-7723	24	26	countable	countable	ADJ
ap-7723	24	27	family	family	NOUN
ap-7723	24	28	of	of	ADP
ap-7723	24	29	disjoint	disjoint	NOUN
ap-7723	24	30	sets	set	NOUN
ap-7723	24	31	in	in	ADP
ap-7723	24	32	b(ω	b(ω	NOUN
ap-7723	24	33	)	)	PUNCT
ap-7723	24	34	and	and	CCONJ
ap-7723	24	35	the	the	DET
ap-7723	24	36	series	series	NOUN
ap-7723	24	37	converges	converge	VERB
ap-7723	24	38	in	in	ADP
ap-7723	24	39	the	the	DET
ap-7723	24	40	weak	weak	ADJ
ap-7723	24	41	operator	operator	NOUN
ap-7723	24	42	topology	topology	NOUN
ap-7723	24	43	.	.	PUNCT
ap-7723	25	1	if	if	SCONJ
ap-7723	25	2	ω	ω	NOUN
ap-7723	25	3	=	=	SYM
ap-7723	25	4	r	r	NOUN
ap-7723	25	5	,	,	PUNCT
ap-7723	25	6	we	we	PRON
ap-7723	25	7	have	have	VERB
ap-7723	25	8	a	a	DET
ap-7723	25	9	real	real	ADJ
ap-7723	25	10	povm	povm	NOUN
ap-7723	25	11	.	.	PUNCT
ap-7723	26	1	if	if	SCONJ
ap-7723	26	2	f	f	PROPN
ap-7723	26	3	(	(	PUNCT
ap-7723	26	4	∆	∆	PROPN
ap-7723	26	5	)	)	PUNCT
ap-7723	26	6	is	be	AUX
ap-7723	26	7	a	a	DET
ap-7723	26	8	projection	projection	NOUN
ap-7723	26	9	operator	operator	NOUN
ap-7723	26	10	for	for	ADP
ap-7723	26	11	every	every	DET
ap-7723	26	12	∆	∆	PROPN
ap-7723	26	13	∈	∈	PROPN
ap-7723	26	14	b(ω	b(ω	ADV
ap-7723	26	15	)	)	PUNCT
ap-7723	26	16	,	,	PUNCT
ap-7723	26	17	we	we	PRON
ap-7723	26	18	recover	recover	VERB
ap-7723	26	19	the	the	DET
ap-7723	26	20	usual	usual	ADJ
ap-7723	26	21	projection	projection	NOUN
ap-7723	26	22	-	-	PUNCT
ap-7723	26	23	valued	value	VERB
ap-7723	26	24	measure	measure	NOUN
ap-7723	26	25	(	(	PUNCT
ap-7723	26	26	pvm	pvm	NOUN
ap-7723	26	27	)	)	PUNCT
ap-7723	26	28	.	.	PUNCT
ap-7723	27	1	a	a	DET
ap-7723	27	2	quantum	quantum	ADJ
ap-7723	27	3	state	state	NOUN
ap-7723	27	4	is	be	AUX
ap-7723	27	5	defined	define	VERB
ap-7723	27	6	as	as	ADP
ap-7723	27	7	a	a	DET
ap-7723	27	8	non	non	ADJ
ap-7723	27	9	-	-	ADJ
ap-7723	27	10	negative	negative	ADJ
ap-7723	27	11	,	,	PUNCT
ap-7723	27	12	bounded	bound	VERB
ap-7723	27	13	self	self	NOUN
ap-7723	27	14	-	-	PUNCT
ap-7723	27	15	adjoint	adjoint	NOUN
ap-7723	27	16	operator	operator	NOUN
ap-7723	27	17	with	with	ADP
ap-7723	27	18	trace	trace	NOUN
ap-7723	27	19	1	1	NUM
ap-7723	27	20	.	.	PUNCT
ap-7723	28	1	the	the	DET
ap-7723	28	2	space	space	NOUN
ap-7723	28	3	of	of	ADP
ap-7723	28	4	states	state	NOUN
ap-7723	28	5	is	be	AUX
ap-7723	28	6	a	a	DET
ap-7723	28	7	convex	convex	ADJ
ap-7723	28	8	space	space	NOUN
ap-7723	28	9	and	and	CCONJ
ap-7723	28	10	is	be	AUX
ap-7723	28	11	denoted	denote	VERB
ap-7723	28	12	by	by	ADP
ap-7723	28	13	s(h	s(h	PROPN
ap-7723	28	14	)	)	PUNCT
ap-7723	28	15	.	.	PUNCT
ap-7723	29	1	a	a	DET
ap-7723	29	2	quantum	quantum	NOUN
ap-7723	29	3	measurement	measurement	NOUN
ap-7723	29	4	corresponds	correspond	VERB
ap-7723	29	5	to	to	ADP
ap-7723	29	6	an	an	DET
ap-7723	29	7	affine	affine	NOUN
ap-7723	29	8	map	map	NOUN
ap-7723	29	9	s(h	s(h	PROPN
ap-7723	29	10	)	)	PUNCT
ap-7723	29	11	7→	7→	NUM
ap-7723	29	12	m+(ω	m+(ω	NOUN
ap-7723	29	13	)	)	PUNCT
ap-7723	29	14	from	from	ADP
ap-7723	29	15	quantum	quantum	ADJ
ap-7723	29	16	states	state	NOUN
ap-7723	29	17	to	to	ADP
ap-7723	29	18	probability	probability	NOUN
ap-7723	29	19	measures	measure	NOUN
ap-7723	29	20	,	,	PUNCT
ap-7723	29	21	ρ	ρ	NOUN
ap-7723	29	22	7→	7→	NUM
ap-7723	29	23	µρ	µρ	ADP
ap-7723	29	24	.	.	PUNCT
ap-7723	30	1	there	there	PRON
ap-7723	30	2	is	be	VERB
ap-7723	30	3	[	[	X
ap-7723	30	4	8	8	NUM
ap-7723	30	5	]	]	PUNCT
ap-7723	30	6	a	a	DET
ap-7723	30	7	one	one	NUM
ap-7723	30	8	-	-	PUNCT
ap-7723	30	9	to	to	ADP
ap-7723	30	10	-	-	PUNCT
ap-7723	30	11	one	one	NUM
ap-7723	30	12	correspondence	correspondence	NOUN
ap-7723	30	13	between	between	ADP
ap-7723	30	14	povms	povms	NOUN
ap-7723	30	15	f	f	NOUN
ap-7723	30	16	:	:	PUNCT
ap-7723	30	17	b(ω	b(ω	X
ap-7723	30	18	)	)	PUNCT
ap-7723	30	19	→	→	PUNCT
ap-7723	30	20	l+	l+	X
ap-7723	30	21	s	s	X
ap-7723	30	22	(	(	PUNCT
ap-7723	30	23	h	h	NOUN
ap-7723	30	24	)	)	PUNCT
ap-7723	30	25	and	and	CCONJ
ap-7723	30	26	affine	affine	PROPN
ap-7723	30	27	maps	map	NOUN
ap-7723	30	28	s(h	s(h	PROPN
ap-7723	30	29	)	)	PUNCT
ap-7723	30	30	7→	7→	NUM
ap-7723	30	31	m+(ω	m+(ω	NOUN
ap-7723	30	32	)	)	PUNCT
ap-7723	30	33	given	give	VERB
ap-7723	30	34	by	by	ADP
ap-7723	30	35	µρ(∆	µρ(∆	NOUN
ap-7723	30	36	)	)	PUNCT
ap-7723	31	1	=	=	SYM
ap-7723	31	2	tr(ρf	tr(ρf	NOUN
ap-7723	31	3	(	(	PUNCT
ap-7723	31	4	∆	∆	PROPN
ap-7723	31	5	)	)	PUNCT
ap-7723	31	6	)	)	PUNCT
ap-7723	31	7	,	,	PUNCT
ap-7723	31	8	∆	∆	PROPN
ap-7723	31	9	∈	∈	PROPN
ap-7723	31	10	b(ω	b(ω	ADV
ap-7723	31	11	)	)	PUNCT
ap-7723	31	12	.	.	PUNCT
ap-7723	32	1	2.2	2.2	NUM
ap-7723	32	2	.	.	PUNCT
ap-7723	32	3	integral	integral	ADJ
ap-7723	32	4	quantization	quantization	NOUN
ap-7723	32	5	quantum	quantum	NOUN
ap-7723	32	6	mechanics	mechanic	NOUN
ap-7723	32	7	is	be	AUX
ap-7723	32	8	usually	usually	ADV
ap-7723	32	9	taught	teach	VERB
ap-7723	32	10	in	in	ADP
ap-7723	32	11	terms	term	NOUN
ap-7723	32	12	of	of	ADP
ap-7723	32	13	projection	projection	NOUN
ap-7723	32	14	operators	operator	NOUN
ap-7723	32	15	and	and	CCONJ
ap-7723	32	16	pvm	pvm	NOUN
ap-7723	32	17	,	,	PUNCT
ap-7723	32	18	but	but	CCONJ
ap-7723	32	19	measurements	measurement	NOUN
ap-7723	32	20	usually	usually	ADV
ap-7723	32	21	8	8	NUM
ap-7723	32	22	https://doi.org/10.14311/ap.2022.62.0008	https://doi.org/10.14311/ap.2022.62.0008	NOUN
ap-7723	32	23	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7723	32	24	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7723	32	25	vol	vol	NOUN
ap-7723	32	26	.	.	PROPN
ap-7723	33	1	62	62	NUM
ap-7723	33	2	no	no	INTJ
ap-7723	33	3	.	.	PUNCT
ap-7723	34	1	1/2022	1/2022	NUM
ap-7723	34	2	quantum	quantum	NOUN
ap-7723	34	3	angles	angle	NOUN
ap-7723	34	4	give	give	VERB
ap-7723	34	5	a	a	DET
ap-7723	34	6	statistical	statistical	ADJ
ap-7723	34	7	distribution	distribution	NOUN
ap-7723	34	8	around	around	ADP
ap-7723	34	9	a	a	DET
ap-7723	34	10	mean	mean	ADJ
ap-7723	34	11	value	value	NOUN
ap-7723	34	12	,	,	PUNCT
ap-7723	34	13	incompatible	incompatible	ADJ
ap-7723	34	14	with	with	ADP
ap-7723	34	15	the	the	DET
ap-7723	34	16	theory	theory	NOUN
ap-7723	34	17	.	.	PUNCT
ap-7723	35	1	we	we	PRON
ap-7723	35	2	recall	recall	VERB
ap-7723	35	3	here	here	ADV
ap-7723	35	4	a	a	DET
ap-7723	35	5	generalization	generalization	NOUN
ap-7723	35	6	of	of	ADP
ap-7723	35	7	a	a	DET
ap-7723	35	8	quantization	quantization	NOUN
ap-7723	35	9	procedure	procedure	NOUN
ap-7723	35	10	,	,	PUNCT
ap-7723	35	11	the	the	DET
ap-7723	35	12	integral	integral	ADJ
ap-7723	35	13	quantization	quantization	NOUN
ap-7723	35	14	,	,	PUNCT
ap-7723	35	15	based	base	VERB
ap-7723	35	16	on	on	ADP
ap-7723	35	17	povms	povms	NOUN
ap-7723	35	18	instead	instead	ADV
ap-7723	35	19	of	of	ADP
ap-7723	35	20	pvm	pvm	NOUN
ap-7723	35	21	.	.	PUNCT
ap-7723	36	1	the	the	DET
ap-7723	36	2	basic	basic	ADJ
ap-7723	36	3	requirements	requirement	NOUN
ap-7723	36	4	of	of	ADP
ap-7723	36	5	this	this	DET
ap-7723	36	6	programme	programme	NOUN
ap-7723	36	7	are	be	AUX
ap-7723	36	8	the	the	DET
ap-7723	36	9	following	following	NOUN
ap-7723	36	10	:	:	PUNCT
ap-7723	36	11	the	the	DET
ap-7723	36	12	quantization	quantization	NOUN
ap-7723	36	13	of	of	ADP
ap-7723	36	14	a	a	DET
ap-7723	36	15	classical	classical	ADJ
ap-7723	36	16	function	function	NOUN
ap-7723	36	17	defined	define	VERB
ap-7723	36	18	on	on	ADP
ap-7723	36	19	a	a	DET
ap-7723	36	20	set	set	NOUN
ap-7723	36	21	x	x	PUNCT
ap-7723	36	22	must	must	AUX
ap-7723	36	23	respect	respect	VERB
ap-7723	36	24	(	(	PUNCT
ap-7723	36	25	1	1	NUM
ap-7723	36	26	.	.	NUM
ap-7723	36	27	)	)	PUNCT
ap-7723	36	28	linearity	linearity	NOUN
ap-7723	36	29	.	.	PUNCT
ap-7723	37	1	quantization	quantization	NOUN
ap-7723	37	2	is	be	AUX
ap-7723	37	3	a	a	DET
ap-7723	37	4	linear	linear	ADJ
ap-7723	37	5	map	map	NOUN
ap-7723	38	1	f	f	PROPN
ap-7723	38	2	7→	7→	NUM
ap-7723	38	3	af	af	VERB
ap-7723	38	4	:	:	PUNCT
ap-7723	39	1	q	q	X
ap-7723	39	2	:	:	PUNCT
ap-7723	39	3	c(x	c(x	NOUN
ap-7723	39	4	)	)	PUNCT
ap-7723	39	5	7→	7→	NUM
ap-7723	40	1	a(h	a(h	PROPN
ap-7723	40	2	)	)	PUNCT
ap-7723	40	3	,	,	PUNCT
ap-7723	40	4	q(f	q(f	PROPN
ap-7723	40	5	)	)	PUNCT
ap-7723	40	6	=	=	PRON
ap-7723	40	7	af	af	PROPN
ap-7723	40	8	,	,	PUNCT
ap-7723	40	9	(	(	PUNCT
ap-7723	40	10	3	3	X
ap-7723	40	11	)	)	PUNCT
ap-7723	40	12	where	where	SCONJ
ap-7723	40	13	•	•	NOUN
ap-7723	40	14	c(x	c(x	NOUN
ap-7723	40	15	)	)	PUNCT
ap-7723	40	16	is	be	AUX
ap-7723	40	17	a	a	DET
ap-7723	40	18	vector	vector	NOUN
ap-7723	40	19	space	space	NOUN
ap-7723	40	20	of	of	ADP
ap-7723	40	21	complex	complex	ADJ
ap-7723	40	22	or	or	CCONJ
ap-7723	40	23	real	real	ADV
ap-7723	40	24	-	-	PUNCT
ap-7723	40	25	valued	value	VERB
ap-7723	40	26	functions	function	NOUN
ap-7723	40	27	f(x	f(x	PROPN
ap-7723	40	28	)	)	PUNCT
ap-7723	40	29	on	on	ADP
ap-7723	40	30	a	a	DET
ap-7723	40	31	set	set	NOUN
ap-7723	40	32	x	x	NOUN
ap-7723	40	33	,	,	PUNCT
ap-7723	40	34	i.e.	i.e.	X
ap-7723	40	35	a	a	DET
ap-7723	40	36	“	"	PUNCT
ap-7723	40	37	classical	classical	ADJ
ap-7723	40	38	”	"	PUNCT
ap-7723	40	39	mathematical	mathematical	ADJ
ap-7723	40	40	model	model	NOUN
ap-7723	40	41	,	,	PUNCT
ap-7723	40	42	•	•	DET
ap-7723	40	43	a(h	a(h	PROPN
ap-7723	40	44	)	)	PUNCT
ap-7723	40	45	is	be	AUX
ap-7723	40	46	a	a	DET
ap-7723	40	47	vector	vector	NOUN
ap-7723	40	48	space	space	NOUN
ap-7723	40	49	of	of	ADP
ap-7723	40	50	linear	linear	PROPN
ap-7723	40	51	operators	operator	NOUN
ap-7723	40	52	in	in	ADP
ap-7723	40	53	some	some	DET
ap-7723	40	54	real	real	ADJ
ap-7723	40	55	or	or	CCONJ
ap-7723	40	56	complex	complex	ADJ
ap-7723	40	57	hilbert	hilbert	NOUN
ap-7723	40	58	space	space	NOUN
ap-7723	40	59	h	h	NOUN
ap-7723	40	60	,	,	PUNCT
ap-7723	40	61	i.e.	i.e.	X
ap-7723	40	62	,	,	PUNCT
ap-7723	40	63	a	a	DET
ap-7723	40	64	“	"	PUNCT
ap-7723	40	65	quantum	quantum	NOUN
ap-7723	40	66	”	"	PUNCT
ap-7723	40	67	mathematical	mathematical	ADJ
ap-7723	40	68	model	model	NOUN
ap-7723	40	69	,	,	PUNCT
ap-7723	40	70	notwithstanding	notwithstanding	ADP
ap-7723	40	71	the	the	DET
ap-7723	40	72	question	question	NOUN
ap-7723	40	73	of	of	ADP
ap-7723	40	74	common	common	ADJ
ap-7723	40	75	domains	domain	NOUN
ap-7723	40	76	in	in	ADP
ap-7723	40	77	the	the	DET
ap-7723	40	78	case	case	NOUN
ap-7723	40	79	of	of	ADP
ap-7723	40	80	unbounded	unbounded	ADJ
ap-7723	40	81	operators	operator	NOUN
ap-7723	40	82	.	.	PUNCT
ap-7723	41	1	(	(	PUNCT
ap-7723	41	2	2	2	NUM
ap-7723	41	3	.	.	NUM
ap-7723	41	4	)	)	PUNCT
ap-7723	41	5	unity	unity	NOUN
ap-7723	41	6	.	.	PUNCT
ap-7723	42	1	the	the	DET
ap-7723	42	2	map	map	NOUN
ap-7723	42	3	(	(	PUNCT
ap-7723	42	4	3	3	X
ap-7723	42	5	)	)	PUNCT
ap-7723	42	6	is	be	AUX
ap-7723	42	7	such	such	ADJ
ap-7723	42	8	that	that	SCONJ
ap-7723	42	9	the	the	DET
ap-7723	42	10	function	function	NOUN
ap-7723	42	11	f	f	NOUN
ap-7723	42	12	=	=	SYM
ap-7723	42	13	1	1	NUM
ap-7723	42	14	is	be	AUX
ap-7723	42	15	mapped	map	VERB
ap-7723	42	16	to	to	ADP
ap-7723	42	17	the	the	DET
ap-7723	42	18	identity	identity	NOUN
ap-7723	42	19	operator	operator	NOUN
ap-7723	42	20	1	1	NUM
ap-7723	42	21	on	on	ADP
ap-7723	42	22	h.	h.	PROPN
ap-7723	42	23	(	(	PUNCT
ap-7723	42	24	3	3	NUM
ap-7723	42	25	.	.	NUM
ap-7723	42	26	)	)	PUNCT
ap-7723	42	27	reality	reality	NOUN
ap-7723	42	28	.	.	PUNCT
ap-7723	43	1	a	a	DET
ap-7723	43	2	real	real	ADJ
ap-7723	43	3	function	function	NOUN
ap-7723	43	4	f	f	PROPN
ap-7723	43	5	is	be	AUX
ap-7723	43	6	mapped	map	VERB
ap-7723	43	7	to	to	ADP
ap-7723	43	8	a	a	DET
ap-7723	43	9	selfadjoint	selfadjoint	NOUN
ap-7723	43	10	or	or	CCONJ
ap-7723	43	11	normal	normal	ADJ
ap-7723	43	12	operator	operator	NOUN
ap-7723	43	13	af	af	VERB
ap-7723	43	14	in	in	ADP
ap-7723	43	15	h	h	NOUN
ap-7723	43	16	or	or	CCONJ
ap-7723	43	17	,	,	PUNCT
ap-7723	43	18	at	at	ADP
ap-7723	43	19	least	least	ADJ
ap-7723	43	20	,	,	PUNCT
ap-7723	43	21	a	a	DET
ap-7723	43	22	symmetric	symmetric	ADJ
ap-7723	43	23	operator	operator	NOUN
ap-7723	43	24	(	(	PUNCT
ap-7723	43	25	in	in	ADP
ap-7723	43	26	the	the	DET
ap-7723	43	27	infinite	infinite	ADJ
ap-7723	43	28	-	-	PUNCT
ap-7723	43	29	dimensional	dimensional	ADJ
ap-7723	43	30	case	case	NOUN
ap-7723	43	31	)	)	PUNCT
ap-7723	43	32	.	.	PUNCT
ap-7723	44	1	(	(	PUNCT
ap-7723	44	2	4	4	NUM
ap-7723	44	3	.	.	PUNCT
ap-7723	44	4	)	)	PUNCT
ap-7723	44	5	covariance	covariance	NOUN
ap-7723	44	6	.	.	PUNCT
ap-7723	45	1	defining	define	VERB
ap-7723	45	2	the	the	DET
ap-7723	45	3	action	action	NOUN
ap-7723	45	4	of	of	ADP
ap-7723	45	5	a	a	DET
ap-7723	45	6	symmetry	symmetry	NOUN
ap-7723	45	7	group	group	NOUN
ap-7723	45	8	g	g	PROPN
ap-7723	45	9	on	on	ADP
ap-7723	45	10	x	x	PUNCT
ap-7723	45	11	by	by	ADP
ap-7723	45	12	(	(	PUNCT
ap-7723	45	13	g	g	PROPN
ap-7723	45	14	,	,	PUNCT
ap-7723	45	15	x	x	NOUN
ap-7723	45	16	)	)	PUNCT
ap-7723	45	17	∈	∈	PROPN
ap-7723	45	18	g×x	g×x	PROPN
ap-7723	45	19	such	such	ADJ
ap-7723	45	20	as	as	ADP
ap-7723	45	21	(	(	PUNCT
ap-7723	45	22	g	g	NOUN
ap-7723	45	23	,	,	PUNCT
ap-7723	45	24	x	x	NOUN
ap-7723	45	25	)	)	PUNCT
ap-7723	45	26	7→	7→	NUM
ap-7723	45	27	g	g	NOUN
ap-7723	45	28	·	·	PUNCT
ap-7723	45	29	x	x	PUNCT
ap-7723	45	30	∈	∈	PROPN
ap-7723	45	31	x	x	PRON
ap-7723	45	32	,	,	PUNCT
ap-7723	45	33	there	there	PRON
ap-7723	45	34	is	be	VERB
ap-7723	45	35	a	a	DET
ap-7723	45	36	unitary	unitary	ADJ
ap-7723	45	37	representation	representation	NOUN
ap-7723	45	38	u	u	NOUN
ap-7723	45	39	of	of	ADP
ap-7723	45	40	g	g	PROPN
ap-7723	45	41	such	such	ADJ
ap-7723	45	42	that	that	SCONJ
ap-7723	45	43	at	at	ADP
ap-7723	45	44	(	(	PUNCT
ap-7723	45	45	g)f	g)f	X
ap-7723	45	46	=	=	SYM
ap-7723	45	47	u(g)af	u(g)af	NOUN
ap-7723	45	48	u(g−1	u(g−1	PROPN
ap-7723	45	49	)	)	PUNCT
ap-7723	45	50	,	,	PUNCT
ap-7723	45	51	with	with	ADP
ap-7723	45	52	(	(	PUNCT
ap-7723	45	53	t	t	PROPN
ap-7723	45	54	(	(	PUNCT
ap-7723	45	55	g)f)(x	g)f)(x	PROPN
ap-7723	45	56	)	)	PUNCT
ap-7723	46	1	=	=	PUNCT
ap-7723	46	2	f	f	PROPN
ap-7723	46	3	(	(	PUNCT
ap-7723	46	4	g−1	g−1	PROPN
ap-7723	46	5	·	·	PUNCT
ap-7723	46	6	x	x	X
ap-7723	46	7	)	)	PUNCT
ap-7723	46	8	.	.	PUNCT
ap-7723	47	1	performing	perform	VERB
ap-7723	47	2	the	the	DET
ap-7723	47	3	integral	integral	ADJ
ap-7723	47	4	quantization	quantization	NOUN
ap-7723	47	5	[	[	X
ap-7723	47	6	9	9	NUM
ap-7723	47	7	]	]	PUNCT
ap-7723	47	8	of	of	ADP
ap-7723	47	9	a	a	DET
ap-7723	47	10	function	function	NOUN
ap-7723	47	11	f(x	f(x	PROPN
ap-7723	47	12	)	)	PUNCT
ap-7723	47	13	on	on	ADP
ap-7723	47	14	a	a	DET
ap-7723	47	15	measure	measure	NOUN
ap-7723	47	16	space	space	NOUN
ap-7723	47	17	(	(	PUNCT
ap-7723	47	18	x	x	NOUN
ap-7723	47	19	,	,	PUNCT
ap-7723	47	20	ν	ν	NOUN
ap-7723	47	21	)	)	PUNCT
ap-7723	47	22	boils	boil	VERB
ap-7723	47	23	down	down	ADP
ap-7723	47	24	to	to	ADP
ap-7723	47	25	the	the	DET
ap-7723	47	26	linear	linear	ADJ
ap-7723	47	27	map	map	NOUN
ap-7723	47	28	:	:	PUNCT
ap-7723	47	29	f	f	PROPN
ap-7723	48	1	7→	7→	NUM
ap-7723	48	2	af	af	PROPN
ap-7723	48	3	=	=	SYM
ap-7723	48	4	∫	∫	PROPN
ap-7723	48	5	x	x	SYM
ap-7723	48	6	m(x	m(x	PROPN
ap-7723	48	7	)	)	PUNCT
ap-7723	48	8	f(x	f(x	PROPN
ap-7723	48	9	)	)	PUNCT
ap-7723	48	10	dν(x	dν(x	NOUN
ap-7723	48	11	)	)	PUNCT
ap-7723	48	12	,	,	PUNCT
ap-7723	48	13	(	(	PUNCT
ap-7723	48	14	4	4	X
ap-7723	48	15	)	)	PUNCT
ap-7723	48	16	where	where	SCONJ
ap-7723	48	17	we	we	PRON
ap-7723	48	18	introduce	introduce	VERB
ap-7723	48	19	a	a	DET
ap-7723	48	20	family	family	NOUN
ap-7723	48	21	of	of	ADP
ap-7723	48	22	operators	operator	NOUN
ap-7723	48	23	m(x	m(x	NOUN
ap-7723	48	24	)	)	PUNCT
ap-7723	49	1	solving	solve	VERB
ap-7723	49	2	the	the	DET
ap-7723	49	3	identity	identity	NOUN
ap-7723	49	4	.	.	PUNCT
ap-7723	50	1	more	more	ADV
ap-7723	50	2	precisely	precisely	ADV
ap-7723	50	3	,	,	PUNCT
ap-7723	50	4	we	we	PRON
ap-7723	50	5	have	have	VERB
ap-7723	50	6	x	x	X
ap-7723	50	7	∋	∋	NOUN
ap-7723	50	8	x	x	SYM
ap-7723	50	9	7→	7→	NUM
ap-7723	50	10	m(x	m(x	PROPN
ap-7723	50	11	)	)	PUNCT
ap-7723	50	12	,	,	PUNCT
ap-7723	50	13	∫	∫	PROPN
ap-7723	50	14	x	x	SYM
ap-7723	50	15	m(x	m(x	PROPN
ap-7723	50	16	)	)	PUNCT
ap-7723	50	17	dν(x	dν(x	NOUN
ap-7723	50	18	)	)	PUNCT
ap-7723	50	19	=	=	SYM
ap-7723	51	1	1	1	X
ap-7723	51	2	.	.	PUNCT
ap-7723	52	1	(	(	PUNCT
ap-7723	52	2	5	5	NUM
ap-7723	52	3	)	)	PUNCT
ap-7723	52	4	if	if	SCONJ
ap-7723	52	5	the	the	DET
ap-7723	52	6	m(x	m(x	NOUN
ap-7723	52	7	)	)	PUNCT
ap-7723	52	8	are	be	AUX
ap-7723	52	9	non	non	ADJ
ap-7723	52	10	-	-	ADJ
ap-7723	52	11	negative	negative	ADJ
ap-7723	52	12	,	,	PUNCT
ap-7723	52	13	they	they	PRON
ap-7723	52	14	provide	provide	VERB
ap-7723	52	15	a	a	DET
ap-7723	52	16	povm	povm	NOUN
ap-7723	52	17	.	.	PUNCT
ap-7723	53	1	indeed	indeed	ADV
ap-7723	53	2	,	,	PUNCT
ap-7723	53	3	the	the	DET
ap-7723	53	4	quantization	quantization	NOUN
ap-7723	53	5	of	of	ADP
ap-7723	53	6	the	the	DET
ap-7723	53	7	characteristic	characteristic	ADJ
ap-7723	53	8	function	function	NOUN
ap-7723	53	9	on	on	ADP
ap-7723	53	10	the	the	DET
ap-7723	53	11	borel	borel	NOUN
ap-7723	53	12	set	set	NOUN
ap-7723	53	13	∆	∆	PROPN
ap-7723	53	14	,	,	PUNCT
ap-7723	53	15	a(χ∆	a(χ∆	NOUN
ap-7723	53	16	)	)	PUNCT
ap-7723	53	17	,	,	PUNCT
ap-7723	53	18	f	f	PROPN
ap-7723	53	19	(	(	PUNCT
ap-7723	53	20	∆	∆	PROPN
ap-7723	53	21	)	)	PUNCT
ap-7723	53	22	:	:	PUNCT
ap-7723	53	23	=	=	PUNCT
ap-7723	53	24	a(χ∆	a(χ∆	NOUN
ap-7723	53	25	)	)	PUNCT
ap-7723	53	26	=	=	SYM
ap-7723	54	1	∫	∫	PROPN
ap-7723	54	2	∆	∆	PROPN
ap-7723	54	3	m(x	m(x	PROPN
ap-7723	54	4	)	)	PUNCT
ap-7723	54	5	dν(x	dν(x	NOUN
ap-7723	54	6	)	)	PUNCT
ap-7723	54	7	.	.	PUNCT
ap-7723	55	1	(	(	PUNCT
ap-7723	55	2	6	6	X
ap-7723	55	3	)	)	PUNCT
ap-7723	55	4	is	be	AUX
ap-7723	55	5	a	a	DET
ap-7723	55	6	povm	povm	NOUN
ap-7723	55	7	which	which	PRON
ap-7723	55	8	provides	provide	VERB
ap-7723	55	9	a	a	DET
ap-7723	55	10	quantization	quantization	NOUN
ap-7723	55	11	procedure	procedure	NOUN
ap-7723	55	12	f	f	NOUN
ap-7723	55	13	7→	7→	NUM
ap-7723	55	14	af	af	NOUN
ap-7723	55	15	=	=	SYM
ap-7723	55	16	∫	∫	PROPN
ap-7723	55	17	x	x	SYM
ap-7723	55	18	f(x	f(x	PROPN
ap-7723	55	19	)	)	PUNCT
ap-7723	55	20	df	df	NOUN
ap-7723	55	21	(	(	PUNCT
ap-7723	55	22	x	x	NOUN
ap-7723	55	23	)	)	PUNCT
ap-7723	55	24	.	.	PUNCT
ap-7723	56	1	3	3	X
ap-7723	56	2	.	.	X
ap-7723	56	3	euclidean	euclidean	ADJ
ap-7723	56	4	plane	plane	NOUN
ap-7723	56	5	as	as	ADP
ap-7723	56	6	hilbert	hilbert	NOUN
ap-7723	56	7	space	space	NOUN
ap-7723	56	8	of	of	ADP
ap-7723	56	9	quantum	quantum	ADJ
ap-7723	56	10	states	state	NOUN
ap-7723	56	11	3.1	3.1	NUM
ap-7723	56	12	.	.	PUNCT
ap-7723	56	13	mixed	mixed	ADJ
ap-7723	56	14	states	state	NOUN
ap-7723	56	15	as	as	SCONJ
ap-7723	56	16	density	density	NOUN
ap-7723	56	17	matrices	matrix	NOUN
ap-7723	56	18	density	density	NOUN
ap-7723	56	19	matrices	matrix	NOUN
ap-7723	56	20	act	act	VERB
ap-7723	56	21	as	as	ADP
ap-7723	56	22	a	a	DET
ap-7723	56	23	family	family	NOUN
ap-7723	56	24	of	of	ADP
ap-7723	56	25	operators	operator	NOUN
ap-7723	56	26	which	which	PRON
ap-7723	56	27	can	can	AUX
ap-7723	56	28	be	be	AUX
ap-7723	56	29	used	use	VERB
ap-7723	56	30	to	to	PART
ap-7723	56	31	perform	perform	VERB
ap-7723	56	32	covariant	covariant	ADJ
ap-7723	56	33	integral	integral	ADJ
ap-7723	56	34	quantization	quantization	NOUN
ap-7723	56	35	.	.	PUNCT
ap-7723	57	1	6	6	NUM
ap-7723	57	2	ı̂	ı̂	NOUN
ap-7723	57	3	=	=	SYM
ap-7723	57	4	|0⟩	|0⟩	PROPN
ap-7723	57	5	≡	≡	PROPN
ap-7723	57	6	(	(	PUNCT
ap-7723	57	7	1	1	NUM
ap-7723	57	8	0	0	NUM
ap-7723	57	9	)	)	PUNCT
ap-7723	58	1	|ϕ⟩	|ϕ⟩	NOUN
ap-7723	58	2	=	=	SYM
ap-7723	58	3	(	(	PUNCT
ap-7723	58	4	cos	cos	ADP
ap-7723	58	5	ϕ	ϕ	PROPN
ap-7723	58	6	sin	sin	PROPN
ap-7723	58	7	ϕ	ϕ	PROPN
ap-7723	58	8	)	)	PUNCT
ap-7723	59	1	↔	↔	PROPN
ap-7723	59	2	eϕ	eϕ	NOUN
ap-7723	60	1	=	=	SYM
ap-7723	60	2	|ϕ⟩⟨ϕ|	|ϕ⟩⟨ϕ|	PROPN
ap-7723	60	3	o	o	X
ap-7723	60	4	⟨0|0⟩	⟨0|0⟩	X
ap-7723	60	5	=	=	SYM
ap-7723	60	6	1	1	NUM
ap-7723	60	7	=	=	SYM
ap-7723	60	8	〈	〈	PROPN
ap-7723	60	9	π	π	PROPN
ap-7723	60	10	2	2	NUM
ap-7723	60	11	∣∣	∣∣	NUM
ap-7723	60	12	π	π	PROPN
ap-7723	60	13	2	2	NUM
ap-7723	60	14	〉	〉	NOUN
ap-7723	60	15	,	,	PUNCT
ap-7723	60	16	⟨0	⟨0	PROPN
ap-7723	60	17	∣∣π	∣∣π	NOUN
ap-7723	60	18	2	2	NUM
ap-7723	60	19	〉	〉	NOUN
ap-7723	60	20	=	=	SYM
ap-7723	60	21	0	0	SYM
ap-7723	60	22	ȷ̂	ȷ̂	NUM
ap-7723	60	23	=	=	PUNCT
ap-7723	61	1	|	|	NOUN
ap-7723	61	2	π	π	PROPN
ap-7723	61	3	2	2	NUM
ap-7723	61	4	⟩	⟩	NOUN
ap-7723	61	5	≡	≡	PROPN
ap-7723	61	6	(	(	PUNCT
ap-7723	61	7	0	0	NUM
ap-7723	61	8	1	1	NUM
ap-7723	61	9	)	)	PUNCT
ap-7723	61	10	1	1	NUM
ap-7723	61	11	ϕ	ϕ	PROPN
ap-7723	61	12	�	�	PROPN
ap-7723	61	13	�	�	PROPN
ap-7723	61	14	�	�	PROPN
ap-7723	61	15	�	�	PROPN
ap-7723	61	16	�	�	PROPN
ap-7723	61	17	�	�	PROPN
ap-7723	61	18	�	�	PROPN
ap-7723	61	19	�	�	PROPN
ap-7723	61	20	�	�	PROPN
ap-7723	61	21	�	�	PROPN
ap-7723	61	22	figure	figure	NOUN
ap-7723	61	23	1	1	NUM
ap-7723	61	24	.	.	PUNCT
ap-7723	62	1	the	the	DET
ap-7723	62	2	euclidean	euclidean	ADJ
ap-7723	62	3	plane	plane	NOUN
ap-7723	62	4	and	and	CCONJ
ap-7723	62	5	its	its	PRON
ap-7723	62	6	unit	unit	NOUN
ap-7723	62	7	vectors	vector	NOUN
ap-7723	62	8	viewed	view	VERB
ap-7723	62	9	as	as	ADP
ap-7723	62	10	pure	pure	ADJ
ap-7723	62	11	quantum	quantum	ADJ
ap-7723	62	12	states	state	NOUN
ap-7723	62	13	in	in	ADP
ap-7723	62	14	dirac	dirac	NOUN
ap-7723	62	15	ket	ket	NOUN
ap-7723	62	16	notations	notation	NOUN
ap-7723	62	17	.	.	PUNCT
ap-7723	63	1	in	in	ADP
ap-7723	63	2	the	the	DET
ap-7723	63	3	context	context	NOUN
ap-7723	63	4	of	of	ADP
ap-7723	63	5	the	the	DET
ap-7723	63	6	euclidean	euclidean	ADJ
ap-7723	63	7	plane	plane	NOUN
ap-7723	63	8	and	and	CCONJ
ap-7723	63	9	its	its	PRON
ap-7723	63	10	rotational	rotational	ADJ
ap-7723	63	11	symmetry	symmetry	NOUN
ap-7723	63	12	,	,	PUNCT
ap-7723	63	13	one	one	NUM
ap-7723	63	14	associates	associate	VERB
ap-7723	63	15	the	the	DET
ap-7723	63	16	polar	polar	ADJ
ap-7723	63	17	angle	angle	NOUN
ap-7723	63	18	ϕ	ϕ	PROPN
ap-7723	63	19	∈	∈	PROPN
ap-7723	64	1	[	[	X
ap-7723	64	2	0	0	NUM
ap-7723	64	3	,	,	PUNCT
ap-7723	64	4	2π	2π	NOUN
ap-7723	64	5	)	)	PUNCT
ap-7723	64	6	with	with	ADP
ap-7723	64	7	the	the	DET
ap-7723	64	8	unit	unit	NOUN
ap-7723	64	9	vector	vector	NOUN
ap-7723	64	10	ûϕ	ûϕ	ADP
ap-7723	64	11	to	to	PART
ap-7723	64	12	define	define	VERB
ap-7723	64	13	the	the	DET
ap-7723	64	14	pure	pure	ADJ
ap-7723	64	15	state	state	NOUN
ap-7723	64	16	|ϕ⟩	|ϕ⟩	ADJ
ap-7723	64	17	:	:	PUNCT
ap-7723	64	18	=	=	SYM
ap-7723	64	19	|ûϕ⟩.	|ûϕ⟩.	ADJ
ap-7723	64	20	as	as	SCONJ
ap-7723	64	21	shown	show	VERB
ap-7723	64	22	in	in	ADP
ap-7723	64	23	figure	figure	NOUN
ap-7723	64	24	1	1	NUM
ap-7723	64	25	,	,	PUNCT
ap-7723	64	26	two	two	NUM
ap-7723	64	27	orthogonal	orthogonal	ADJ
ap-7723	64	28	pure	pure	ADJ
ap-7723	64	29	states	state	NOUN
ap-7723	64	30	ı̂	ı̂	PUNCT
ap-7723	64	31	=	=	SYM
ap-7723	64	32	|0⟩	|0⟩	NOUN
ap-7723	64	33	and	and	CCONJ
ap-7723	64	34	ȷ̂	ȷ̂	NUM
ap-7723	64	35	=	=	PUNCT
ap-7723	64	36	∣∣∣π2	∣∣∣π2	PROPN
ap-7723	64	37	〉	〉	NOUN
ap-7723	64	38	are	be	AUX
ap-7723	64	39	readily	readily	ADV
ap-7723	64	40	identified	identify	VERB
ap-7723	64	41	with	with	ADP
ap-7723	64	42	the	the	DET
ap-7723	64	43	unit	unit	NOUN
ap-7723	64	44	vectors	vector	NOUN
ap-7723	64	45	spanning	span	VERB
ap-7723	64	46	the	the	DET
ap-7723	64	47	plane	plane	NOUN
ap-7723	64	48	.	.	PUNCT
ap-7723	65	1	in	in	ADP
ap-7723	65	2	this	this	DET
ap-7723	65	3	configuration	configuration	NOUN
ap-7723	65	4	,	,	PUNCT
ap-7723	65	5	the	the	DET
ap-7723	65	6	pure	pure	ADJ
ap-7723	65	7	state	state	NOUN
ap-7723	65	8	|ϕ⟩	|ϕ⟩	PROPN
ap-7723	65	9	is	be	AUX
ap-7723	65	10	defined	define	VERB
ap-7723	65	11	by	by	ADP
ap-7723	65	12	an	an	DET
ap-7723	65	13	anticlockwise	anticlockwise	NOUN
ap-7723	65	14	rotation	rotation	NOUN
ap-7723	65	15	of	of	ADP
ap-7723	65	16	angle	angle	PROPN
ap-7723	65	17	ϕ	ϕ	PROPN
ap-7723	65	18	of	of	ADP
ap-7723	65	19	the	the	DET
ap-7723	65	20	pure	pure	ADJ
ap-7723	65	21	state	state	NOUN
ap-7723	65	22	|0⟩.	|0⟩.	VERB
ap-7723	65	23	denoting	denote	VERB
ap-7723	65	24	the	the	DET
ap-7723	65	25	orthogonal	orthogonal	ADJ
ap-7723	65	26	projectors	projector	NOUN
ap-7723	65	27	on	on	ADP
ap-7723	65	28	ı̂	ı̂	PUNCT
ap-7723	65	29	and	and	CCONJ
ap-7723	65	30	ȷ̂	ȷ̂	NUM
ap-7723	65	31	by	by	ADP
ap-7723	65	32	|0⟩⟨0|	|0⟩⟨0|	NOUN
ap-7723	65	33	and	and	CCONJ
ap-7723	65	34	∣∣π	∣∣π	PROPN
ap-7723	65	35	2	2	NUM
ap-7723	65	36	〉	〉	NOUN
ap-7723	65	37	〈	〈	PROPN
ap-7723	65	38	π	π	PROPN
ap-7723	65	39	2	2	NUM
ap-7723	65	40	∣∣	∣∣	NUM
ap-7723	65	41	respectively	respectively	ADV
ap-7723	65	42	,	,	PUNCT
ap-7723	65	43	we	we	PRON
ap-7723	65	44	visualize	visualize	VERB
ap-7723	65	45	the	the	DET
ap-7723	65	46	resolution	resolution	NOUN
ap-7723	65	47	of	of	ADP
ap-7723	65	48	the	the	DET
ap-7723	65	49	identity	identity	NOUN
ap-7723	65	50	as	as	SCONJ
ap-7723	65	51	follows	follow	VERB
ap-7723	65	52	1	1	NUM
ap-7723	65	53	=	=	SYM
ap-7723	65	54	|0⟩⟨0|	|0⟩⟨0|	NOUN
ap-7723	65	55	+	+	CCONJ
ap-7723	65	56	∣∣∣π2〉〈π	∣∣∣π2〉〈π	ADJ
ap-7723	65	57	2	2	NUM
ap-7723	65	58	∣∣∣	∣∣∣	NOUN
ap-7723	65	59	⇕	⇕	NOUN
ap-7723	65	60	(	(	PUNCT
ap-7723	65	61	1	1	NUM
ap-7723	65	62	0	0	NUM
ap-7723	65	63	0	0	NUM
ap-7723	65	64	1	1	NUM
ap-7723	65	65	)	)	PUNCT
ap-7723	65	66	=	=	PUNCT
ap-7723	66	1	(	(	PUNCT
ap-7723	66	2	1	1	NUM
ap-7723	66	3	0	0	NUM
ap-7723	66	4	0	0	NUM
ap-7723	66	5	0	0	NUM
ap-7723	66	6	)	)	PUNCT
ap-7723	67	1	+	+	CCONJ
ap-7723	67	2	(	(	PUNCT
ap-7723	67	3	0	0	NUM
ap-7723	67	4	0	0	NUM
ap-7723	67	5	0	0	NUM
ap-7723	67	6	1	1	NUM
ap-7723	67	7	)	)	PUNCT
ap-7723	67	8	.	.	PUNCT
ap-7723	68	1	(	(	PUNCT
ap-7723	68	2	7	7	X
ap-7723	68	3	)	)	PUNCT
ap-7723	68	4	recalling	recall	VERB
ap-7723	68	5	that	that	SCONJ
ap-7723	68	6	a	a	DET
ap-7723	68	7	pure	pure	ADJ
ap-7723	68	8	state	state	NOUN
ap-7723	68	9	in	in	ADP
ap-7723	68	10	the	the	DET
ap-7723	68	11	plane	plane	NOUN
ap-7723	68	12	,	,	PUNCT
ap-7723	68	13	equivalently	equivalently	ADV
ap-7723	68	14	an	an	DET
ap-7723	68	15	orientation	orientation	NOUN
ap-7723	68	16	,	,	PUNCT
ap-7723	68	17	can	can	AUX
ap-7723	68	18	be	be	AUX
ap-7723	68	19	decomposed	decompose	VERB
ap-7723	68	20	as	as	ADP
ap-7723	68	21	|ϕ⟩	|ϕ⟩	ADJ
ap-7723	68	22	=	=	SYM
ap-7723	68	23	cos	cos	ADP
ap-7723	68	24	ϕ	ϕ	PROPN
ap-7723	68	25	|0⟩	|0⟩	NOUN
ap-7723	68	26	+	+	CCONJ
ap-7723	68	27	sin	sin	NOUN
ap-7723	68	28	ϕ	ϕ	PROPN
ap-7723	68	29	∣∣π	∣∣π	NOUN
ap-7723	68	30	2	2	NUM
ap-7723	68	31	〉	〉	NOUN
ap-7723	68	32	,	,	PUNCT
ap-7723	68	33	with	with	ADP
ap-7723	68	34	⟨0|ϕ⟩	⟨0|ϕ⟩	PROPN
ap-7723	69	1	=	=	PUNCT
ap-7723	69	2	cos	cos	PROPN
ap-7723	69	3	ϕ	ϕ	PROPN
ap-7723	69	4	and	and	CCONJ
ap-7723	69	5	〈	〈	PROPN
ap-7723	69	6	π	π	NOUN
ap-7723	69	7	2	2	NUM
ap-7723	69	8	∣∣ϕ	∣∣ϕ	NOUN
ap-7723	69	9	〉	〉	NOUN
ap-7723	69	10	=	=	PUNCT
ap-7723	69	11	sin	sin	NOUN
ap-7723	69	12	ϕ	ϕ	NOUN
ap-7723	69	13	,	,	PUNCT
ap-7723	69	14	it	it	PRON
ap-7723	69	15	is	be	AUX
ap-7723	69	16	straightforward	straightforward	ADJ
ap-7723	69	17	to	to	PART
ap-7723	69	18	find	find	VERB
ap-7723	69	19	the	the	DET
ap-7723	69	20	orthogonal	orthogonal	ADJ
ap-7723	69	21	projector	projector	NOUN
ap-7723	69	22	corresponding	correspond	VERB
ap-7723	69	23	to	to	ADP
ap-7723	69	24	the	the	DET
ap-7723	69	25	pure	pure	ADJ
ap-7723	69	26	state	state	NOUN
ap-7723	69	27	|ϕ⟩	|ϕ⟩	PROPN
ap-7723	69	28	,	,	PUNCT
ap-7723	69	29	eϕ	eϕ	PROPN
ap-7723	70	1	=	=	PUNCT
ap-7723	70	2	(	(	PUNCT
ap-7723	70	3	cos2	cos2	PROPN
ap-7723	70	4	ϕ	ϕ	PROPN
ap-7723	70	5	cos	cos	PROPN
ap-7723	70	6	ϕ	ϕ	PROPN
ap-7723	70	7	sin	sin	PROPN
ap-7723	70	8	ϕ	ϕ	PROPN
ap-7723	70	9	cos	cos	PROPN
ap-7723	70	10	ϕ	ϕ	PROPN
ap-7723	70	11	sin	sin	PROPN
ap-7723	70	12	ϕ	ϕ	PROPN
ap-7723	70	13	sin2	sin2	PROPN
ap-7723	70	14	ϕ	ϕ	PROPN
ap-7723	70	15	)	)	PUNCT
ap-7723	70	16	,	,	PUNCT
ap-7723	70	17	(	(	PUNCT
ap-7723	70	18	8)	8)	NUM
ap-7723	70	19	from	from	ADP
ap-7723	70	20	which	which	PRON
ap-7723	70	21	we	we	PRON
ap-7723	70	22	can	can	AUX
ap-7723	70	23	construct	construct	VERB
ap-7723	70	24	the	the	DET
ap-7723	70	25	density	density	NOUN
ap-7723	70	26	matrix	matrix	NOUN
ap-7723	70	27	corresponding	correspond	VERB
ap-7723	70	28	to	to	ADP
ap-7723	70	29	all	all	DET
ap-7723	70	30	the	the	DET
ap-7723	70	31	mixed	mixed	ADJ
ap-7723	70	32	states	state	NOUN
ap-7723	70	33	ρ	ρ	NOUN
ap-7723	70	34	=	=	PUNCT
ap-7723	70	35	(	(	PUNCT
ap-7723	70	36	1	1	NUM
ap-7723	70	37	+	+	CCONJ
ap-7723	70	38	r	r	NOUN
ap-7723	70	39	2	2	NUM
ap-7723	70	40	)	)	PUNCT
ap-7723	70	41	eϕ	eϕ	NOUN
ap-7723	71	1	+	+	CCONJ
ap-7723	71	2	(	(	PUNCT
ap-7723	71	3	1	1	NUM
ap-7723	71	4	−	−	NOUN
ap-7723	71	5	r	r	NOUN
ap-7723	71	6	2	2	NUM
ap-7723	71	7	)	)	PUNCT
ap-7723	71	8	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	71	9	,	,	PUNCT
ap-7723	71	10	0	0	NUM
ap-7723	71	11	≤	≤	NUM
ap-7723	71	12	r	r	NOUN
ap-7723	71	13	≤	≤	NUM
ap-7723	71	14	1	1	NUM
ap-7723	71	15	.	.	PUNCT
ap-7723	72	1	(	(	PUNCT
ap-7723	72	2	9	9	NUM
ap-7723	72	3	)	)	PUNCT
ap-7723	72	4	in	in	ADP
ap-7723	72	5	this	this	DET
ap-7723	72	6	expression	expression	NOUN
ap-7723	72	7	,	,	PUNCT
ap-7723	72	8	the	the	DET
ap-7723	72	9	parameter	parameter	NOUN
ap-7723	72	10	r	r	NOUN
ap-7723	72	11	represents	represent	VERB
ap-7723	72	12	the	the	DET
ap-7723	72	13	degree	degree	NOUN
ap-7723	72	14	of	of	ADP
ap-7723	72	15	mixing	mix	VERB
ap-7723	72	16	.	.	PUNCT
ap-7723	73	1	hence	hence	ADV
ap-7723	73	2	the	the	DET
ap-7723	73	3	upper	upper	ADJ
ap-7723	73	4	half	half	ADJ
ap-7723	73	5	-	-	PUNCT
ap-7723	73	6	disk	disk	NOUN
ap-7723	73	7	(	(	PUNCT
ap-7723	73	8	r	r	NOUN
ap-7723	73	9	,	,	PUNCT
ap-7723	73	10	ϕ	ϕ	NOUN
ap-7723	73	11	)	)	PUNCT
ap-7723	73	12	,	,	PUNCT
ap-7723	74	1	0	0	NUM
ap-7723	74	2	≤	≤	NUM
ap-7723	74	3	r	r	NOUN
ap-7723	74	4	≤	≤	NUM
ap-7723	74	5	1	1	NUM
ap-7723	74	6	,	,	PUNCT
ap-7723	74	7	0	0	NUM
ap-7723	74	8	≤	≤	NOUN
ap-7723	74	9	ϕ	ϕ	NOUN
ap-7723	74	10	<	<	X
ap-7723	74	11	π	π	X
ap-7723	74	12	is	be	AUX
ap-7723	74	13	in	in	ADP
ap-7723	74	14	one	one	NUM
ap-7723	74	15	-	-	PUNCT
ap-7723	74	16	to	to	ADP
ap-7723	74	17	-	-	PUNCT
ap-7723	74	18	one	one	NUM
ap-7723	74	19	correspondence	correspondence	NOUN
ap-7723	74	20	9	9	NUM
ap-7723	74	21	r.	r.	PROPN
ap-7723	74	22	beneduci	beneduci	PROPN
ap-7723	74	23	,	,	PUNCT
ap-7723	74	24	e.	e.	PROPN
ap-7723	74	25	frion	frion	PROPN
ap-7723	74	26	,	,	PUNCT
ap-7723	74	27	j.-p	j.-p	PROPN
ap-7723	74	28	.	.	PUNCT
ap-7723	75	1	gazeau	gazeau	PROPN
ap-7723	75	2	acta	acta	PROPN
ap-7723	75	3	polytechnica	polytechnica	PROPN
ap-7723	75	4	with	with	ADP
ap-7723	75	5	the	the	DET
ap-7723	75	6	set	set	NOUN
ap-7723	75	7	of	of	ADP
ap-7723	75	8	density	density	NOUN
ap-7723	75	9	matrices	matrix	NOUN
ap-7723	75	10	ρ	ρ	PROPN
ap-7723	75	11	≡	≡	PROPN
ap-7723	75	12	ρr,ϕ	ρr,ϕ	PROPN
ap-7723	75	13	written	write	VERB
ap-7723	75	14	as	as	ADP
ap-7723	75	15	ρr,ϕ	ρr,ϕ	PUNCT
ap-7723	75	16	=	=	SYM
ap-7723	75	17	1	1	NUM
ap-7723	75	18	21	21	NUM
ap-7723	75	19	+	+	CCONJ
ap-7723	75	20	r	r	NOUN
ap-7723	75	21	2r(ϕ)σ3r(−ϕ	2r(ϕ)σ3r(−ϕ	NUM
ap-7723	75	22	)	)	PUNCT
ap-7723	75	23	=	=	PUNCT
ap-7723	76	1	(	(	PUNCT
ap-7723	76	2	1	1	NUM
ap-7723	76	3	2	2	NUM
ap-7723	76	4	+	+	CCONJ
ap-7723	76	5	r	r	NOUN
ap-7723	76	6	2	2	NUM
ap-7723	76	7	cos	cos	ADP
ap-7723	76	8	2ϕ	2ϕ	NUM
ap-7723	76	9	r	r	NOUN
ap-7723	76	10	2	2	NUM
ap-7723	76	11	sin	sin	NOUN
ap-7723	76	12	2ϕ	2ϕ	NUM
ap-7723	76	13	r	r	NOUN
ap-7723	76	14	2	2	NUM
ap-7723	76	15	sin	sin	NOUN
ap-7723	76	16	2ϕ	2ϕ	NUM
ap-7723	76	17	1	1	NUM
ap-7723	76	18	2	2	NUM
ap-7723	76	19	−	−	NOUN
ap-7723	76	20	r	r	NOUN
ap-7723	76	21	2	2	NUM
ap-7723	76	22	cos	cos	ADP
ap-7723	76	23	2ϕ	2ϕ	NUM
ap-7723	76	24	)	)	PUNCT
ap-7723	77	1	=	=	SYM
ap-7723	77	2	1	1	NUM
ap-7723	77	3	2	2	NUM
ap-7723	77	4	(	(	PUNCT
ap-7723	77	5	1	1	NUM
ap-7723	77	6	+	+	CCONJ
ap-7723	77	7	rσ2ϕ	rσ2ϕ	NOUN
ap-7723	77	8	)	)	PUNCT
ap-7723	77	9	,	,	PUNCT
ap-7723	77	10	(	(	PUNCT
ap-7723	77	11	10	10	NUM
ap-7723	77	12	)	)	PUNCT
ap-7723	77	13	where	where	SCONJ
ap-7723	77	14	r(ϕ	r(ϕ	NOUN
ap-7723	77	15	)	)	PUNCT
ap-7723	77	16	=	=	PRON
ap-7723	78	1	(	(	PUNCT
ap-7723	78	2	cos	cos	INTJ
ap-7723	78	3	ϕ	ϕ	PROPN
ap-7723	78	4	−	−	PROPN
ap-7723	78	5	sin	sin	NOUN
ap-7723	78	6	ϕ	ϕ	PROPN
ap-7723	78	7	sin	sin	PROPN
ap-7723	78	8	ϕ	ϕ	PROPN
ap-7723	78	9	cos	cos	PROPN
ap-7723	78	10	ϕ	ϕ	PROPN
ap-7723	78	11	)	)	PUNCT
ap-7723	78	12	is	be	AUX
ap-7723	78	13	a	a	DET
ap-7723	78	14	rotation	rotation	NOUN
ap-7723	78	15	matrix	matrix	NOUN
ap-7723	78	16	in	in	ADP
ap-7723	78	17	the	the	DET
ap-7723	78	18	plane	plane	NOUN
ap-7723	78	19	,	,	PUNCT
ap-7723	78	20	and	and	CCONJ
ap-7723	78	21	σϕ	σϕ	INTJ
ap-7723	78	22	:	:	PUNCT
ap-7723	78	23	=	=	SYM
ap-7723	78	24	cos	cos	PROPN
ap-7723	78	25	ϕ	ϕ	PROPN
ap-7723	78	26	σ3	σ3	PROPN
ap-7723	78	27	+	+	CCONJ
ap-7723	78	28	sin	sin	PROPN
ap-7723	78	29	ϕ	ϕ	PROPN
ap-7723	78	30	σ1	σ1	PROPN
ap-7723	78	31	≡	≡	PROPN
ap-7723	79	1	−→σ	−→σ	PROPN
ap-7723	79	2	·	·	PUNCT
ap-7723	79	3	ûϕ	ûϕ	NUM
ap-7723	79	4	=	=	PRON
ap-7723	79	5	(	(	PUNCT
ap-7723	79	6	cos	cos	PROPN
ap-7723	79	7	ϕ	ϕ	PROPN
ap-7723	79	8	sin	sin	PROPN
ap-7723	79	9	ϕ	ϕ	PROPN
ap-7723	79	10	sin	sin	NOUN
ap-7723	79	11	ϕ	ϕ	PROPN
ap-7723	79	12	−	−	PROPN
ap-7723	79	13	cos	cos	PROPN
ap-7723	79	14	ϕ	ϕ	PROPN
ap-7723	79	15	)	)	PUNCT
ap-7723	79	16	=	=	SYM
ap-7723	79	17	r(ϕ	r(ϕ	PROPN
ap-7723	79	18	)	)	PUNCT
ap-7723	79	19	σ3	σ3	NOUN
ap-7723	79	20	.	.	PUNCT
ap-7723	80	1	(	(	PUNCT
ap-7723	80	2	11	11	NUM
ap-7723	80	3	)	)	PUNCT
ap-7723	80	4	the	the	DET
ap-7723	80	5	observable	observable	ADJ
ap-7723	80	6	σϕ	σϕ	NOUN
ap-7723	80	7	has	have	AUX
ap-7723	80	8	eigenvalues	eigenvalue	VERB
ap-7723	80	9	{	{	PUNCT
ap-7723	80	10	±1	±1	VERB
ap-7723	80	11	}	}	PUNCT
ap-7723	80	12	and	and	CCONJ
ap-7723	80	13	eigenvectors	eigenvector	VERB
ap-7723	80	14	∣∣∣ϕ	∣∣∣ϕ	NOUN
ap-7723	80	15	2	2	NUM
ap-7723	80	16	〉	〉	NOUN
ap-7723	80	17	and	and	CCONJ
ap-7723	80	18	∣∣∣ϕ+π	∣∣∣ϕ+π	SYM
ap-7723	80	19	2	2	NUM
ap-7723	80	20	〉	〉	NOUN
ap-7723	80	21	respectively	respectively	ADV
ap-7723	80	22	.	.	PUNCT
ap-7723	81	1	it	it	PRON
ap-7723	81	2	plays	play	VERB
ap-7723	81	3	a	a	DET
ap-7723	81	4	crucial	crucial	ADJ
ap-7723	81	5	rôle	rôle	NOUN
ap-7723	81	6	since	since	SCONJ
ap-7723	81	7	,	,	PUNCT
ap-7723	81	8	as	as	SCONJ
ap-7723	81	9	we	we	PRON
ap-7723	81	10	show	show	VERB
ap-7723	81	11	right	right	ADV
ap-7723	81	12	after	after	ADV
ap-7723	81	13	,	,	PUNCT
ap-7723	81	14	it	it	PRON
ap-7723	81	15	is	be	AUX
ap-7723	81	16	at	at	ADP
ap-7723	81	17	the	the	DET
ap-7723	81	18	core	core	NOUN
ap-7723	81	19	of	of	ADP
ap-7723	81	20	both	both	CCONJ
ap-7723	81	21	the	the	DET
ap-7723	81	22	non	non	ADJ
ap-7723	81	23	-	-	ADJ
ap-7723	81	24	commutative	commutative	ADJ
ap-7723	81	25	character	character	NOUN
ap-7723	81	26	and	and	CCONJ
ap-7723	81	27	the	the	DET
ap-7723	81	28	entanglement	entanglement	NOUN
ap-7723	81	29	of	of	ADP
ap-7723	81	30	two	two	NUM
ap-7723	81	31	quantum	quantum	ADJ
ap-7723	81	32	states	state	NOUN
ap-7723	81	33	of	of	ADP
ap-7723	81	34	the	the	DET
ap-7723	81	35	real	real	ADJ
ap-7723	81	36	space	space	NOUN
ap-7723	81	37	.	.	PUNCT
ap-7723	82	1	it	it	PRON
ap-7723	82	2	is	be	AUX
ap-7723	82	3	a	a	DET
ap-7723	82	4	typical	typical	ADJ
ap-7723	82	5	observable	observable	ADJ
ap-7723	82	6	used	use	VERB
ap-7723	82	7	to	to	PART
ap-7723	82	8	illustrate	illustrate	VERB
ap-7723	82	9	quantum	quantum	ADJ
ap-7723	82	10	formalism	formalism	NOUN
ap-7723	82	11	[	[	X
ap-7723	82	12	4	4	NUM
ap-7723	82	13	]	]	PUNCT
ap-7723	82	14	.	.	PUNCT
ap-7723	83	1	3.2	3.2	NUM
ap-7723	83	2	.	.	PUNCT
ap-7723	84	1	describing	describe	VERB
ap-7723	84	2	non	non	ADJ
ap-7723	84	3	-	-	ADJ
ap-7723	84	4	commutativity	commutativity	ADJ
ap-7723	84	5	and	and	CCONJ
ap-7723	84	6	finding	find	VERB
ap-7723	84	7	naimark	naimark	ADJ
ap-7723	84	8	extensions	extension	NOUN
ap-7723	84	9	through	through	ADP
ap-7723	84	10	rotations	rotation	NOUN
ap-7723	84	11	let	let	VERB
ap-7723	84	12	us	we	PRON
ap-7723	84	13	apply	apply	VERB
ap-7723	84	14	integral	integral	ADJ
ap-7723	84	15	quantization	quantization	NOUN
ap-7723	84	16	with	with	ADP
ap-7723	84	17	the	the	DET
ap-7723	84	18	real	real	ADJ
ap-7723	84	19	density	density	NOUN
ap-7723	84	20	matrices	matrix	NOUN
ap-7723	84	21	(	(	PUNCT
ap-7723	84	22	10	10	NUM
ap-7723	84	23	)	)	PUNCT
ap-7723	84	24	.	.	PUNCT
ap-7723	85	1	with	with	ADP
ap-7723	85	2	x	x	X
ap-7723	85	3	=	=	SYM
ap-7723	85	4	s1	s1	PROPN
ap-7723	85	5	,	,	PUNCT
ap-7723	85	6	the	the	DET
ap-7723	85	7	unit	unit	NOUN
ap-7723	85	8	circle	circle	NOUN
ap-7723	85	9	,	,	PUNCT
ap-7723	85	10	equipped	equip	VERB
ap-7723	85	11	with	with	ADP
ap-7723	85	12	the	the	DET
ap-7723	85	13	measure	measure	NOUN
ap-7723	85	14	dν(x	dν(x	NOUN
ap-7723	85	15	)	)	PUNCT
ap-7723	85	16	=	=	PRON
ap-7723	85	17	dϕ	dϕ	PROPN
ap-7723	85	18	π	π	X
ap-7723	85	19	,	,	PUNCT
ap-7723	85	20	ϕ	ϕ	PROPN
ap-7723	85	21	∈	∈	PROPN
ap-7723	86	1	[	[	X
ap-7723	86	2	0	0	NUM
ap-7723	86	3	,	,	PUNCT
ap-7723	86	4	2π	2π	NOUN
ap-7723	86	5	)	)	PUNCT
ap-7723	86	6	,	,	PUNCT
ap-7723	86	7	we	we	PRON
ap-7723	86	8	obtain	obtain	VERB
ap-7723	86	9	the	the	DET
ap-7723	86	10	resolution	resolution	NOUN
ap-7723	86	11	of	of	ADP
ap-7723	86	12	the	the	DET
ap-7723	86	13	identity	identity	NOUN
ap-7723	86	14	for	for	ADP
ap-7723	86	15	an	an	DET
ap-7723	86	16	arbitrary	arbitrary	ADJ
ap-7723	86	17	ϕ0,∫	ϕ0,∫	ADJ
ap-7723	86	18	2π	2π	NOUN
ap-7723	86	19	0	0	PUNCT
ap-7723	87	1	ρr,ϕ+ϕ0	ρr,ϕ+ϕ0	NOUN
ap-7723	87	2	dϕ	dϕ	NOUN
ap-7723	87	3	π	π	NOUN
ap-7723	87	4	=	=	SYM
ap-7723	87	5	1	1	X
ap-7723	87	6	.	.	PUNCT
ap-7723	88	1	(	(	PUNCT
ap-7723	88	2	12	12	NUM
ap-7723	88	3	)	)	PUNCT
ap-7723	88	4	hence	hence	ADV
ap-7723	88	5	,	,	PUNCT
ap-7723	88	6	quantizing	quantize	VERB
ap-7723	88	7	a	a	DET
ap-7723	88	8	function	function	NOUN
ap-7723	88	9	(	(	PUNCT
ap-7723	88	10	or	or	CCONJ
ap-7723	88	11	distribution	distribution	NOUN
ap-7723	88	12	)	)	PUNCT
ap-7723	88	13	f(ϕ	f(ϕ	PROPN
ap-7723	88	14	)	)	PUNCT
ap-7723	88	15	on	on	ADP
ap-7723	88	16	the	the	DET
ap-7723	88	17	circle	circle	NOUN
ap-7723	88	18	is	be	AUX
ap-7723	88	19	done	do	VERB
ap-7723	88	20	through	through	ADP
ap-7723	88	21	the	the	DET
ap-7723	88	22	map	map	NOUN
ap-7723	88	23	f	f	PROPN
ap-7723	88	24	7→	7→	NUM
ap-7723	89	1	af	af	NOUN
ap-7723	89	2	=	=	SYM
ap-7723	89	3	∫	∫	PROPN
ap-7723	89	4	2π	2π	PROPN
ap-7723	89	5	0	0	NUM
ap-7723	89	6	f(ϕ)ρr,ϕ+ϕ0	f(ϕ)ρr,ϕ+ϕ0	NOUN
ap-7723	89	7	dϕ	dϕ	NOUN
ap-7723	89	8	π	π	NOUN
ap-7723	89	9	=	=	PUNCT
ap-7723	89	10	(	(	PUNCT
ap-7723	89	11	⟨f⟩	⟨f⟩	PROPN
ap-7723	90	1	+	+	CCONJ
ap-7723	90	2	r	r	NOUN
ap-7723	90	3	2	2	NUM
ap-7723	90	4	cc	cc	NOUN
ap-7723	90	5	(	(	PUNCT
ap-7723	90	6	rϕ0f	rϕ0f	PROPN
ap-7723	90	7	)	)	PUNCT
ap-7723	90	8	r	r	NOUN
ap-7723	90	9	2	2	NUM
ap-7723	90	10	cs	cs	X
ap-7723	90	11	(	(	PUNCT
ap-7723	90	12	rϕ0f	rϕ0f	PROPN
ap-7723	90	13	)	)	PUNCT
ap-7723	90	14	r	r	NOUN
ap-7723	90	15	2	2	NUM
ap-7723	90	16	cs	cs	X
ap-7723	90	17	(	(	PUNCT
ap-7723	90	18	rϕ0f	rϕ0f	PROPN
ap-7723	90	19	)	)	PUNCT
ap-7723	90	20	⟨f⟩	⟨f⟩	PROPN
ap-7723	91	1	−	−	NOUN
ap-7723	91	2	r	r	NOUN
ap-7723	91	3	2	2	NUM
ap-7723	91	4	cc	cc	NOUN
ap-7723	91	5	(	(	PUNCT
ap-7723	91	6	rϕ0f	rϕ0f	PROPN
ap-7723	91	7	)	)	PUNCT
ap-7723	91	8	)	)	PUNCT
ap-7723	92	1	=	=	PUNCT
ap-7723	92	2	⟨f⟩1	⟨f⟩1	NOUN
ap-7723	92	3	+	+	CCONJ
ap-7723	92	4	r	r	NOUN
ap-7723	92	5	2	2	NUM
ap-7723	92	6	[	[	X
ap-7723	92	7	cc	cc	X
ap-7723	92	8	(	(	PUNCT
ap-7723	92	9	rϕ0f	rϕ0f	PROPN
ap-7723	92	10	)	)	PUNCT
ap-7723	92	11	σ3	σ3	NOUN
ap-7723	92	12	+	+	CCONJ
ap-7723	92	13	cs	cs	PROPN
ap-7723	92	14	(	(	PUNCT
ap-7723	92	15	rϕ0f	rϕ0f	PROPN
ap-7723	92	16	)	)	PUNCT
ap-7723	92	17	σ1	σ1	PROPN
ap-7723	92	18	]	]	PUNCT
ap-7723	92	19	,	,	PUNCT
ap-7723	92	20	(	(	PUNCT
ap-7723	92	21	13	13	NUM
ap-7723	92	22	)	)	PUNCT
ap-7723	92	23	with	with	ADP
ap-7723	92	24	⟨f⟩	⟨f⟩	PROPN
ap-7723	92	25	:	:	PUNCT
ap-7723	92	26	=	=	SYM
ap-7723	92	27	1	1	NUM
ap-7723	92	28	2π	2π	NUM
ap-7723	92	29	∫	∫	PROPN
ap-7723	92	30	2π	2π	NOUN
ap-7723	92	31	0	0	PUNCT
ap-7723	92	32	f(ϕ	f(ϕ	ADJ
ap-7723	92	33	)	)	PUNCT
ap-7723	92	34	dϕ	dϕ	VERB
ap-7723	92	35	the	the	DET
ap-7723	92	36	average	average	NOUN
ap-7723	92	37	of	of	ADP
ap-7723	92	38	f	f	PROPN
ap-7723	92	39	on	on	ADP
ap-7723	92	40	the	the	DET
ap-7723	92	41	unit	unit	NOUN
ap-7723	92	42	circle	circle	NOUN
ap-7723	92	43	and	and	CCONJ
ap-7723	92	44	rϕ0(f)(ϕ	rϕ0(f)(ϕ	NOUN
ap-7723	92	45	)	)	PUNCT
ap-7723	92	46	:	:	PUNCT
ap-7723	93	1	=	=	PUNCT
ap-7723	93	2	f(ϕ	f(ϕ	PROPN
ap-7723	93	3	−	−	PROPN
ap-7723	93	4	ϕ0	ϕ0	NOUN
ap-7723	93	5	)	)	PUNCT
ap-7723	93	6	.	.	PUNCT
ap-7723	94	1	here	here	ADV
ap-7723	94	2	we	we	PRON
ap-7723	94	3	have	have	AUX
ap-7723	94	4	defined	define	VERB
ap-7723	94	5	cosine	cosine	NOUN
ap-7723	94	6	and	and	CCONJ
ap-7723	94	7	sine	sine	ADJ
ap-7723	94	8	doubled	double	VERB
ap-7723	94	9	angle	angle	NOUN
ap-7723	94	10	fourier	fourier	NOUN
ap-7723	94	11	coefficients	coefficient	NOUN
ap-7723	94	12	of	of	ADP
ap-7723	94	13	f	f	PROPN
ap-7723	94	14	cc	cc	PROPN
ap-7723	94	15	s	s	PROPN
ap-7723	94	16	(	(	PUNCT
ap-7723	94	17	f	f	X
ap-7723	94	18	)	)	PUNCT
ap-7723	94	19	=	=	SYM
ap-7723	95	1	∫	∫	PROPN
ap-7723	95	2	2π	2π	NOUN
ap-7723	95	3	0	0	PUNCT
ap-7723	95	4	f(ϕ	f(ϕ	ADJ
ap-7723	95	5	)	)	PUNCT
ap-7723	96	1	{	{	PUNCT
ap-7723	96	2	cos	cos	ADP
ap-7723	96	3	sin	sin	PROPN
ap-7723	96	4	2ϕ	2ϕ	VERB
ap-7723	96	5	dϕ	dϕ	NOUN
ap-7723	96	6	π	π	X
ap-7723	96	7	.	.	PUNCT
ap-7723	97	1	(	(	PUNCT
ap-7723	97	2	14	14	NUM
ap-7723	97	3	)	)	PUNCT
ap-7723	97	4	in	in	ADP
ap-7723	97	5	[	[	X
ap-7723	97	6	6	6	NUM
ap-7723	97	7	]	]	PUNCT
ap-7723	97	8	,	,	PUNCT
ap-7723	97	9	we	we	PRON
ap-7723	97	10	drew	draw	VERB
ap-7723	97	11	three	three	NUM
ap-7723	97	12	consequences	consequence	NOUN
ap-7723	97	13	from	from	ADP
ap-7723	97	14	this	this	DET
ap-7723	97	15	result	result	NOUN
ap-7723	97	16	.	.	PUNCT
ap-7723	98	1	the	the	DET
ap-7723	98	2	first	first	ADJ
ap-7723	98	3	consequence	consequence	NOUN
ap-7723	98	4	is	be	AUX
ap-7723	98	5	that	that	SCONJ
ap-7723	98	6	,	,	PUNCT
ap-7723	98	7	upon	upon	SCONJ
ap-7723	98	8	identification	identification	NOUN
ap-7723	98	9	of	of	ADP
ap-7723	98	10	r3	r3	PROPN
ap-7723	98	11	with	with	ADP
ap-7723	98	12	the	the	DET
ap-7723	98	13	subspace	subspace	NOUN
ap-7723	98	14	v3	v3	PROPN
ap-7723	98	15	=	=	SYM
ap-7723	98	16	span	span	PROPN
ap-7723	98	17	{	{	PUNCT
ap-7723	98	18	e0(ϕ	e0(ϕ	NOUN
ap-7723	98	19	)	)	PUNCT
ap-7723	98	20	:	:	PUNCT
ap-7723	99	1	=	=	SYM
ap-7723	99	2	1√	1√	PROPN
ap-7723	99	3	2	2	NUM
ap-7723	99	4	,	,	PUNCT
ap-7723	99	5	e1(ϕ	e1(ϕ	PROPN
ap-7723	99	6	)	)	PUNCT
ap-7723	99	7	:	:	PUNCT
ap-7723	100	1	=	=	SYM
ap-7723	100	2	cos	cos	X
ap-7723	100	3	2ϕ	2ϕ	NUM
ap-7723	100	4	,	,	PUNCT
ap-7723	100	5	e2(ϕ	e2(ϕ	NUM
ap-7723	100	6	)	)	PUNCT
ap-7723	100	7	:	:	PUNCT
ap-7723	100	8	=	=	PUNCT
ap-7723	100	9	sin	sin	NOUN
ap-7723	100	10	2ϕ	2ϕ	VERB
ap-7723	100	11	}	}	PUNCT
ap-7723	100	12	in	in	ADP
ap-7723	100	13	l2(s1	l2(s1	NOUN
ap-7723	100	14	,	,	PUNCT
ap-7723	100	15	dϕ/π	dϕ/π	PROPN
ap-7723	100	16	)	)	PUNCT
ap-7723	100	17	,	,	PUNCT
ap-7723	100	18	the	the	DET
ap-7723	100	19	integral	integral	ADJ
ap-7723	100	20	quantization	quantization	NOUN
ap-7723	100	21	map	map	NOUN
ap-7723	100	22	with	with	ADP
ap-7723	100	23	ρr,ϕ+ϕ0	ρr,ϕ+ϕ0	NOUN
ap-7723	100	24	yields	yield	VERB
ap-7723	100	25	a	a	DET
ap-7723	100	26	noncommutative	noncommutative	ADJ
ap-7723	100	27	version	version	NOUN
ap-7723	100	28	of	of	ADP
ap-7723	100	29	r3	r3	PROPN
ap-7723	100	30	:	:	PUNCT
ap-7723	100	31	ae0	ae0	PROPN
ap-7723	100	32	=	=	SYM
ap-7723	100	33	1√	1√	PROPN
ap-7723	100	34	2	2	NUM
ap-7723	100	35	,	,	PUNCT
ap-7723	100	36	ae1	ae1	PROPN
ap-7723	100	37	=	=	SYM
ap-7723	100	38	r	r	NOUN
ap-7723	100	39	2	2	NUM
ap-7723	100	40	[	[	X
ap-7723	100	41	cos	cos	PROPN
ap-7723	100	42	2ϕ0	2ϕ0	NUM
ap-7723	100	43	σ3	σ3	NOUN
ap-7723	100	44	+	+	CCONJ
ap-7723	100	45	sin	sin	PROPN
ap-7723	100	46	2ϕ0	2ϕ0	NUM
ap-7723	100	47	σ1	σ1	NOUN
ap-7723	100	48	]	]	PUNCT
ap-7723	100	49	≡	≡	PROPN
ap-7723	100	50	r	r	NOUN
ap-7723	100	51	2σ2ϕ0	2σ2ϕ0	NUM
ap-7723	100	52	,	,	PUNCT
ap-7723	100	53	ae2	ae2	PROPN
ap-7723	101	1	=	=	SYM
ap-7723	101	2	r	r	NOUN
ap-7723	101	3	2	2	NUM
ap-7723	101	4	[	[	X
ap-7723	101	5	−	−	X
ap-7723	101	6	sin	sin	NOUN
ap-7723	101	7	2ϕ0	2ϕ0	NUM
ap-7723	101	8	σ3	σ3	NOUN
ap-7723	101	9	+	+	CCONJ
ap-7723	101	10	cos	cos	PROPN
ap-7723	101	11	2ϕ0	2ϕ0	NUM
ap-7723	101	12	σ1	σ1	NOUN
ap-7723	101	13	]	]	PUNCT
ap-7723	101	14	≡	≡	PROPN
ap-7723	101	15	r	r	NOUN
ap-7723	101	16	2σ2ϕ0+π/2	2σ2ϕ0+π/2	NUM
ap-7723	101	17	.	.	PUNCT
ap-7723	102	1	now	now	ADV
ap-7723	102	2	,	,	PUNCT
ap-7723	102	3	the	the	DET
ap-7723	102	4	commutation	commutation	NOUN
ap-7723	102	5	rule	rule	NOUN
ap-7723	102	6	reads	read	VERB
ap-7723	102	7	[	[	X
ap-7723	102	8	ae1	ae1	PROPN
ap-7723	102	9	,	,	PUNCT
ap-7723	102	10	ae2	ae2	PROPN
ap-7723	102	11	]	]	PUNCT
ap-7723	103	1	=	=	SYM
ap-7723	103	2	−r2	−r2	PROPN
ap-7723	103	3	2	2	NUM
ap-7723	103	4	τ2	τ2	NOUN
ap-7723	103	5	,	,	PUNCT
ap-7723	103	6	τ2	τ2	NOUN
ap-7723	103	7	:	:	PUNCT
ap-7723	103	8	=	=	SYM
ap-7723	103	9	(	(	PUNCT
ap-7723	103	10	0	0	NUM
ap-7723	103	11	−1	−1	NOUN
ap-7723	103	12	1	1	NUM
ap-7723	103	13	0	0	NUM
ap-7723	103	14	)	)	PUNCT
ap-7723	104	1	=	=	SYM
ap-7723	104	2	−iσ2	−iσ2	PROPN
ap-7723	104	3	,	,	PUNCT
ap-7723	104	4	which	which	PRON
ap-7723	104	5	depends	depend	VERB
ap-7723	104	6	on	on	ADP
ap-7723	104	7	the	the	DET
ap-7723	104	8	real	real	ADJ
ap-7723	104	9	version	version	NOUN
ap-7723	104	10	of	of	ADP
ap-7723	104	11	the	the	DET
ap-7723	104	12	last	last	ADJ
ap-7723	104	13	pauli	pauli	PROPN
ap-7723	104	14	matrix	matrix	NOUN
ap-7723	104	15	and	and	CCONJ
ap-7723	104	16	on	on	ADP
ap-7723	104	17	the	the	DET
ap-7723	104	18	degree	degree	NOUN
ap-7723	104	19	of	of	ADP
ap-7723	104	20	mixing	mix	VERB
ap-7723	104	21	.	.	PUNCT
ap-7723	105	1	a	a	DET
ap-7723	105	2	second	second	ADJ
ap-7723	105	3	consequence	consequence	NOUN
ap-7723	105	4	,	,	PUNCT
ap-7723	105	5	typical	typical	ADJ
ap-7723	105	6	of	of	ADP
ap-7723	105	7	quantummechanical	quantummechanical	ADJ
ap-7723	105	8	ensembles	ensemble	NOUN
ap-7723	105	9	,	,	PUNCT
ap-7723	105	10	is	be	AUX
ap-7723	105	11	that	that	SCONJ
ap-7723	105	12	all	all	DET
ap-7723	105	13	functions	function	NOUN
ap-7723	105	14	f(ϕ	f(ϕ	PROPN
ap-7723	105	15	)	)	PUNCT
ap-7723	105	16	in	in	ADP
ap-7723	105	17	v3	v3	PROPN
ap-7723	105	18	yielding	yield	VERB
ap-7723	105	19	density	density	NOUN
ap-7723	105	20	matrices	matrix	NOUN
ap-7723	105	21	through	through	ADP
ap-7723	105	22	this	this	DET
ap-7723	105	23	map	map	NOUN
ap-7723	105	24	imply	imply	VERB
ap-7723	105	25	that	that	PRON
ap-7723	105	26	ρs	ρs	ADP
ap-7723	105	27	,	,	PUNCT
ap-7723	105	28	θ	θ	PROPN
ap-7723	105	29	=	=	SYM
ap-7723	106	1	∫	∫	PROPN
ap-7723	106	2	2π	2π	NOUN
ap-7723	106	3	0	0	PUNCT
ap-7723	107	1	[	[	PUNCT
ap-7723	107	2	1	1	NUM
ap-7723	107	3	2	2	NUM
ap-7723	107	4	+	+	SYM
ap-7723	107	5	s	s	NOUN
ap-7723	107	6	r	r	NOUN
ap-7723	107	7	cos	cos	ADP
ap-7723	107	8	2ϕ	2ϕ	NUM
ap-7723	107	9	]	]	PUNCT
ap-7723	108	1	︸	︸	X
ap-7723	108	2	︷︷	︷︷	PROPN
ap-7723	108	3	︸	︸	X
ap-7723	108	4	f(ϕ	f(ϕ	PROPN
ap-7723	108	5	)	)	PUNCT
ap-7723	108	6	ρr,ϕ+θ	ρr,ϕ+θ	NOUN
ap-7723	108	7	dϕ	dϕ	ADP
ap-7723	108	8	π	π	X
ap-7723	108	9	.	.	PUNCT
ap-7723	109	1	(	(	PUNCT
ap-7723	109	2	15	15	NUM
ap-7723	109	3	)	)	PUNCT
ap-7723	109	4	if	if	SCONJ
ap-7723	109	5	r	r	NOUN
ap-7723	109	6	≥	≥	NOUN
ap-7723	109	7	2s	2s	NOUN
ap-7723	109	8	,	,	PUNCT
ap-7723	109	9	this	this	DET
ap-7723	109	10	continuous	continuous	ADJ
ap-7723	109	11	superposition	superposition	NOUN
ap-7723	109	12	of	of	ADP
ap-7723	109	13	mixed	mixed	ADJ
ap-7723	109	14	states	state	NOUN
ap-7723	109	15	is	be	AUX
ap-7723	109	16	convex	convex	ADJ
ap-7723	109	17	.	.	PUNCT
ap-7723	110	1	therefore	therefore	ADV
ap-7723	110	2	,	,	PUNCT
ap-7723	110	3	a	a	DET
ap-7723	110	4	mixed	mixed	ADJ
ap-7723	110	5	state	state	NOUN
ap-7723	110	6	is	be	AUX
ap-7723	110	7	composed	compose	VERB
ap-7723	110	8	of	of	ADP
ap-7723	110	9	an	an	DET
ap-7723	110	10	infinite	infinite	ADJ
ap-7723	110	11	number	number	NOUN
ap-7723	110	12	of	of	ADP
ap-7723	110	13	other	other	ADJ
ap-7723	110	14	mixed	mixed	ADJ
ap-7723	110	15	states	state	NOUN
ap-7723	110	16	.	.	PUNCT
ap-7723	111	1	this	this	PRON
ap-7723	111	2	has	have	VERB
ap-7723	111	3	consequences	consequence	NOUN
ap-7723	111	4	in	in	ADP
ap-7723	111	5	quantum	quantum	ADJ
ap-7723	111	6	cryptography	cryptography	NOUN
ap-7723	111	7	,	,	PUNCT
ap-7723	111	8	for	for	ADP
ap-7723	111	9	example	example	NOUN
ap-7723	111	10	,	,	PUNCT
ap-7723	111	11	since	since	SCONJ
ap-7723	111	12	the	the	DET
ap-7723	111	13	initial	initial	ADJ
ap-7723	111	14	signal	signal	NOUN
ap-7723	111	15	can	can	AUX
ap-7723	111	16	not	not	PART
ap-7723	111	17	be	be	AUX
ap-7723	111	18	recovered	recover	VERB
ap-7723	111	19	from	from	ADP
ap-7723	111	20	the	the	DET
ap-7723	111	21	output	output	NOUN
ap-7723	111	22	.	.	PUNCT
ap-7723	112	1	the	the	DET
ap-7723	112	2	third	third	ADJ
ap-7723	112	3	and	and	CCONJ
ap-7723	112	4	last	last	ADJ
ap-7723	112	5	consequence	consequence	NOUN
ap-7723	112	6	we	we	PRON
ap-7723	112	7	mention	mention	VERB
ap-7723	112	8	here	here	ADV
ap-7723	112	9	concerns	concern	VERB
ap-7723	112	10	the	the	DET
ap-7723	112	11	naimark	naimark	ADJ
ap-7723	112	12	extension	extension	NOUN
ap-7723	112	13	of	of	ADP
ap-7723	112	14	a	a	DET
ap-7723	112	15	function	function	NOUN
ap-7723	112	16	defined	define	VERB
ap-7723	112	17	on	on	ADP
ap-7723	112	18	the	the	DET
ap-7723	112	19	circle	circle	NOUN
ap-7723	112	20	.	.	PUNCT
ap-7723	113	1	in	in	ADP
ap-7723	113	2	particular	particular	ADJ
ap-7723	113	3	,	,	PUNCT
ap-7723	113	4	we	we	PRON
ap-7723	113	5	focus	focus	VERB
ap-7723	113	6	on	on	ADP
ap-7723	113	7	the	the	DET
ap-7723	113	8	toeplitz	toeplitz	NOUN
ap-7723	113	9	quantization	quantization	NOUN
ap-7723	113	10	of	of	ADP
ap-7723	113	11	f(ϕ	f(ϕ	PROPN
ap-7723	113	12	)	)	PUNCT
ap-7723	113	13	,	,	PUNCT
ap-7723	113	14	which	which	PRON
ap-7723	113	15	is	be	AUX
ap-7723	113	16	a	a	DET
ap-7723	113	17	kind	kind	NOUN
ap-7723	113	18	of	of	ADP
ap-7723	113	19	integral	integral	ADJ
ap-7723	113	20	quantization	quantization	NOUN
ap-7723	113	21	.	.	PUNCT
ap-7723	114	1	in	in	ADP
ap-7723	114	2	[	[	X
ap-7723	114	3	6	6	NUM
ap-7723	114	4	]	]	PUNCT
ap-7723	114	5	,	,	PUNCT
ap-7723	114	6	we	we	PRON
ap-7723	114	7	used	use	VERB
ap-7723	114	8	this	this	DET
ap-7723	114	9	framework	framework	NOUN
ap-7723	114	10	to	to	PART
ap-7723	114	11	show	show	VERB
ap-7723	114	12	there	there	PRON
ap-7723	114	13	exist	exist	VERB
ap-7723	114	14	orthogonal	orthogonal	ADJ
ap-7723	114	15	projectors	projector	NOUN
ap-7723	114	16	from	from	ADP
ap-7723	114	17	l2(s1	l2(s1	NOUN
ap-7723	114	18	,	,	PUNCT
ap-7723	114	19	dϕ/π	dϕ/π	NOUN
ap-7723	114	20	)	)	PUNCT
ap-7723	114	21	to	to	PART
ap-7723	114	22	r2	r2	VERB
ap-7723	114	23	such	such	ADJ
ap-7723	114	24	that	that	PRON
ap-7723	114	25	for	for	ADP
ap-7723	114	26	a	a	DET
ap-7723	114	27	function	function	NOUN
ap-7723	114	28	f(ϕ	f(ϕ	PROPN
ap-7723	114	29	)	)	PUNCT
ap-7723	114	30	the	the	DET
ap-7723	114	31	multiplication	multiplication	NOUN
ap-7723	114	32	operator	operator	NOUN
ap-7723	114	33	on	on	ADP
ap-7723	114	34	l2(s1	l2(s1	NOUN
ap-7723	114	35	,	,	PUNCT
ap-7723	114	36	dϕ/π	dϕ/π	PROPN
ap-7723	114	37	)	)	PUNCT
ap-7723	114	38	,	,	PUNCT
ap-7723	114	39	defined	define	VERB
ap-7723	114	40	by	by	ADP
ap-7723	114	41	v	v	NUM
ap-7723	114	42	7→	7→	PROPN
ap-7723	114	43	mf	mf	VERB
ap-7723	114	44	v	v	NOUN
ap-7723	114	45	=	=	SYM
ap-7723	114	46	fv	fv	PROPN
ap-7723	114	47	,	,	PUNCT
ap-7723	114	48	(	(	PUNCT
ap-7723	114	49	16	16	NUM
ap-7723	114	50	)	)	PUNCT
ap-7723	114	51	maps	map	NOUN
ap-7723	114	52	mf	mf	PRON
ap-7723	114	53	to	to	ADP
ap-7723	114	54	af	af	PROPN
ap-7723	114	55	.	.	PUNCT
ap-7723	115	1	they	they	PRON
ap-7723	115	2	are	be	AUX
ap-7723	115	3	precisely	precisely	ADV
ap-7723	115	4	naimark	naimark	ADJ
ap-7723	115	5	’s	’s	PART
ap-7723	115	6	extensions	extension	NOUN
ap-7723	115	7	of	of	ADP
ap-7723	115	8	povms	povms	NOUN
ap-7723	115	9	represented	represent	VERB
ap-7723	115	10	by	by	ADP
ap-7723	115	11	density	density	NOUN
ap-7723	115	12	matrices	matrix	NOUN
ap-7723	115	13	(	(	PUNCT
ap-7723	115	14	see	see	VERB
ap-7723	115	15	[	[	X
ap-7723	115	16	6	6	NUM
ap-7723	115	17	]	]	PUNCT
ap-7723	115	18	for	for	ADP
ap-7723	115	19	details	detail	NOUN
ap-7723	115	20	)	)	PUNCT
ap-7723	115	21	.	.	PUNCT
ap-7723	116	1	3.3	3.3	NUM
ap-7723	116	2	.	.	PUNCT
ap-7723	117	1	linear	linear	ADJ
ap-7723	117	2	polarization	polarization	NOUN
ap-7723	117	3	of	of	ADP
ap-7723	117	4	light	light	NOUN
ap-7723	117	5	as	as	ADP
ap-7723	117	6	a	a	DET
ap-7723	117	7	quantum	quantum	ADJ
ap-7723	117	8	phenomenon	phenomenon	NOUN
ap-7723	117	9	in	in	ADP
ap-7723	117	10	this	this	DET
ap-7723	117	11	section	section	NOUN
ap-7723	117	12	,	,	PUNCT
ap-7723	117	13	we	we	PRON
ap-7723	117	14	recall	recall	VERB
ap-7723	117	15	that	that	SCONJ
ap-7723	117	16	the	the	DET
ap-7723	117	17	polarization	polarization	NOUN
ap-7723	117	18	tensor	tensor	NOUN
ap-7723	117	19	of	of	ADP
ap-7723	117	20	light	light	NOUN
ap-7723	117	21	can	can	AUX
ap-7723	117	22	be	be	AUX
ap-7723	117	23	expressed	express	VERB
ap-7723	117	24	as	as	ADP
ap-7723	117	25	a	a	DET
ap-7723	117	26	density	density	NOUN
ap-7723	117	27	matrix	matrix	NOUN
ap-7723	117	28	,	,	PUNCT
ap-7723	117	29	which	which	PRON
ap-7723	117	30	allows	allow	VERB
ap-7723	117	31	us	we	PRON
ap-7723	117	32	to	to	PART
ap-7723	117	33	relate	relate	VERB
ap-7723	117	34	the	the	DET
ap-7723	117	35	polarization	polarization	NOUN
ap-7723	117	36	of	of	ADP
ap-7723	117	37	light	light	NOUN
ap-7723	117	38	to	to	ADP
ap-7723	117	39	quantum	quantum	ADJ
ap-7723	117	40	phenomena	phenomenon	NOUN
ap-7723	117	41	such	such	ADJ
ap-7723	117	42	as	as	ADP
ap-7723	117	43	the	the	DET
ap-7723	117	44	malus	malus	ADJ
ap-7723	117	45	law	law	NOUN
ap-7723	117	46	and	and	CCONJ
ap-7723	117	47	the	the	DET
ap-7723	117	48	incompatibility	incompatibility	NOUN
ap-7723	117	49	between	between	ADP
ap-7723	117	50	two	two	NUM
ap-7723	117	51	sequential	sequential	ADJ
ap-7723	117	52	measurements	measurement	NOUN
ap-7723	117	53	[	[	X
ap-7723	117	54	6	6	NUM
ap-7723	117	55	]	]	PUNCT
ap-7723	117	56	.	.	PUNCT
ap-7723	118	1	first	first	ADV
ap-7723	118	2	,	,	PUNCT
ap-7723	118	3	remember	remember	VERB
ap-7723	118	4	that	that	SCONJ
ap-7723	118	5	a	a	DET
ap-7723	118	6	complex	complex	ADV
ap-7723	118	7	-	-	PUNCT
ap-7723	118	8	valued	value	VERB
ap-7723	118	9	electric	electric	ADJ
ap-7723	118	10	field	field	NOUN
ap-7723	118	11	for	for	ADP
ap-7723	118	12	a	a	DET
ap-7723	118	13	propagating	propagate	VERB
ap-7723	118	14	quasi	quasi	ADJ
ap-7723	118	15	-	-	ADJ
ap-7723	118	16	monochromatic	monochromatic	ADJ
ap-7723	118	17	electromagnetic	electromagnetic	ADJ
ap-7723	118	18	wave	wave	NOUN
ap-7723	118	19	along	along	ADP
ap-7723	118	20	the	the	DET
ap-7723	118	21	z	z	NOUN
ap-7723	118	22	-	-	PUNCT
ap-7723	118	23	axis	axis	NOUN
ap-7723	118	24	reads	read	NOUN
ap-7723	118	25	as	as	ADP
ap-7723	118	26	−→	−→	NOUN
ap-7723	118	27	e	e	NOUN
ap-7723	118	28	(	(	PUNCT
ap-7723	118	29	t	t	NOUN
ap-7723	118	30	)	)	PUNCT
ap-7723	118	31	=	=	SYM
ap-7723	118	32	−→	−→	NOUN
ap-7723	118	33	e0(t	e0(t	NUM
ap-7723	118	34	)	)	PUNCT
ap-7723	118	35	eiωt	eiωt	NOUN
ap-7723	118	36	=	=	PUNCT
ap-7723	118	37	ex	ex	X
ap-7723	118	38	ı̂	ı̂	PUNCT
ap-7723	118	39	+	+	CCONJ
ap-7723	118	40	ey	ey	INTJ
ap-7723	118	41	ȷ̂	ȷ̂	NUM
ap-7723	118	42	=	=	SYM
ap-7723	118	43	(	(	PUNCT
ap-7723	118	44	eα	eα	NOUN
ap-7723	118	45	)	)	PUNCT
ap-7723	118	46	,	,	PUNCT
ap-7723	118	47	(	(	PUNCT
ap-7723	118	48	17	17	NUM
ap-7723	118	49	)	)	PUNCT
ap-7723	118	50	in	in	ADP
ap-7723	118	51	which	which	PRON
ap-7723	118	52	we	we	PRON
ap-7723	118	53	have	have	AUX
ap-7723	118	54	used	use	VERB
ap-7723	118	55	the	the	DET
ap-7723	118	56	previous	previous	ADJ
ap-7723	118	57	notations	notation	NOUN
ap-7723	118	58	for	for	ADP
ap-7723	118	59	the	the	DET
ap-7723	118	60	unit	unit	NOUN
ap-7723	118	61	vectors	vector	NOUN
ap-7723	118	62	in	in	ADP
ap-7723	118	63	the	the	DET
ap-7723	118	64	plane	plane	NOUN
ap-7723	118	65	.	.	PUNCT
ap-7723	119	1	the	the	DET
ap-7723	119	2	polarization	polarization	NOUN
ap-7723	119	3	is	be	AUX
ap-7723	119	4	determined	determine	VERB
ap-7723	119	5	by	by	ADP
ap-7723	119	6	−→	−→	NOUN
ap-7723	119	7	e0(t	e0(t	NOUN
ap-7723	119	8	)	)	PUNCT
ap-7723	119	9	.	.	PUNCT
ap-7723	120	1	it	it	PRON
ap-7723	120	2	slowly	slowly	ADV
ap-7723	120	3	varies	vary	VERB
ap-7723	120	4	with	with	ADP
ap-7723	120	5	time	time	NOUN
ap-7723	120	6	,	,	PUNCT
ap-7723	120	7	and	and	CCONJ
ap-7723	120	8	can	can	AUX
ap-7723	120	9	be	be	AUX
ap-7723	120	10	10	10	NUM
ap-7723	120	11	vol	vol	NOUN
ap-7723	120	12	.	.	PUNCT
ap-7723	121	1	62	62	NUM
ap-7723	121	2	no	no	INTJ
ap-7723	121	3	.	.	PUNCT
ap-7723	122	1	1/2022	1/2022	NUM
ap-7723	122	2	quantum	quantum	NOUN
ap-7723	122	3	angles	angle	NOUN
ap-7723	122	4	measured	measure	VERB
ap-7723	122	5	through	through	ADP
ap-7723	122	6	nicol	nicol	NOUN
ap-7723	122	7	prisms	prism	NOUN
ap-7723	122	8	,	,	PUNCT
ap-7723	122	9	or	or	CCONJ
ap-7723	122	10	other	other	ADJ
ap-7723	122	11	devices	device	NOUN
ap-7723	122	12	,	,	PUNCT
ap-7723	122	13	by	by	ADP
ap-7723	122	14	measuring	measure	VERB
ap-7723	122	15	the	the	DET
ap-7723	122	16	intensity	intensity	NOUN
ap-7723	122	17	of	of	ADP
ap-7723	122	18	the	the	DET
ap-7723	122	19	light	light	NOUN
ap-7723	122	20	yielded	yield	VERB
ap-7723	122	21	by	by	ADP
ap-7723	122	22	mean	mean	ADJ
ap-7723	122	23	values	value	NOUN
ap-7723	122	24	∝	∝	PROPN
ap-7723	122	25	eαeβ	eαeβ	NOUN
ap-7723	122	26	,	,	PUNCT
ap-7723	122	27	eαe∗	eαe∗	X
ap-7723	122	28	β	β	NOUN
ap-7723	122	29	and	and	CCONJ
ap-7723	122	30	conjugates	conjugate	NOUN
ap-7723	122	31	.	.	PUNCT
ap-7723	123	1	due	due	ADP
ap-7723	123	2	to	to	ADP
ap-7723	123	3	rapidly	rapidly	ADV
ap-7723	123	4	oscillating	oscillate	VERB
ap-7723	123	5	factors	factor	NOUN
ap-7723	123	6	and	and	CCONJ
ap-7723	123	7	a	a	DET
ap-7723	123	8	null	null	ADJ
ap-7723	123	9	temporal	temporal	ADJ
ap-7723	123	10	average	average	ADJ
ap-7723	123	11	⟨·⟩t	⟨·⟩t	NOUN
ap-7723	123	12	,	,	PUNCT
ap-7723	123	13	a	a	DET
ap-7723	123	14	partially	partially	ADV
ap-7723	123	15	polarized	polarize	VERB
ap-7723	123	16	light	light	NOUN
ap-7723	123	17	is	be	AUX
ap-7723	123	18	described	describe	VERB
ap-7723	123	19	by	by	ADP
ap-7723	123	20	the	the	DET
ap-7723	123	21	2	2	NUM
ap-7723	123	22	×	×	NOUN
ap-7723	123	23	2	2	NUM
ap-7723	123	24	hermitian	hermitian	ADJ
ap-7723	123	25	matrix	matrix	NOUN
ap-7723	123	26	(	(	PUNCT
ap-7723	123	27	stokes	stoke	NOUN
ap-7723	123	28	parameters	parameter	NOUN
ap-7723	123	29	)	)	PUNCT
ap-7723	124	1	[	[	X
ap-7723	124	2	10–12	10–12	NUM
ap-7723	124	3	]	]	X
ap-7723	124	4	1	1	NUM
ap-7723	124	5	j	j	PROPN
ap-7723	124	6	(	(	PUNCT
ap-7723	124	7	⟨e0xe∗	⟨e0xe∗	NOUN
ap-7723	124	8	0x⟩t	0x⟩t	VERB
ap-7723	124	9	〈	〈	PROPN
ap-7723	124	10	e0xe∗	e0xe∗	NOUN
ap-7723	124	11	0y	0y	X
ap-7723	124	12	〉	〉	PROPN
ap-7723	124	13	t	t	NOUN
ap-7723	124	14	⟨e0ye∗	⟨e0ye∗	NOUN
ap-7723	124	15	0x⟩t	0x⟩t	VERB
ap-7723	124	16	〈	〈	NOUN
ap-7723	124	17	e0ye∗	e0ye∗	NOUN
ap-7723	124	18	0y	0y	NUM
ap-7723	124	19	〉	〉	X
ap-7723	124	20	t	t	NOUN
ap-7723	124	21	)	)	PUNCT
ap-7723	124	22	≡	≡	PROPN
ap-7723	124	23	ρr,ϕ	ρr,ϕ	PUNCT
ap-7723	125	1	+	+	CCONJ
ap-7723	125	2	a	a	DET
ap-7723	125	3	2	2	NUM
ap-7723	125	4	σ2	σ2	NOUN
ap-7723	125	5	=	=	SYM
ap-7723	125	6	1	1	NUM
ap-7723	126	1	+	+	CCONJ
ap-7723	126	2	r	r	NOUN
ap-7723	126	3	2	2	NUM
ap-7723	126	4	eϕ	eϕ	NOUN
ap-7723	126	5	+	+	NOUN
ap-7723	126	6	1	1	NUM
ap-7723	126	7	−	−	NOUN
ap-7723	126	8	r	r	NOUN
ap-7723	126	9	2	2	NUM
ap-7723	126	10	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	126	11	+	+	CCONJ
ap-7723	126	12	ia2	ia2	ADJ
ap-7723	126	13	τ2	τ2	NOUN
ap-7723	126	14	.	.	PUNCT
ap-7723	127	1	here	here	ADV
ap-7723	127	2	,	,	PUNCT
ap-7723	127	3	j	j	PROPN
ap-7723	127	4	describes	describe	VERB
ap-7723	127	5	the	the	DET
ap-7723	127	6	intensity	intensity	NOUN
ap-7723	127	7	of	of	ADP
ap-7723	127	8	the	the	DET
ap-7723	127	9	wave	wave	NOUN
ap-7723	127	10	.	.	PUNCT
ap-7723	128	1	in	in	ADP
ap-7723	128	2	the	the	DET
ap-7723	128	3	second	second	ADJ
ap-7723	128	4	line	line	NOUN
ap-7723	128	5	,	,	PUNCT
ap-7723	128	6	it	it	PRON
ap-7723	128	7	is	be	AUX
ap-7723	128	8	clear	clear	ADJ
ap-7723	128	9	that	that	SCONJ
ap-7723	128	10	the	the	DET
ap-7723	128	11	degree	degree	NOUN
ap-7723	128	12	of	of	ADP
ap-7723	128	13	mixing	mix	VERB
ap-7723	128	14	r	r	NOUN
ap-7723	128	15	describes	describe	VERB
ap-7723	128	16	linear	linear	PROPN
ap-7723	128	17	polarization	polarization	NOUN
ap-7723	128	18	,	,	PUNCT
ap-7723	128	19	while	while	SCONJ
ap-7723	128	20	the	the	DET
ap-7723	128	21	parameter	parameter	NOUN
ap-7723	128	22	a	a	DET
ap-7723	128	23	(	(	PUNCT
ap-7723	128	24	−1	−1	NOUN
ap-7723	128	25	≤	≤	NOUN
ap-7723	128	26	a	a	DET
ap-7723	128	27	≤	≤	NUM
ap-7723	128	28	1	1	NUM
ap-7723	128	29	)	)	PUNCT
ap-7723	128	30	is	be	AUX
ap-7723	128	31	related	relate	VERB
ap-7723	128	32	to	to	ADP
ap-7723	128	33	circular	circular	ADJ
ap-7723	128	34	polarization	polarization	NOUN
ap-7723	128	35	.	.	PUNCT
ap-7723	129	1	in	in	ADP
ap-7723	129	2	real	real	ADJ
ap-7723	129	3	space	space	NOUN
ap-7723	129	4	,	,	PUNCT
ap-7723	129	5	we	we	PRON
ap-7723	129	6	have	have	VERB
ap-7723	129	7	a	a	DET
ap-7723	129	8	=	=	SYM
ap-7723	129	9	0	0	NUM
ap-7723	129	10	,	,	PUNCT
ap-7723	129	11	so	so	SCONJ
ap-7723	129	12	we	we	PRON
ap-7723	129	13	effectively	effectively	ADV
ap-7723	129	14	describe	describe	VERB
ap-7723	129	15	the	the	DET
ap-7723	129	16	linear	linear	ADJ
ap-7723	129	17	polarization	polarization	NOUN
ap-7723	129	18	of	of	ADP
ap-7723	129	19	light	light	NOUN
ap-7723	129	20	.	.	PUNCT
ap-7723	130	1	6	6	NUM
ap-7723	130	2	k̂	k̂	NOUN
ap-7723	130	3	ȷ̂	ȷ̂	NUM
ap-7723	130	4	ı̂	ı̂	ADP
ap-7723	130	5	�	�	PROPN
ap-7723	130	6	�	�	PROPN
ap-7723	130	7	�	�	PROPN
ap-7723	130	8	�	�	PROPN
ap-7723	130	9	�	�	PROPN
ap-7723	130	10	�	�	PROPN
ap-7723	130	11	�	�	PROPN
ap-7723	130	12	�	�	PROPN
ap-7723	130	13	�	�	PROPN
ap-7723	130	14	�	�	PROPN
ap-7723	130	15	•h	•h	PROPN
ap-7723	130	16	hhhy	hhhy	PROPN
ap-7723	130	17	re	re	PROPN
ap-7723	130	18	(	(	PUNCT
ap-7723	130	19	−→	−→	NOUN
ap-7723	130	20	e	e	NOUN
ap-7723	130	21	)	)	PUNCT
ap-7723	131	1	y	y	PROPN
ap-7723	131	2	z	z	NOUN
ap-7723	131	3	x	x	VERB
ap-7723	131	4	we	we	PRON
ap-7723	131	5	now	now	ADV
ap-7723	131	6	wish	wish	VERB
ap-7723	131	7	to	to	PART
ap-7723	131	8	describe	describe	VERB
ap-7723	131	9	the	the	DET
ap-7723	131	10	interaction	interaction	NOUN
ap-7723	131	11	between	between	ADP
ap-7723	131	12	a	a	DET
ap-7723	131	13	polarizer	polarizer	NOUN
ap-7723	131	14	and	and	CCONJ
ap-7723	131	15	a	a	DET
ap-7723	131	16	partially	partially	ADV
ap-7723	131	17	linear	linear	ADJ
ap-7723	131	18	polarized	polarize	VERB
ap-7723	131	19	light	light	NOUN
ap-7723	131	20	as	as	ADP
ap-7723	131	21	a	a	DET
ap-7723	131	22	quantum	quantum	ADJ
ap-7723	131	23	measurement	measurement	NOUN
ap-7723	131	24	.	.	PUNCT
ap-7723	132	1	we	we	PRON
ap-7723	132	2	need	need	VERB
ap-7723	132	3	to	to	PART
ap-7723	132	4	introduce	introduce	VERB
ap-7723	132	5	two	two	NUM
ap-7723	132	6	planes	plane	NOUN
ap-7723	132	7	and	and	CCONJ
ap-7723	132	8	their	their	PRON
ap-7723	132	9	tensor	tensor	NOUN
ap-7723	132	10	product	product	NOUN
ap-7723	132	11	:	:	PUNCT
ap-7723	132	12	the	the	DET
ap-7723	132	13	first	first	ADJ
ap-7723	132	14	one	one	NOUN
ap-7723	132	15	is	be	AUX
ap-7723	132	16	the	the	DET
ap-7723	132	17	hilbert	hilbert	NOUN
ap-7723	132	18	space	space	NOUN
ap-7723	132	19	on	on	ADP
ap-7723	132	20	which	which	PRON
ap-7723	132	21	act	act	VERB
ap-7723	132	22	the	the	DET
ap-7723	132	23	states	state	NOUN
ap-7723	132	24	ρm	ρm	ADP
ap-7723	132	25	s	s	PROPN
ap-7723	132	26	,	,	PUNCT
ap-7723	132	27	θ	θ	PROPN
ap-7723	132	28	of	of	ADP
ap-7723	132	29	the	the	DET
ap-7723	132	30	polarizer	polarizer	NOUN
ap-7723	132	31	viewed	view	VERB
ap-7723	132	32	as	as	ADP
ap-7723	132	33	an	an	DET
ap-7723	132	34	orientation	orientation	NOUN
ap-7723	132	35	pointer	pointer	NOUN
ap-7723	132	36	.	.	PUNCT
ap-7723	133	1	note	note	VERB
ap-7723	133	2	that	that	SCONJ
ap-7723	133	3	the	the	DET
ap-7723	133	4	action	action	NOUN
ap-7723	133	5	of	of	ADP
ap-7723	133	6	the	the	DET
ap-7723	133	7	generator	generator	NOUN
ap-7723	133	8	of	of	ADP
ap-7723	133	9	rotations	rotation	NOUN
ap-7723	133	10	τ2	τ2	NOUN
ap-7723	133	11	=	=	SYM
ap-7723	133	12	−iσ2	−iσ2	PROPN
ap-7723	133	13	on	on	ADP
ap-7723	133	14	these	these	DET
ap-7723	133	15	states	state	NOUN
ap-7723	133	16	corresponds	correspond	VERB
ap-7723	133	17	to	to	ADP
ap-7723	133	18	a	a	DET
ap-7723	133	19	π/2	π/2	NUM
ap-7723	133	20	rotation	rotation	NOUN
ap-7723	133	21	:	:	PUNCT
ap-7723	133	22	τ2ρm	τ2ρm	X
ap-7723	134	1	s	s	X
ap-7723	134	2	,	,	PUNCT
ap-7723	134	3	θτ−1	θτ−1	PROPN
ap-7723	134	4	2	2	NUM
ap-7723	134	5	=	=	SYM
ap-7723	134	6	−τ2ρm	−τ2ρm	NUM
ap-7723	134	7	s	s	NOUN
ap-7723	134	8	,	,	PUNCT
ap-7723	134	9	θτ2	θτ2	X
ap-7723	134	10	=	=	PUNCT
ap-7723	134	11	ρm	ρm	PROPN
ap-7723	134	12	s	s	PROPN
ap-7723	134	13	,	,	PUNCT
ap-7723	134	14	θ+π/2	θ+π/2	PROPN
ap-7723	134	15	.	.	PUNCT
ap-7723	135	1	(	(	PUNCT
ap-7723	135	2	18	18	NUM
ap-7723	135	3	)	)	PUNCT
ap-7723	135	4	the	the	DET
ap-7723	135	5	second	second	ADJ
ap-7723	135	6	plane	plane	NOUN
ap-7723	135	7	is	be	AUX
ap-7723	135	8	the	the	DET
ap-7723	135	9	hilbert	hilbert	NOUN
ap-7723	135	10	space	space	NOUN
ap-7723	135	11	on	on	ADP
ap-7723	135	12	which	which	PRON
ap-7723	135	13	act	act	VERB
ap-7723	135	14	the	the	DET
ap-7723	135	15	partially	partially	ADV
ap-7723	135	16	linearized	linearize	VERB
ap-7723	135	17	polarization	polarization	NOUN
ap-7723	135	18	states	state	NOUN
ap-7723	135	19	ρl	ρl	ADP
ap-7723	135	20	r,ϕ	r,ϕ	NOUN
ap-7723	135	21	of	of	ADP
ap-7723	135	22	the	the	DET
ap-7723	135	23	plane	plane	NOUN
ap-7723	135	24	wave	wave	NOUN
ap-7723	135	25	crossing	cross	VERB
ap-7723	135	26	the	the	DET
ap-7723	135	27	polarizer	polarizer	NOUN
ap-7723	135	28	.	.	PUNCT
ap-7723	136	1	its	its	PRON
ap-7723	136	2	spectral	spectral	ADJ
ap-7723	136	3	decomposition	decomposition	NOUN
ap-7723	136	4	corresponds	correspond	VERB
ap-7723	136	5	to	to	ADP
ap-7723	136	6	the	the	DET
ap-7723	136	7	incoherent	incoherent	ADJ
ap-7723	136	8	superposition	superposition	NOUN
ap-7723	136	9	of	of	ADP
ap-7723	136	10	two	two	NUM
ap-7723	136	11	completely	completely	ADV
ap-7723	136	12	linearly	linearly	ADV
ap-7723	136	13	polarized	polarize	VERB
ap-7723	136	14	waves	wave	NOUN
ap-7723	136	15	ρl	ρl	ADP
ap-7723	136	16	r,ϕ	r,ϕ	NOUN
ap-7723	136	17	=	=	NOUN
ap-7723	136	18	1	1	NUM
ap-7723	137	1	+	+	CCONJ
ap-7723	137	2	r	r	NOUN
ap-7723	137	3	2	2	NUM
ap-7723	137	4	eϕ	eϕ	NOUN
ap-7723	137	5	+	+	NOUN
ap-7723	137	6	1	1	NUM
ap-7723	137	7	−	−	NOUN
ap-7723	137	8	r	r	NOUN
ap-7723	137	9	2	2	NUM
ap-7723	137	10	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	137	11	.	.	PUNCT
ap-7723	138	1	(	(	PUNCT
ap-7723	138	2	19	19	NUM
ap-7723	138	3	)	)	PUNCT
ap-7723	138	4	the	the	DET
ap-7723	138	5	pointer	pointer	NOUN
ap-7723	138	6	detects	detect	VERB
ap-7723	138	7	an	an	DET
ap-7723	138	8	orientation	orientation	NOUN
ap-7723	138	9	in	in	ADP
ap-7723	138	10	the	the	DET
ap-7723	138	11	plane	plane	NOUN
ap-7723	138	12	determined	determine	VERB
ap-7723	138	13	by	by	ADP
ap-7723	138	14	the	the	DET
ap-7723	138	15	angle	angle	NOUN
ap-7723	138	16	ϕ.	ϕ.	PROPN
ap-7723	138	17	through	through	ADP
ap-7723	138	18	the	the	DET
ap-7723	138	19	interaction	interaction	NOUN
ap-7723	138	20	pointer	pointer	NOUN
ap-7723	138	21	-	-	PUNCT
ap-7723	138	22	system	system	NOUN
ap-7723	138	23	,	,	PUNCT
ap-7723	138	24	we	we	PRON
ap-7723	138	25	generate	generate	VERB
ap-7723	138	26	a	a	DET
ap-7723	138	27	measurement	measurement	NOUN
ap-7723	138	28	whose	whose	DET
ap-7723	138	29	time	time	NOUN
ap-7723	138	30	duration	duration	NOUN
ap-7723	138	31	is	be	AUX
ap-7723	138	32	the	the	DET
ap-7723	138	33	interval	interval	NOUN
ap-7723	139	1	i	i	PRON
ap-7723	139	2	m	m	VERB
ap-7723	139	3	=	=	PUNCT
ap-7723	139	4	(	(	PUNCT
ap-7723	139	5	tm	tm	PROPN
ap-7723	139	6	−	−	PROPN
ap-7723	139	7	η	η	PROPN
ap-7723	139	8	,	,	PUNCT
ap-7723	139	9	tm	tm	PROPN
ap-7723	139	10	+	+	PROPN
ap-7723	139	11	η	η	NOUN
ap-7723	139	12	)	)	PUNCT
ap-7723	139	13	centred	centre	VERB
ap-7723	139	14	at	at	ADP
ap-7723	139	15	tm	tm	PROPN
ap-7723	139	16	.	.	PUNCT
ap-7723	140	1	the	the	DET
ap-7723	140	2	interaction	interaction	NOUN
ap-7723	140	3	is	be	AUX
ap-7723	140	4	described	describe	VERB
ap-7723	140	5	by	by	ADP
ap-7723	140	6	the	the	DET
ap-7723	140	7	(	(	PUNCT
ap-7723	140	8	pseudo-	pseudo-	ADJ
ap-7723	140	9	)	)	PUNCT
ap-7723	140	10	hamiltonian	hamiltonian	ADJ
ap-7723	140	11	operator	operator	NOUN
ap-7723	140	12	h̃int(t	h̃int(t	NOUN
ap-7723	140	13	)	)	PUNCT
ap-7723	141	1	=	=	NOUN
ap-7723	142	1	gη	gη	ADP
ap-7723	142	2	m	m	VERB
ap-7723	142	3	(	(	PUNCT
ap-7723	142	4	t)τ2	t)τ2	NOUN
ap-7723	142	5	⊗	⊗	PROPN
ap-7723	142	6	ρl	ρl	ADP
ap-7723	142	7	r,ϕ	r,ϕ	PROPN
ap-7723	142	8	,	,	PUNCT
ap-7723	142	9	(	(	PUNCT
ap-7723	142	10	20	20	NUM
ap-7723	142	11	)	)	PUNCT
ap-7723	142	12	where	where	SCONJ
ap-7723	142	13	gη	gη	NOUN
ap-7723	142	14	m	m	PROPN
ap-7723	142	15	is	be	AUX
ap-7723	142	16	a	a	DET
ap-7723	142	17	dirac	dirac	NOUN
ap-7723	142	18	sequence	sequence	NOUN
ap-7723	142	19	with	with	ADP
ap-7723	142	20	support	support	NOUN
ap-7723	142	21	in	in	ADP
ap-7723	142	22	i	i	PRON
ap-7723	142	23	m	m	VERB
ap-7723	142	24	,	,	PUNCT
ap-7723	142	25	i.e.	i.e.	X
ap-7723	142	26	,	,	PUNCT
ap-7723	142	27	lim	lim	PROPN
ap-7723	142	28	η→0	η→0	X
ap-7723	142	29	∫	∫	PROPN
ap-7723	143	1	+	+	PROPN
ap-7723	143	2	∞	∞	PROPN
ap-7723	143	3	−∞	−∞	X
ap-7723	143	4	dt	dt	NOUN
ap-7723	143	5	f(t	f(t	NOUN
ap-7723	143	6	)	)	PUNCT
ap-7723	143	7	gη	gη	ADP
ap-7723	143	8	m	m	PROPN
ap-7723	143	9	(	(	PUNCT
ap-7723	143	10	t	t	PROPN
ap-7723	143	11	)	)	PUNCT
ap-7723	143	12	=	=	NUM
ap-7723	143	13	f(tm	f(tm	NOUN
ap-7723	143	14	)	)	PUNCT
ap-7723	143	15	.	.	PUNCT
ap-7723	144	1	the	the	DET
ap-7723	144	2	interaction	interaction	NOUN
ap-7723	144	3	(	(	PUNCT
ap-7723	144	4	20	20	NUM
ap-7723	144	5	)	)	PUNCT
ap-7723	144	6	is	be	AUX
ap-7723	144	7	the	the	DET
ap-7723	144	8	tensor	tensor	NOUN
ap-7723	144	9	product	product	NOUN
ap-7723	144	10	of	of	ADP
ap-7723	144	11	an	an	DET
ap-7723	144	12	antisymmetric	antisymmetric	ADJ
ap-7723	144	13	operator	operator	NOUN
ap-7723	144	14	for	for	ADP
ap-7723	144	15	the	the	DET
ap-7723	144	16	pointer	pointer	NOUN
ap-7723	144	17	with	with	ADP
ap-7723	144	18	an	an	DET
ap-7723	144	19	operator	operator	NOUN
ap-7723	144	20	for	for	ADP
ap-7723	144	21	the	the	DET
ap-7723	144	22	system	system	NOUN
ap-7723	144	23	which	which	PRON
ap-7723	144	24	is	be	AUX
ap-7723	144	25	symmetric	symmetric	ADJ
ap-7723	144	26	(	(	PUNCT
ap-7723	144	27	i.e.	i.e.	X
ap-7723	144	28	,	,	PUNCT
ap-7723	144	29	hamiltonian	hamiltonian	ADJ
ap-7723	144	30	)	)	PUNCT
ap-7723	144	31	.	.	PUNCT
ap-7723	145	1	the	the	DET
ap-7723	145	2	operator	operator	NOUN
ap-7723	145	3	defined	define	VERB
ap-7723	145	4	for	for	ADP
ap-7723	145	5	t0	t0	PROPN
ap-7723	145	6	<	<	X
ap-7723	145	7	tm	tm	PROPN
ap-7723	145	8	−	−	PROPN
ap-7723	145	9	η	η	PROPN
ap-7723	145	10	as	as	ADP
ap-7723	145	11	u(t	u(t	NOUN
ap-7723	145	12	,	,	PUNCT
ap-7723	145	13	t0	t0	NOUN
ap-7723	145	14	)	)	PUNCT
ap-7723	145	15	=	=	SYM
ap-7723	145	16	exp	exp	NOUN
ap-7723	145	17	[	[	X
ap-7723	145	18	∫	∫	X
ap-7723	145	19	t	t	PROPN
ap-7723	145	20	t0	t0	PROPN
ap-7723	145	21	dt′	dt′	VERB
ap-7723	145	22	gη	gη	NOUN
ap-7723	145	23	m	m	PROPN
ap-7723	145	24	(	(	PUNCT
ap-7723	145	25	t′	t′	NUM
ap-7723	146	1	)	)	PUNCT
ap-7723	146	2	τ2	τ2	PROPN
ap-7723	146	3	⊗	⊗	PROPN
ap-7723	146	4	ρl	ρl	PROPN
ap-7723	146	5	r,ϕ	r,ϕ	PROPN
ap-7723	146	6	]	]	X
ap-7723	146	7	=	=	SYM
ap-7723	146	8	exp	exp	NOUN
ap-7723	146	9	[	[	PUNCT
ap-7723	146	10	gη	gη	NOUN
ap-7723	146	11	m	m	PROPN
ap-7723	146	12	(	(	PUNCT
ap-7723	146	13	t	t	NOUN
ap-7723	146	14	)	)	PUNCT
ap-7723	146	15	τ2	τ2	PROPN
ap-7723	146	16	⊗	⊗	PROPN
ap-7723	146	17	ρl	ρl	PROPN
ap-7723	146	18	r,ϕ	r,ϕ	PROPN
ap-7723	146	19	]	]	PUNCT
ap-7723	146	20	,	,	PUNCT
ap-7723	146	21	(	(	PUNCT
ap-7723	146	22	21	21	NUM
ap-7723	146	23	)	)	PUNCT
ap-7723	146	24	with	with	ADP
ap-7723	146	25	gη	gη	NOUN
ap-7723	146	26	m	m	PROPN
ap-7723	146	27	(	(	PUNCT
ap-7723	146	28	t	t	PROPN
ap-7723	146	29	)	)	PUNCT
ap-7723	146	30	=	=	SYM
ap-7723	147	1	∫	∫	PROPN
ap-7723	147	2	t	t	PROPN
ap-7723	147	3	t0	t0	PROPN
ap-7723	147	4	dt′	dt′	VERB
ap-7723	147	5	gη	gη	NOUN
ap-7723	147	6	m	m	NOUN
ap-7723	147	7	(	(	PUNCT
ap-7723	147	8	t′	t′	NUM
ap-7723	147	9	)	)	PUNCT
ap-7723	147	10	,	,	PUNCT
ap-7723	147	11	is	be	AUX
ap-7723	147	12	a	a	DET
ap-7723	147	13	unitary	unitary	ADJ
ap-7723	147	14	evolution	evolution	NOUN
ap-7723	147	15	operator	operator	NOUN
ap-7723	147	16	.	.	PUNCT
ap-7723	148	1	from	from	ADP
ap-7723	148	2	the	the	DET
ap-7723	148	3	formula	formula	NOUN
ap-7723	148	4	involving	involve	VERB
ap-7723	148	5	an	an	DET
ap-7723	148	6	orthogonal	orthogonal	ADJ
ap-7723	148	7	projector	projector	NOUN
ap-7723	148	8	p	p	NOUN
ap-7723	148	9	,	,	PUNCT
ap-7723	148	10	exp(θτ2	exp(θτ2	PROPN
ap-7723	148	11	⊗	⊗	PROPN
ap-7723	148	12	p	p	NOUN
ap-7723	148	13	)	)	PUNCT
ap-7723	148	14	=	=	PUNCT
ap-7723	148	15	r(θ	r(θ	NOUN
ap-7723	148	16	)	)	PUNCT
ap-7723	149	1	⊗	⊗	PROPN
ap-7723	149	2	p	p	NOUN
ap-7723	150	1	+	+	NOUN
ap-7723	150	2	1	1	NUM
ap-7723	150	3	⊗	⊗	NOUN
ap-7723	150	4	(	(	PUNCT
ap-7723	150	5	1	1	NUM
ap-7723	150	6	−	−	PROPN
ap-7723	150	7	p	p	NOUN
ap-7723	150	8	)	)	PUNCT
ap-7723	150	9	,	,	PUNCT
ap-7723	150	10	(	(	PUNCT
ap-7723	150	11	22	22	X
ap-7723	150	12	)	)	PUNCT
ap-7723	150	13	we	we	PRON
ap-7723	150	14	obtain	obtain	VERB
ap-7723	150	15	u(t	u(t	NOUN
ap-7723	150	16	,	,	PUNCT
ap-7723	150	17	t0	t0	NOUN
ap-7723	150	18	)	)	PUNCT
ap-7723	151	1	=	=	NOUN
ap-7723	151	2	r	r	NOUN
ap-7723	151	3	(	(	PUNCT
ap-7723	151	4	gη	gη	INTJ
ap-7723	151	5	m	m	PROPN
ap-7723	151	6	(	(	PUNCT
ap-7723	151	7	t	t	PROPN
ap-7723	151	8	)	)	PUNCT
ap-7723	151	9	1	1	NUM
ap-7723	152	1	+	+	CCONJ
ap-7723	152	2	r	r	NOUN
ap-7723	152	3	2	2	NUM
ap-7723	152	4	)	)	PUNCT
ap-7723	152	5	⊗	⊗	PROPN
ap-7723	152	6	eϕ	eϕ	PROPN
ap-7723	153	1	+	+	CCONJ
ap-7723	153	2	r	r	NOUN
ap-7723	153	3	(	(	PUNCT
ap-7723	153	4	gη	gη	INTJ
ap-7723	153	5	m	m	PROPN
ap-7723	153	6	(	(	PUNCT
ap-7723	153	7	t	t	PROPN
ap-7723	153	8	)	)	PUNCT
ap-7723	153	9	1	1	NUM
ap-7723	153	10	−	−	NOUN
ap-7723	153	11	r	r	NOUN
ap-7723	153	12	2	2	NUM
ap-7723	153	13	)	)	PUNCT
ap-7723	153	14	⊗	⊗	NUM
ap-7723	153	15	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	153	16	.	.	PUNCT
ap-7723	154	1	(	(	PUNCT
ap-7723	154	2	23	23	NUM
ap-7723	154	3	)	)	PUNCT
ap-7723	154	4	for	for	ADP
ap-7723	154	5	t0	t0	PROPN
ap-7723	154	6	<	<	X
ap-7723	154	7	tm	tm	PROPN
ap-7723	154	8	−	−	PROPN
ap-7723	154	9	η	η	PROPN
ap-7723	154	10	and	and	CCONJ
ap-7723	154	11	t	t	PROPN
ap-7723	154	12	>	>	PUNCT
ap-7723	154	13	tm	tm	PROPN
ap-7723	154	14	+	+	PROPN
ap-7723	154	15	η	η	PROPN
ap-7723	154	16	,	,	PUNCT
ap-7723	154	17	we	we	PRON
ap-7723	154	18	finally	finally	ADV
ap-7723	154	19	obtain	obtain	VERB
ap-7723	154	20	u(t	u(t	NOUN
ap-7723	154	21	,	,	PUNCT
ap-7723	154	22	t0	t0	NOUN
ap-7723	154	23	)	)	PUNCT
ap-7723	155	1	=	=	SYM
ap-7723	155	2	r	r	NOUN
ap-7723	155	3	(	(	PUNCT
ap-7723	155	4	1	1	NUM
ap-7723	155	5	+	+	CCONJ
ap-7723	155	6	r	r	NOUN
ap-7723	155	7	2	2	NUM
ap-7723	155	8	)	)	PUNCT
ap-7723	155	9	⊗	⊗	PROPN
ap-7723	155	10	eϕ	eϕ	PROPN
ap-7723	156	1	+	+	CCONJ
ap-7723	156	2	r	r	NOUN
ap-7723	156	3	(	(	PUNCT
ap-7723	156	4	1	1	NUM
ap-7723	156	5	−	−	NOUN
ap-7723	156	6	r	r	NOUN
ap-7723	156	7	2	2	NUM
ap-7723	156	8	)	)	PUNCT
ap-7723	156	9	⊗	⊗	NUM
ap-7723	156	10	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	156	11	.	.	PUNCT
ap-7723	157	1	(	(	PUNCT
ap-7723	157	2	24	24	NUM
ap-7723	157	3	)	)	PUNCT
ap-7723	157	4	preparing	prepare	VERB
ap-7723	157	5	the	the	DET
ap-7723	157	6	polarizer	polarizer	NOUN
ap-7723	157	7	in	in	ADP
ap-7723	157	8	the	the	DET
ap-7723	157	9	state	state	NOUN
ap-7723	157	10	ρm	ρm	ADP
ap-7723	157	11	s0,θ0	s0,θ0	PROPN
ap-7723	157	12	,	,	PUNCT
ap-7723	157	13	we	we	PRON
ap-7723	157	14	obtain	obtain	VERB
ap-7723	157	15	the	the	DET
ap-7723	157	16	evolution	evolution	NOUN
ap-7723	157	17	u(t	u(t	NOUN
ap-7723	157	18	,	,	PUNCT
ap-7723	157	19	t0	t0	NOUN
ap-7723	157	20	)	)	PUNCT
ap-7723	157	21	ρm	ρm	ADP
ap-7723	158	1	s0,θ0	s0,θ0	PROPN
ap-7723	158	2	⊗	⊗	PROPN
ap-7723	158	3	ρl	ρl	ADP
ap-7723	158	4	r0,ϕ0	r0,ϕ0	PROPN
ap-7723	158	5	u(t	u(t	PROPN
ap-7723	158	6	,	,	PUNCT
ap-7723	158	7	t0)†	t0)†	NOUN
ap-7723	158	8	of	of	ADP
ap-7723	158	9	the	the	DET
ap-7723	158	10	initial	initial	ADJ
ap-7723	158	11	state	state	NOUN
ap-7723	158	12	for	for	ADP
ap-7723	158	13	t	t	PROPN
ap-7723	158	14	>	>	PUNCT
ap-7723	158	15	tm	tm	PROPN
ap-7723	158	16	+	+	PROPN
ap-7723	158	17	η	η	PROPN
ap-7723	158	18	ρm	ρm	PRON
ap-7723	158	19	s0,θ0	s0,θ0	PROPN
ap-7723	158	20	+	+	CCONJ
ap-7723	158	21	1+r	1+r	NUM
ap-7723	158	22	2	2	NUM
ap-7723	158	23	⊗	⊗	NUM
ap-7723	158	24	1	1	NUM
ap-7723	159	1	+	+	CCONJ
ap-7723	159	2	r0	r0	NOUN
ap-7723	159	3	cos	cos	ADP
ap-7723	159	4	2(ϕ	2(ϕ	NUM
ap-7723	159	5	−	−	PROPN
ap-7723	159	6	ϕ0	ϕ0	NOUN
ap-7723	159	7	)	)	PUNCT
ap-7723	159	8	2	2	NUM
ap-7723	159	9	eϕ	eϕ	NOUN
ap-7723	159	10	+	+	CCONJ
ap-7723	159	11	ρm	ρm	PRON
ap-7723	160	1	s0,θ0	s0,θ0	PROPN
ap-7723	160	2	+	+	CCONJ
ap-7723	160	3	1−r	1−r	NUM
ap-7723	160	4	2	2	NUM
ap-7723	160	5	⊗	⊗	PROPN
ap-7723	160	6	1	1	NUM
ap-7723	160	7	−	−	NOUN
ap-7723	160	8	r0	r0	NOUN
ap-7723	160	9	cos	cos	ADP
ap-7723	160	10	2(ϕ	2(ϕ	NUM
ap-7723	160	11	−	−	PROPN
ap-7723	160	12	ϕ0	ϕ0	NOUN
ap-7723	160	13	)	)	PUNCT
ap-7723	160	14	2	2	NUM
ap-7723	160	15	eϕ+π/2	eϕ+π/2	NOUN
ap-7723	160	16	+	+	CCONJ
ap-7723	160	17	1	1	NUM
ap-7723	160	18	4	4	NUM
ap-7723	160	19	(	(	PUNCT
ap-7723	160	20	r(r	r(r	NOUN
ap-7723	160	21	)	)	PUNCT
ap-7723	160	22	+	+	NUM
ap-7723	160	23	s0σ2θ0	s0σ2θ0	NOUN
ap-7723	160	24	+	+	NOUN
ap-7723	160	25	1	1	NUM
ap-7723	160	26	)	)	PUNCT
ap-7723	160	27	⊗	⊗	PROPN
ap-7723	160	28	r0	r0	NOUN
ap-7723	160	29	sin	sin	VERB
ap-7723	160	30	2(ϕ	2(ϕ	NUM
ap-7723	160	31	−	−	PROPN
ap-7723	160	32	ϕ0	ϕ0	NOUN
ap-7723	160	33	)	)	PUNCT
ap-7723	160	34	eϕτ2	eϕτ2	NOUN
ap-7723	160	35	−	−	NOUN
ap-7723	160	36	1	1	NUM
ap-7723	160	37	4	4	NUM
ap-7723	160	38	(	(	PUNCT
ap-7723	160	39	r(−r	r(−r	NOUN
ap-7723	160	40	)	)	PUNCT
ap-7723	160	41	+	+	CCONJ
ap-7723	160	42	s0σ2θ0	s0σ2θ0	NOUN
ap-7723	160	43	+	+	NOUN
ap-7723	160	44	1	1	NUM
ap-7723	160	45	)	)	PUNCT
ap-7723	160	46	⊗	⊗	PROPN
ap-7723	160	47	r0	r0	NOUN
ap-7723	160	48	sin	sin	VERB
ap-7723	160	49	2(ϕ	2(ϕ	NUM
ap-7723	160	50	−	−	PROPN
ap-7723	160	51	ϕ0	ϕ0	NOUN
ap-7723	160	52	)	)	PUNCT
ap-7723	160	53	τ2eϕ	τ2eϕ	PUNCT
ap-7723	160	54	.	.	PUNCT
ap-7723	161	1	(	(	PUNCT
ap-7723	161	2	25	25	NUM
ap-7723	161	3	)	)	PUNCT
ap-7723	161	4	therefore	therefore	ADV
ap-7723	161	5	,	,	PUNCT
ap-7723	161	6	the	the	DET
ap-7723	161	7	probability	probability	NOUN
ap-7723	161	8	for	for	SCONJ
ap-7723	161	9	the	the	DET
ap-7723	161	10	pointer	pointer	NOUN
ap-7723	161	11	to	to	PART
ap-7723	161	12	rotate	rotate	VERB
ap-7723	161	13	by	by	ADP
ap-7723	161	14	1+r	1+r	NUM
ap-7723	161	15	2	2	NUM
ap-7723	161	16	,	,	PUNCT
ap-7723	161	17	corresponding	correspond	VERB
ap-7723	161	18	to	to	ADP
ap-7723	161	19	the	the	DET
ap-7723	161	20	polarization	polarization	NOUN
ap-7723	161	21	along	along	ADP
ap-7723	161	22	the	the	DET
ap-7723	161	23	orientation	orientation	NOUN
ap-7723	161	24	ϕ	ϕ	NOUN
ap-7723	161	25	is	be	AUX
ap-7723	161	26	tr	tr	VERB
ap-7723	161	27	[	[	X
ap-7723	161	28	(	(	PUNCT
ap-7723	161	29	u(t	u(t	NOUN
ap-7723	161	30	,	,	PUNCT
ap-7723	161	31	t0	t0	NOUN
ap-7723	161	32	)	)	PUNCT
ap-7723	161	33	ρm	ρm	ADP
ap-7723	162	1	s0,θ0	s0,θ0	PROPN
ap-7723	162	2	⊗	⊗	PROPN
ap-7723	162	3	ρl	ρl	ADP
ap-7723	162	4	r0,ϕ0	r0,ϕ0	PROPN
ap-7723	162	5	u(t	u(t	PROPN
ap-7723	162	6	,	,	PUNCT
ap-7723	162	7	t0)†	t0)†	NOUN
ap-7723	162	8	)	)	PUNCT
ap-7723	162	9	(	(	PUNCT
ap-7723	162	10	1	1	NUM
ap-7723	162	11	⊗	⊗	PROPN
ap-7723	162	12	eϕ	eϕ	PROPN
ap-7723	162	13	)	)	PUNCT
ap-7723	162	14	]	]	PUNCT
ap-7723	163	1	=	=	SYM
ap-7723	163	2	1	1	NUM
ap-7723	163	3	+	+	NUM
ap-7723	163	4	r0	r0	NOUN
ap-7723	163	5	cos	cos	ADP
ap-7723	163	6	2(ϕ	2(ϕ	NUM
ap-7723	163	7	−	−	PROPN
ap-7723	163	8	ϕ0	ϕ0	NOUN
ap-7723	163	9	)	)	PUNCT
ap-7723	163	10	2	2	NUM
ap-7723	163	11	,	,	PUNCT
ap-7723	163	12	(	(	PUNCT
ap-7723	163	13	26	26	NUM
ap-7723	163	14	)	)	PUNCT
ap-7723	163	15	that	that	SCONJ
ap-7723	163	16	for	for	ADP
ap-7723	163	17	the	the	DET
ap-7723	163	18	completely	completely	ADV
ap-7723	163	19	linear	linear	ADJ
ap-7723	163	20	polarization	polarization	NOUN
ap-7723	163	21	of	of	ADP
ap-7723	163	22	the	the	DET
ap-7723	163	23	light	light	ADJ
ap-7723	163	24	,	,	PUNCT
ap-7723	163	25	i.e.	i.e.	X
ap-7723	163	26	r0	r0	NOUN
ap-7723	163	27	=	=	SYM
ap-7723	163	28	1	1	NUM
ap-7723	163	29	,	,	PUNCT
ap-7723	163	30	becomes	become	VERB
ap-7723	163	31	the	the	DET
ap-7723	163	32	familiar	familiar	ADJ
ap-7723	163	33	malus	malus	NOUN
ap-7723	163	34	law	law	NOUN
ap-7723	163	35	,	,	PUNCT
ap-7723	163	36	cos2(ϕ	cos2(ϕ	NOUN
ap-7723	163	37	−	−	PROPN
ap-7723	163	38	ϕ0	ϕ0	NOUN
ap-7723	163	39	)	)	PUNCT
ap-7723	163	40	.	.	PUNCT
ap-7723	164	1	similarly	similarly	ADV
ap-7723	164	2	,	,	PUNCT
ap-7723	164	3	the	the	DET
ap-7723	164	4	second	second	ADJ
ap-7723	164	5	term	term	NOUN
ap-7723	164	6	gives	give	VERB
ap-7723	164	7	the	the	DET
ap-7723	164	8	probability	probability	NOUN
ap-7723	164	9	for	for	ADP
ap-7723	164	10	the	the	DET
ap-7723	164	11	perpendicular	perpendicular	ADJ
ap-7723	164	12	orientation	orientation	NOUN
ap-7723	164	13	ϕ	ϕ	NOUN
ap-7723	164	14	+	+	CCONJ
ap-7723	164	15	π/2	π/2	NUM
ap-7723	164	16	and	and	CCONJ
ap-7723	164	17	the	the	DET
ap-7723	164	18	pointer	pointer	NOUN
ap-7723	164	19	rotation	rotation	NOUN
ap-7723	164	20	by	by	ADP
ap-7723	164	21	1−r	1−r	NUM
ap-7723	164	22	2	2	NUM
ap-7723	164	23	tr	tr	VERB
ap-7723	164	24	[	[	X
ap-7723	164	25	(	(	PUNCT
ap-7723	164	26	u(t	u(t	NOUN
ap-7723	164	27	,	,	PUNCT
ap-7723	164	28	t0	t0	NOUN
ap-7723	164	29	)	)	PUNCT
ap-7723	164	30	ρm	ρm	ADP
ap-7723	164	31	s0,θ0	s0,θ0	PROPN
ap-7723	164	32	⊗	⊗	PROPN
ap-7723	165	1	ρl	ρl	ADP
ap-7723	165	2	r0,ϕ0	r0,ϕ0	PROPN
ap-7723	165	3	u(t	u(t	PROPN
ap-7723	165	4	,	,	PUNCT
ap-7723	165	5	t0)†	t0)†	NOUN
ap-7723	165	6	)	)	PUNCT
ap-7723	165	7	(	(	PUNCT
ap-7723	165	8	1	1	NUM
ap-7723	165	9	⊗	⊗	PROPN
ap-7723	165	10	eϕ+π/2	eϕ+π/2	NUM
ap-7723	165	11	)	)	PUNCT
ap-7723	165	12	]	]	PUNCT
ap-7723	166	1	=	=	SYM
ap-7723	167	1	1	1	NUM
ap-7723	167	2	−	−	NOUN
ap-7723	167	3	r0	r0	NOUN
ap-7723	167	4	cos	cos	ADP
ap-7723	167	5	2(ϕ	2(ϕ	NUM
ap-7723	167	6	−	−	PROPN
ap-7723	167	7	ϕ0	ϕ0	NOUN
ap-7723	167	8	)	)	PUNCT
ap-7723	167	9	2	2	NUM
ap-7723	167	10	,	,	PUNCT
ap-7723	167	11	(	(	PUNCT
ap-7723	167	12	27	27	NUM
ap-7723	167	13	)	)	PUNCT
ap-7723	167	14	corresponding	correspond	VERB
ap-7723	167	15	(	(	PUNCT
ap-7723	167	16	in	in	ADP
ap-7723	167	17	the	the	DET
ap-7723	167	18	case	case	NOUN
ap-7723	167	19	r0	r0	NOUN
ap-7723	167	20	=	=	NOUN
ap-7723	167	21	1	1	NUM
ap-7723	167	22	)	)	PUNCT
ap-7723	167	23	to	to	ADP
ap-7723	167	24	the	the	DET
ap-7723	167	25	malus	malus	ADJ
ap-7723	167	26	law	law	NOUN
ap-7723	167	27	sin2(ϕ	sin2(ϕ	NUM
ap-7723	167	28	−	−	PROPN
ap-7723	167	29	ϕ0	ϕ0	NOUN
ap-7723	167	30	)	)	PUNCT
ap-7723	167	31	.	.	PUNCT
ap-7723	168	1	11	11	NUM
ap-7723	168	2	r.	r.	PROPN
ap-7723	168	3	beneduci	beneduci	PROPN
ap-7723	168	4	,	,	PUNCT
ap-7723	168	5	e.	e.	PROPN
ap-7723	168	6	frion	frion	PROPN
ap-7723	168	7	,	,	PUNCT
ap-7723	168	8	j.-p	j.-p	PROPN
ap-7723	168	9	.	.	PUNCT
ap-7723	169	1	gazeau	gazeau	PROPN
ap-7723	169	2	acta	acta	PROPN
ap-7723	169	3	polytechnica	polytechnica	PROPN
ap-7723	169	4	4	4	NUM
ap-7723	169	5	.	.	PUNCT
ap-7723	169	6	entanglement	entanglement	NOUN
ap-7723	169	7	and	and	CCONJ
ap-7723	169	8	isomorphisms	isomorphism	NOUN
ap-7723	169	9	in	in	ADP
ap-7723	169	10	this	this	DET
ap-7723	169	11	section	section	NOUN
ap-7723	169	12	,	,	PUNCT
ap-7723	169	13	we	we	PRON
ap-7723	169	14	develop	develop	VERB
ap-7723	169	15	our	our	PRON
ap-7723	169	16	previous	previous	ADJ
ap-7723	169	17	results	result	NOUN
ap-7723	169	18	further	far	ADV
ap-7723	169	19	by	by	ADP
ap-7723	169	20	giving	give	VERB
ap-7723	169	21	an	an	DET
ap-7723	169	22	interpretation	interpretation	NOUN
ap-7723	169	23	in	in	ADP
ap-7723	169	24	terms	term	NOUN
ap-7723	169	25	of	of	ADP
ap-7723	169	26	quantum	quantum	ADJ
ap-7723	169	27	entanglement	entanglement	NOUN
ap-7723	169	28	.	.	PUNCT
ap-7723	170	1	previously	previously	ADV
ap-7723	170	2	,	,	PUNCT
ap-7723	170	3	we	we	PRON
ap-7723	170	4	described	describe	VERB
ap-7723	170	5	the	the	DET
ap-7723	170	6	interaction	interaction	NOUN
ap-7723	170	7	between	between	ADP
ap-7723	170	8	a	a	DET
ap-7723	170	9	polarizer	polarizer	NOUN
ap-7723	170	10	and	and	CCONJ
ap-7723	170	11	a	a	DET
ap-7723	170	12	light	light	ADJ
ap-7723	170	13	ray	ray	NOUN
ap-7723	170	14	as	as	ADP
ap-7723	170	15	the	the	DET
ap-7723	170	16	tensor	tensor	NOUN
ap-7723	170	17	product	product	NOUN
ap-7723	170	18	(	(	PUNCT
ap-7723	170	19	20	20	NUM
ap-7723	170	20	)	)	PUNCT
ap-7723	170	21	,	,	PUNCT
ap-7723	170	22	which	which	PRON
ap-7723	170	23	is	be	AUX
ap-7723	170	24	analogous	analogous	ADJ
ap-7723	170	25	to	to	ADP
ap-7723	170	26	the	the	DET
ap-7723	170	27	quantum	quantum	ADJ
ap-7723	170	28	entanglement	entanglement	NOUN
ap-7723	170	29	of	of	ADP
ap-7723	170	30	states	state	NOUN
ap-7723	170	31	,	,	PUNCT
ap-7723	170	32	since	since	SCONJ
ap-7723	170	33	it	it	PRON
ap-7723	170	34	is	be	AUX
ap-7723	170	35	a	a	DET
ap-7723	170	36	logical	logical	ADJ
ap-7723	170	37	consequence	consequence	NOUN
ap-7723	170	38	of	of	ADP
ap-7723	170	39	the	the	DET
ap-7723	170	40	construction	construction	NOUN
ap-7723	170	41	of	of	ADP
ap-7723	170	42	tensor	tensor	NOUN
ap-7723	170	43	products	product	NOUN
ap-7723	170	44	of	of	ADP
ap-7723	170	45	hilbert	hilbert	PROPN
ap-7723	170	46	spaces	space	NOUN
ap-7723	170	47	for	for	ADP
ap-7723	170	48	describing	describe	VERB
ap-7723	170	49	quantum	quantum	ADJ
ap-7723	170	50	states	state	NOUN
ap-7723	170	51	of	of	ADP
ap-7723	170	52	composite	composite	ADJ
ap-7723	170	53	system	system	NOUN
ap-7723	170	54	.	.	PUNCT
ap-7723	171	1	in	in	ADP
ap-7723	171	2	the	the	DET
ap-7723	171	3	present	present	ADJ
ap-7723	171	4	case	case	NOUN
ap-7723	171	5	,	,	PUNCT
ap-7723	171	6	we	we	PRON
ap-7723	171	7	are	be	AUX
ap-7723	171	8	in	in	ADP
ap-7723	171	9	presence	presence	NOUN
ap-7723	171	10	of	of	ADP
ap-7723	171	11	a	a	DET
ap-7723	171	12	remarkable	remarkable	ADJ
ap-7723	171	13	sequence	sequence	NOUN
ap-7723	171	14	of	of	ADP
ap-7723	171	15	vector	vector	NOUN
ap-7723	171	16	space	space	NOUN
ap-7723	171	17	isomorphisms	isomorphism	NOUN
ap-7723	171	18	due	due	ADP
ap-7723	171	19	to	to	ADP
ap-7723	171	20	the	the	DET
ap-7723	171	21	fact	fact	NOUN
ap-7723	171	22	that	that	SCONJ
ap-7723	171	23	2	2	NUM
ap-7723	171	24	×	×	NOUN
ap-7723	171	25	2	2	NUM
ap-7723	171	26	=	=	SYM
ap-7723	171	27	2	2	NUM
ap-7723	171	28	+	+	CCONJ
ap-7723	171	29	2	2	NUM
ap-7723	171	30	1	1	NUM
ap-7723	171	31	:	:	PUNCT
ap-7723	171	32	r2	r2	PROPN
ap-7723	171	33	⊗	⊗	PROPN
ap-7723	171	34	r2	r2	PROPN
ap-7723	171	35	∼=	∼=	PROPN
ap-7723	171	36	r2	r2	NOUN
ap-7723	171	37	×	×	NOUN
ap-7723	171	38	r2	r2	NOUN
ap-7723	171	39	∼=	∼=	PROPN
ap-7723	171	40	r2	r2	PROPN
ap-7723	171	41	⊕	⊕	PROPN
ap-7723	171	42	r2	r2	PROPN
ap-7723	171	43	∼=	∼=	PROPN
ap-7723	171	44	c2	c2	PROPN
ap-7723	171	45	∼=	∼=	PROPN
ap-7723	171	46	h	h	NOUN
ap-7723	171	47	,	,	PUNCT
ap-7723	171	48	(	(	PUNCT
ap-7723	171	49	28	28	NUM
ap-7723	171	50	)	)	PUNCT
ap-7723	171	51	where	where	SCONJ
ap-7723	171	52	h	h	NOUN
ap-7723	171	53	is	be	AUX
ap-7723	171	54	the	the	DET
ap-7723	171	55	field	field	NOUN
ap-7723	171	56	of	of	ADP
ap-7723	171	57	quaternions	quaternion	NOUN
ap-7723	171	58	.	.	PUNCT
ap-7723	172	1	therefore	therefore	ADV
ap-7723	172	2	,	,	PUNCT
ap-7723	172	3	the	the	DET
ap-7723	172	4	description	description	NOUN
ap-7723	172	5	of	of	ADP
ap-7723	172	6	the	the	DET
ap-7723	172	7	entanglement	entanglement	NOUN
ap-7723	172	8	in	in	ADP
ap-7723	172	9	a	a	DET
ap-7723	172	10	real	real	ADJ
ap-7723	172	11	hilbert	hilbert	NOUN
ap-7723	172	12	space	space	NOUN
ap-7723	172	13	is	be	AUX
ap-7723	172	14	equivalent	equivalent	ADJ
ap-7723	172	15	to	to	ADP
ap-7723	172	16	the	the	DET
ap-7723	172	17	description	description	NOUN
ap-7723	172	18	of	of	ADP
ap-7723	172	19	a	a	DET
ap-7723	172	20	single	single	ADJ
ap-7723	172	21	system	system	NOUN
ap-7723	172	22	(	(	PUNCT
ap-7723	172	23	e.g.	e.g.	ADV
ap-7723	172	24	,	,	PUNCT
ap-7723	172	25	a	a	DET
ap-7723	172	26	spin	spin	NOUN
ap-7723	172	27	1/2	1/2	NUM
ap-7723	172	28	)	)	PUNCT
ap-7723	172	29	in	in	ADP
ap-7723	172	30	the	the	DET
ap-7723	172	31	complex	complex	ADJ
ap-7723	172	32	hilbert	hilbert	PROPN
ap-7723	172	33	space	space	NOUN
ap-7723	172	34	c2	c2	PROPN
ap-7723	172	35	,	,	PUNCT
ap-7723	172	36	or	or	CCONJ
ap-7723	172	37	in	in	ADP
ap-7723	172	38	h.	h.	PROPN
ap-7723	172	39	in	in	ADP
ap-7723	172	40	section	section	NOUN
ap-7723	172	41	4.3	4.3	NUM
ap-7723	172	42	we	we	PRON
ap-7723	172	43	develop	develop	VERB
ap-7723	172	44	such	such	DET
ap-7723	172	45	an	an	DET
ap-7723	172	46	observation	observation	NOUN
ap-7723	172	47	.	.	PUNCT
ap-7723	173	1	4.1	4.1	NUM
ap-7723	173	2	.	.	PUNCT
ap-7723	173	3	bell	bell	PROPN
ap-7723	173	4	states	state	NOUN
ap-7723	173	5	and	and	CCONJ
ap-7723	173	6	quantum	quantum	NOUN
ap-7723	173	7	correlations	correlation	NOUN
ap-7723	173	8	it	it	PRON
ap-7723	173	9	is	be	AUX
ap-7723	173	10	straightforward	straightforward	ADJ
ap-7723	173	11	to	to	PART
ap-7723	173	12	transpose	transpose	VERB
ap-7723	173	13	into	into	ADP
ap-7723	173	14	the	the	DET
ap-7723	173	15	present	present	NOUN
ap-7723	173	16	setting	set	VERB
ap-7723	173	17	the	the	DET
ap-7723	173	18	1964	1964	NUM
ap-7723	173	19	analysis	analysis	NOUN
ap-7723	173	20	and	and	CCONJ
ap-7723	173	21	result	result	NOUN
ap-7723	173	22	presented	present	VERB
ap-7723	173	23	by	by	ADP
ap-7723	173	24	bell	bell	NOUN
ap-7723	173	25	in	in	ADP
ap-7723	173	26	his	his	PRON
ap-7723	173	27	discussion	discussion	NOUN
ap-7723	173	28	about	about	ADP
ap-7723	173	29	the	the	DET
ap-7723	173	30	epr	epr	PROPN
ap-7723	173	31	paper	paper	NOUN
ap-7723	174	1	[	[	X
ap-7723	174	2	13	13	NUM
ap-7723	174	3	]	]	PUNCT
ap-7723	174	4	and	and	CCONJ
ap-7723	174	5	about	about	ADP
ap-7723	174	6	the	the	DET
ap-7723	174	7	subsequent	subsequent	ADJ
ap-7723	174	8	bohm	bohm	PROPN
ap-7723	174	9	’s	’s	PART
ap-7723	174	10	approaches	approach	NOUN
ap-7723	174	11	based	base	VERB
ap-7723	174	12	on	on	ADP
ap-7723	174	13	the	the	DET
ap-7723	174	14	assumption	assumption	NOUN
ap-7723	174	15	of	of	ADP
ap-7723	174	16	hidden	hidden	ADJ
ap-7723	174	17	variables	variable	NOUN
ap-7723	174	18	[	[	X
ap-7723	174	19	14	14	NUM
ap-7723	174	20	]	]	PUNCT
ap-7723	174	21	.	.	PUNCT
ap-7723	175	1	we	we	PRON
ap-7723	175	2	only	only	ADV
ap-7723	175	3	need	need	VERB
ap-7723	175	4	to	to	PART
ap-7723	175	5	replace	replace	VERB
ap-7723	175	6	the	the	DET
ap-7723	175	7	bell	bell	NOUN
ap-7723	175	8	spin	spin	VERB
ap-7723	175	9	one	one	NUM
ap-7723	175	10	-	-	PUNCT
ap-7723	175	11	half	half	NOUN
ap-7723	175	12	particles	particle	NOUN
ap-7723	175	13	with	with	ADP
ap-7723	175	14	the	the	DET
ap-7723	175	15	horizontal	horizontal	ADJ
ap-7723	175	16	(	(	PUNCT
ap-7723	175	17	i.e.	i.e.	X
ap-7723	175	18	,	,	PUNCT
ap-7723	175	19	+1	+1	ADJ
ap-7723	175	20	)	)	PUNCT
ap-7723	175	21	and	and	CCONJ
ap-7723	175	22	vertical	vertical	ADJ
ap-7723	175	23	(	(	PUNCT
ap-7723	175	24	i.e.	i.e.	X
ap-7723	175	25	,	,	PUNCT
ap-7723	175	26	−1	−1	NOUN
ap-7723	175	27	)	)	PUNCT
ap-7723	175	28	quantum	quantum	NOUN
ap-7723	175	29	orientations	orientation	NOUN
ap-7723	175	30	in	in	ADP
ap-7723	175	31	the	the	DET
ap-7723	175	32	plane	plane	NOUN
ap-7723	175	33	as	as	ADP
ap-7723	175	34	the	the	DET
ap-7723	175	35	only	only	ADJ
ap-7723	175	36	possible	possible	ADJ
ap-7723	175	37	issues	issue	NOUN
ap-7723	175	38	of	of	ADP
ap-7723	175	39	the	the	DET
ap-7723	175	40	observable	observable	ADJ
ap-7723	175	41	σϕ	σϕ	NOUN
ap-7723	175	42	(	(	PUNCT
ap-7723	175	43	11	11	NUM
ap-7723	175	44	)	)	PUNCT
ap-7723	175	45	,	,	PUNCT
ap-7723	175	46	supposing	suppose	VERB
ap-7723	175	47	that	that	SCONJ
ap-7723	175	48	there	there	PRON
ap-7723	175	49	exists	exist	VERB
ap-7723	175	50	a	a	DET
ap-7723	175	51	pointer	pointer	NOUN
ap-7723	175	52	device	device	NOUN
ap-7723	175	53	designed	design	VERB
ap-7723	175	54	for	for	ADP
ap-7723	175	55	measuring	measure	VERB
ap-7723	175	56	such	such	ADJ
ap-7723	175	57	orientations	orientation	NOUN
ap-7723	175	58	with	with	ADP
ap-7723	175	59	outcomes	outcome	NOUN
ap-7723	175	60	±1	±1	VERB
ap-7723	175	61	only	only	ADV
ap-7723	175	62	.	.	PUNCT
ap-7723	176	1	in	in	ADP
ap-7723	176	2	order	order	NOUN
ap-7723	176	3	to	to	PART
ap-7723	176	4	define	define	VERB
ap-7723	176	5	bell	bell	NOUN
ap-7723	176	6	states	state	NOUN
ap-7723	176	7	and	and	CCONJ
ap-7723	176	8	their	their	PRON
ap-7723	176	9	quantum	quantum	ADJ
ap-7723	176	10	correlations	correlation	NOUN
ap-7723	176	11	,	,	PUNCT
ap-7723	176	12	let	let	VERB
ap-7723	176	13	us	we	PRON
ap-7723	176	14	first	first	ADV
ap-7723	176	15	write	write	VERB
ap-7723	176	16	the	the	DET
ap-7723	176	17	canonical	canonical	ADJ
ap-7723	176	18	,	,	PUNCT
ap-7723	176	19	orthonormal	orthonormal	ADJ
ap-7723	176	20	basis	basis	NOUN
ap-7723	176	21	of	of	ADP
ap-7723	176	22	the	the	DET
ap-7723	176	23	tensor	tensor	NOUN
ap-7723	176	24	product	product	NOUN
ap-7723	176	25	r2	r2	PROPN
ap-7723	176	26	a	a	DET
ap-7723	176	27	⊗	⊗	PROPN
ap-7723	176	28	r2	r2	PROPN
ap-7723	176	29	b	b	PROPN
ap-7723	176	30	,	,	PUNCT
ap-7723	176	31	the	the	DET
ap-7723	176	32	first	first	ADJ
ap-7723	176	33	factor	factor	NOUN
ap-7723	176	34	being	be	AUX
ap-7723	176	35	for	for	ADP
ap-7723	176	36	system	system	NOUN
ap-7723	176	37	“	"	PUNCT
ap-7723	176	38	a	a	PRON
ap-7723	176	39	”	"	PUNCT
ap-7723	176	40	and	and	CCONJ
ap-7723	176	41	the	the	DET
ap-7723	176	42	other	other	ADJ
ap-7723	176	43	for	for	ADP
ap-7723	176	44	system	system	NOUN
ap-7723	176	45	“	"	PUNCT
ap-7723	176	46	b	b	NOUN
ap-7723	176	47	”	"	PUNCT
ap-7723	176	48	,	,	PUNCT
ap-7723	176	49	as	as	ADP
ap-7723	176	50	|0⟩a	|0⟩a	ADJ
ap-7723	176	51	⊗	⊗	ADJ
ap-7723	176	52	|0⟩b	|0⟩b	NOUN
ap-7723	176	53	,	,	PUNCT
ap-7723	176	54	∣∣∣π2〉a	∣∣∣π2〉a	PROPN
ap-7723	176	55	⊗	⊗	PROPN
ap-7723	176	56	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	176	57	,	,	PUNCT
ap-7723	176	58	|0⟩a	|0⟩a	PROPN
ap-7723	176	59	⊗	⊗	PROPN
ap-7723	176	60	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	176	61	,	,	PUNCT
ap-7723	176	62	∣∣∣π2〉a	∣∣∣π2〉a	PROPN
ap-7723	176	63	⊗	⊗	PROPN
ap-7723	176	64	|0⟩b	|0⟩b	PROPN
ap-7723	176	65	.	.	PUNCT
ap-7723	177	1	(	(	PUNCT
ap-7723	177	2	29	29	NUM
ap-7723	177	3	)	)	PUNCT
ap-7723	177	4	the	the	DET
ap-7723	177	5	states	state	NOUN
ap-7723	177	6	|0⟩	|0⟩	VERB
ap-7723	177	7	and	and	CCONJ
ap-7723	177	8	∣∣π	∣∣π	PROPN
ap-7723	177	9	2	2	NUM
ap-7723	177	10	〉	〉	NOUN
ap-7723	177	11	pertain	pertain	VERB
ap-7723	177	12	to	to	ADP
ap-7723	177	13	a	a	DET
ap-7723	177	14	or	or	CCONJ
ap-7723	177	15	b	b	NOUN
ap-7723	177	16	,	,	PUNCT
ap-7723	177	17	and	and	CCONJ
ap-7723	177	18	are	be	AUX
ap-7723	177	19	named	name	VERB
ap-7723	177	20	“	"	PUNCT
ap-7723	177	21	q	q	ADJ
ap-7723	177	22	-	-	PUNCT
ap-7723	177	23	bit	bit	NOUN
ap-7723	177	24	”	"	PUNCT
ap-7723	177	25	or	or	CCONJ
ap-7723	177	26	“	"	PUNCT
ap-7723	177	27	qubit	qubit	NOUN
ap-7723	177	28	”	"	PUNCT
ap-7723	177	29	in	in	ADP
ap-7723	177	30	the	the	DET
ap-7723	177	31	standard	standard	ADJ
ap-7723	177	32	language	language	NOUN
ap-7723	177	33	of	of	ADP
ap-7723	177	34	quantum	quantum	ADJ
ap-7723	177	35	information	information	NOUN
ap-7723	177	36	.	.	PUNCT
ap-7723	178	1	since	since	SCONJ
ap-7723	178	2	they	they	PRON
ap-7723	178	3	are	be	AUX
ap-7723	178	4	pure	pure	ADJ
ap-7723	178	5	states	state	NOUN
ap-7723	178	6	,	,	PUNCT
ap-7723	178	7	they	they	PRON
ap-7723	178	8	can	can	AUX
ap-7723	178	9	be	be	AUX
ap-7723	178	10	associated	associate	VERB
ap-7723	178	11	to	to	ADP
ap-7723	178	12	a	a	DET
ap-7723	178	13	pointer	pointer	NOUN
ap-7723	178	14	measuring	measure	VERB
ap-7723	178	15	the	the	DET
ap-7723	178	16	horizontal	horizontal	ADJ
ap-7723	178	17	(	(	PUNCT
ap-7723	178	18	resp	resp	NOUN
ap-7723	178	19	.	.	PUNCT
ap-7723	179	1	vertical	vertical	ADJ
ap-7723	179	2	)	)	PUNCT
ap-7723	179	3	direction	direction	NOUN
ap-7723	179	4	or	or	CCONJ
ap-7723	179	5	polarisation	polarisation	NOUN
ap-7723	179	6	described	describe	VERB
ap-7723	179	7	by	by	ADP
ap-7723	179	8	the	the	DET
ap-7723	179	9	state	state	NOUN
ap-7723	179	10	|0⟩	|0⟩	NOUN
ap-7723	179	11	(	(	PUNCT
ap-7723	179	12	resp	resp	NOUN
ap-7723	179	13	.	.	PUNCT
ap-7723	180	1	∣∣π	∣∣π	NOUN
ap-7723	180	2	2	2	NUM
ap-7723	180	3	〉	〉	NOUN
ap-7723	180	4	)	)	PUNCT
ap-7723	180	5	.	.	PUNCT
ap-7723	181	1	there	there	PRON
ap-7723	181	2	are	be	VERB
ap-7723	181	3	four	four	NUM
ap-7723	181	4	bell	bell	NOUN
ap-7723	181	5	pure	pure	ADJ
ap-7723	181	6	states	state	NOUN
ap-7723	181	7	in	in	ADP
ap-7723	181	8	r2	r2	PROPN
ap-7723	181	9	a	a	DET
ap-7723	181	10	⊗r2	⊗r2	PROPN
ap-7723	181	11	b	b	NOUN
ap-7723	181	12	,	,	PUNCT
ap-7723	181	13	namely	namely	ADV
ap-7723	181	14	|φ±⟩	|φ±⟩	PROPN
ap-7723	181	15	=	=	SYM
ap-7723	181	16	1√	1√	PROPN
ap-7723	181	17	2	2	NUM
ap-7723	181	18	(	(	PUNCT
ap-7723	181	19	|0⟩a	|0⟩a	ADJ
ap-7723	181	20	⊗	⊗	PROPN
ap-7723	181	21	|0⟩b	|0⟩b	PROPN
ap-7723	181	22	±	±	NUM
ap-7723	181	23	∣∣∣π2〉a	∣∣∣π2〉a	PROPN
ap-7723	181	24	⊗	⊗	PROPN
ap-7723	181	25	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	181	26	)	)	PUNCT
ap-7723	181	27	,	,	PUNCT
ap-7723	181	28	(	(	PUNCT
ap-7723	181	29	30	30	NUM
ap-7723	181	30	)	)	PUNCT
ap-7723	181	31	|ψ±⟩	|ψ±⟩	NOUN
ap-7723	181	32	=	=	SYM
ap-7723	181	33	1√	1√	PROPN
ap-7723	181	34	2	2	NUM
ap-7723	181	35	(	(	PUNCT
ap-7723	181	36	±|0⟩a	±|0⟩a	PROPN
ap-7723	181	37	⊗	⊗	PROPN
ap-7723	181	38	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	182	1	+	+	CCONJ
ap-7723	182	2	∣∣∣π2〉a	∣∣∣π2〉a	PROPN
ap-7723	182	3	⊗	⊗	PROPN
ap-7723	182	4	|0⟩b	|0⟩b	ADV
ap-7723	182	5	)	)	PUNCT
ap-7723	182	6	.	.	PUNCT
ap-7723	183	1	(	(	PUNCT
ap-7723	183	2	31	31	NUM
ap-7723	183	3	)	)	PUNCT
ap-7723	183	4	1remind	1remind	NUM
ap-7723	183	5	that	that	PRON
ap-7723	183	6	dim(v	dim(v	PROPN
ap-7723	183	7	⊗	⊗	PROPN
ap-7723	183	8	w	w	PROPN
ap-7723	183	9	)	)	PUNCT
ap-7723	184	1	=	=	SYM
ap-7723	184	2	dimv	dimv	NOUN
ap-7723	184	3	dimw	dimw	NOUN
ap-7723	184	4	while	while	SCONJ
ap-7723	184	5	dim(v	dim(v	PROPN
ap-7723	184	6	×	×	PROPN
ap-7723	184	7	w	w	NOUN
ap-7723	184	8	)	)	PUNCT
ap-7723	185	1	=	=	SYM
ap-7723	185	2	dimv	dimv	NOUN
ap-7723	185	3	+	+	NUM
ap-7723	185	4	dimw	dimw	NOUN
ap-7723	185	5	for	for	ADP
ap-7723	185	6	2	2	NUM
ap-7723	185	7	finite	finite	ADJ
ap-7723	185	8	-	-	ADJ
ap-7723	185	9	dimensional	dimensional	ADJ
ap-7723	185	10	vector	vector	NOUN
ap-7723	185	11	spaces	space	NOUN
ap-7723	185	12	v	v	VERB
ap-7723	186	1	and	and	CCONJ
ap-7723	186	2	w	w	NOUN
ap-7723	186	3	we	we	PRON
ap-7723	186	4	say	say	VERB
ap-7723	186	5	that	that	SCONJ
ap-7723	186	6	they	they	PRON
ap-7723	186	7	represent	represent	VERB
ap-7723	186	8	maximally	maximally	ADV
ap-7723	186	9	entangled	entangle	VERB
ap-7723	186	10	quantum	quantum	ADJ
ap-7723	186	11	states	state	NOUN
ap-7723	186	12	of	of	ADP
ap-7723	186	13	two	two	NUM
ap-7723	186	14	qubits	qubit	NOUN
ap-7723	186	15	.	.	PUNCT
ap-7723	187	1	consider	consider	VERB
ap-7723	187	2	for	for	ADP
ap-7723	187	3	instance	instance	NOUN
ap-7723	187	4	the	the	DET
ap-7723	187	5	state	state	NOUN
ap-7723	187	6	|φ+⟩.	|φ+⟩.	NOUN
ap-7723	187	7	if	if	SCONJ
ap-7723	187	8	the	the	DET
ap-7723	187	9	pointer	pointer	NOUN
ap-7723	187	10	associated	associate	VERB
ap-7723	187	11	to	to	ADP
ap-7723	187	12	a	a	DET
ap-7723	187	13	measures	measure	NOUN
ap-7723	187	14	its	its	PRON
ap-7723	187	15	qubit	qubit	NOUN
ap-7723	187	16	in	in	ADP
ap-7723	187	17	the	the	DET
ap-7723	187	18	standard	standard	ADJ
ap-7723	187	19	basis	basis	NOUN
ap-7723	187	20	,	,	PUNCT
ap-7723	187	21	the	the	DET
ap-7723	187	22	outcome	outcome	NOUN
ap-7723	187	23	would	would	AUX
ap-7723	187	24	be	be	AUX
ap-7723	187	25	perfectly	perfectly	ADV
ap-7723	187	26	random	random	ADJ
ap-7723	187	27	,	,	PUNCT
ap-7723	187	28	with	with	ADP
ap-7723	187	29	either	either	DET
ap-7723	187	30	possibility	possibility	NOUN
ap-7723	187	31	having	have	VERB
ap-7723	187	32	a	a	DET
ap-7723	187	33	probability	probability	NOUN
ap-7723	187	34	1/2	1/2	NUM
ap-7723	187	35	.	.	PUNCT
ap-7723	188	1	but	but	CCONJ
ap-7723	188	2	if	if	SCONJ
ap-7723	188	3	the	the	DET
ap-7723	188	4	pointer	pointer	NOUN
ap-7723	188	5	associated	associate	VERB
ap-7723	188	6	to	to	ADP
ap-7723	188	7	b	b	NOUN
ap-7723	188	8	then	then	ADV
ap-7723	188	9	measures	measure	VERB
ap-7723	188	10	its	its	PRON
ap-7723	188	11	qubit	qubit	NOUN
ap-7723	188	12	instead	instead	ADV
ap-7723	188	13	,	,	PUNCT
ap-7723	188	14	the	the	DET
ap-7723	188	15	outcome	outcome	NOUN
ap-7723	188	16	,	,	PUNCT
ap-7723	188	17	although	although	SCONJ
ap-7723	188	18	random	random	ADJ
ap-7723	188	19	for	for	ADP
ap-7723	188	20	it	it	PRON
ap-7723	188	21	alone	alone	ADV
ap-7723	188	22	,	,	PUNCT
ap-7723	188	23	is	be	AUX
ap-7723	188	24	the	the	DET
ap-7723	188	25	same	same	ADJ
ap-7723	188	26	as	as	ADP
ap-7723	188	27	the	the	DET
ap-7723	188	28	one	one	NOUN
ap-7723	188	29	a	a	DET
ap-7723	188	30	gets	get	NOUN
ap-7723	188	31	.	.	PUNCT
ap-7723	189	1	there	there	PRON
ap-7723	189	2	is	be	VERB
ap-7723	189	3	quantum	quantum	ADJ
ap-7723	189	4	correlation	correlation	NOUN
ap-7723	189	5	.	.	PUNCT
ap-7723	190	1	4.2	4.2	NUM
ap-7723	190	2	.	.	PUNCT
ap-7723	190	3	bell	bell	PROPN
ap-7723	190	4	inequality	inequality	NOUN
ap-7723	190	5	and	and	CCONJ
ap-7723	190	6	its	its	PRON
ap-7723	190	7	violation	violation	NOUN
ap-7723	190	8	let	let	VERB
ap-7723	190	9	us	we	PRON
ap-7723	190	10	consider	consider	VERB
ap-7723	190	11	a	a	DET
ap-7723	190	12	bipartite	bipartite	ADJ
ap-7723	190	13	system	system	NOUN
ap-7723	190	14	in	in	ADP
ap-7723	190	15	the	the	DET
ap-7723	190	16	state	state	NOUN
ap-7723	190	17	ψ−.	ψ−.	NOUN
ap-7723	190	18	in	in	ADP
ap-7723	190	19	such	such	DET
ap-7723	190	20	a	a	DET
ap-7723	190	21	state	state	NOUN
ap-7723	190	22	,	,	PUNCT
ap-7723	190	23	if	if	SCONJ
ap-7723	190	24	a	a	DET
ap-7723	190	25	measurement	measurement	NOUN
ap-7723	190	26	of	of	ADP
ap-7723	190	27	the	the	DET
ap-7723	190	28	component	component	NOUN
ap-7723	190	29	σa	σa	INTJ
ap-7723	190	30	ϕa	ϕa	NOUN
ap-7723	190	31	:	:	PUNCT
ap-7723	190	32	=	=	SYM
ap-7723	190	33	−→σ	−→σ	NUM
ap-7723	190	34	a	a	DET
ap-7723	190	35	·	·	PUNCT
ap-7723	190	36	ûϕa	ûϕa	ADJ
ap-7723	190	37	(	(	PUNCT
ap-7723	190	38	ûϕa	ûϕa	ADJ
ap-7723	190	39	is	be	AUX
ap-7723	190	40	an	an	DET
ap-7723	190	41	unit	unit	NOUN
ap-7723	190	42	vector	vector	NOUN
ap-7723	190	43	with	with	ADP
ap-7723	190	44	polar	polar	ADJ
ap-7723	190	45	angle	angle	NOUN
ap-7723	190	46	ϕa	ϕa	PROPN
ap-7723	190	47	)	)	PUNCT
ap-7723	190	48	yields	yield	VERB
ap-7723	190	49	the	the	DET
ap-7723	190	50	value	value	NOUN
ap-7723	190	51	+1	+1	PROPN
ap-7723	190	52	(	(	PUNCT
ap-7723	190	53	polarization	polarization	NOUN
ap-7723	190	54	along	along	ADP
ap-7723	190	55	the	the	DET
ap-7723	190	56	direction	direction	NOUN
ap-7723	190	57	ϕa/2	ϕa/2	PROPN
ap-7723	190	58	)	)	PUNCT
ap-7723	190	59	,	,	PUNCT
ap-7723	190	60	then	then	ADV
ap-7723	190	61	a	a	DET
ap-7723	190	62	measurement	measurement	NOUN
ap-7723	190	63	of	of	ADP
ap-7723	190	64	σb	σb	ADP
ap-7723	190	65	ϕb	ϕb	INTJ
ap-7723	191	1	when	when	SCONJ
ap-7723	191	2	ϕb	ϕb	ADV
ap-7723	191	3	=	=	VERB
ap-7723	191	4	ϕa	ϕa	PROPN
ap-7723	191	5	must	must	AUX
ap-7723	191	6	yield	yield	VERB
ap-7723	191	7	the	the	DET
ap-7723	191	8	value	value	NOUN
ap-7723	191	9	−1	−1	NOUN
ap-7723	191	10	(	(	PUNCT
ap-7723	191	11	polarization	polarization	NOUN
ap-7723	191	12	along	along	ADP
ap-7723	191	13	the	the	DET
ap-7723	191	14	direction	direction	NOUN
ap-7723	191	15	ϕa+π	ϕa+π	NOUN
ap-7723	191	16	2	2	NUM
ap-7723	191	17	)	)	PUNCT
ap-7723	191	18	,	,	PUNCT
ap-7723	191	19	and	and	CCONJ
ap-7723	191	20	vice	vice	NOUN
ap-7723	191	21	-	-	NOUN
ap-7723	191	22	versa	versa	NOUN
ap-7723	191	23	.	.	PUNCT
ap-7723	192	1	from	from	ADP
ap-7723	192	2	a	a	DET
ap-7723	192	3	classical	classical	ADJ
ap-7723	192	4	perspective	perspective	NOUN
ap-7723	192	5	,	,	PUNCT
ap-7723	192	6	the	the	DET
ap-7723	192	7	explanation	explanation	NOUN
ap-7723	192	8	of	of	ADP
ap-7723	192	9	such	such	DET
ap-7723	192	10	a	a	DET
ap-7723	192	11	correlation	correlation	NOUN
ap-7723	192	12	needs	need	VERB
ap-7723	192	13	a	a	DET
ap-7723	192	14	predetermination	predetermination	NOUN
ap-7723	192	15	by	by	ADP
ap-7723	192	16	means	mean	NOUN
ap-7723	192	17	of	of	ADP
ap-7723	192	18	the	the	DET
ap-7723	192	19	existence	existence	NOUN
ap-7723	192	20	of	of	ADP
ap-7723	192	21	hidden	hidden	ADJ
ap-7723	192	22	parameters	parameter	NOUN
ap-7723	192	23	λ	λ	X
ap-7723	192	24	in	in	ADP
ap-7723	192	25	some	some	DET
ap-7723	192	26	set	set	NOUN
ap-7723	192	27	λ	λ	NOUN
ap-7723	192	28	.	.	PUNCT
ap-7723	192	29	assuming	assume	VERB
ap-7723	192	30	the	the	DET
ap-7723	192	31	two	two	NUM
ap-7723	192	32	measurements	measurement	NOUN
ap-7723	192	33	to	to	PART
ap-7723	192	34	be	be	AUX
ap-7723	192	35	separated	separate	VERB
ap-7723	192	36	by	by	ADP
ap-7723	192	37	a	a	DET
ap-7723	192	38	space	space	NOUN
ap-7723	192	39	-	-	PUNCT
ap-7723	192	40	like	like	ADJ
ap-7723	192	41	interval	interval	NOUN
ap-7723	192	42	,	,	PUNCT
ap-7723	192	43	the	the	DET
ap-7723	192	44	result	result	NOUN
ap-7723	192	45	εa	εa	PROPN
ap-7723	192	46	∈	∈	PROPN
ap-7723	192	47	{	{	PUNCT
ap-7723	192	48	−1	−1	NOUN
ap-7723	192	49	,	,	PUNCT
ap-7723	192	50	+1	+1	PROPN
ap-7723	192	51	}	}	PUNCT
ap-7723	192	52	(	(	PUNCT
ap-7723	192	53	resp	resp	NOUN
ap-7723	192	54	.	.	PUNCT
ap-7723	193	1	εb	εb	ADP
ap-7723	193	2	∈	∈	PROPN
ap-7723	193	3	{	{	PUNCT
ap-7723	193	4	−1	−1	NOUN
ap-7723	193	5	,	,	PUNCT
ap-7723	193	6	+1	+1	PROPN
ap-7723	193	7	}	}	PUNCT
ap-7723	193	8	)	)	PUNCT
ap-7723	193	9	of	of	ADP
ap-7723	193	10	measuring	measure	VERB
ap-7723	193	11	σa	σa	PROPN
ap-7723	193	12	ϕa	ϕa	PROPN
ap-7723	193	13	(	(	PUNCT
ap-7723	193	14	resp	resp	NOUN
ap-7723	193	15	.	.	PUNCT
ap-7723	194	1	σb	σb	ADP
ap-7723	194	2	ϕb	ϕb	PROPN
ap-7723	194	3	)	)	PUNCT
ap-7723	194	4	is	be	AUX
ap-7723	194	5	then	then	ADV
ap-7723	194	6	determined	determine	VERB
ap-7723	194	7	by	by	ADP
ap-7723	194	8	ϕa	ϕa	PROPN
ap-7723	194	9	and	and	CCONJ
ap-7723	194	10	λ	λ	X
ap-7723	194	11	only	only	ADV
ap-7723	194	12	(	(	PUNCT
ap-7723	194	13	locality	locality	NOUN
ap-7723	194	14	assumption	assumption	NOUN
ap-7723	194	15	)	)	PUNCT
ap-7723	194	16	,	,	PUNCT
ap-7723	194	17	not	not	PART
ap-7723	194	18	by	by	ADP
ap-7723	194	19	ϕb	ϕb	ADP
ap-7723	194	20	,	,	PUNCT
ap-7723	194	21	i.e.	i.e.	X
ap-7723	194	22	εa	εa	X
ap-7723	194	23	=	=	SYM
ap-7723	194	24	εa(ϕa	εa(ϕa	PROPN
ap-7723	194	25	,	,	PUNCT
ap-7723	194	26	λ	λ	X
ap-7723	194	27	)	)	PUNCT
ap-7723	194	28	(	(	PUNCT
ap-7723	194	29	resp	resp	NOUN
ap-7723	194	30	.	.	PUNCT
ap-7723	195	1	εb	εb	ADP
ap-7723	195	2	=	=	PUNCT
ap-7723	195	3	εb(ϕb	εb(ϕb	PROPN
ap-7723	195	4	,	,	PUNCT
ap-7723	195	5	λ	λ	NOUN
ap-7723	195	6	)	)	PUNCT
ap-7723	195	7	)	)	PUNCT
ap-7723	195	8	.	.	PUNCT
ap-7723	196	1	given	give	VERB
ap-7723	196	2	a	a	DET
ap-7723	196	3	probability	probability	NOUN
ap-7723	196	4	distribution	distribution	NOUN
ap-7723	196	5	ρ(λ	ρ(λ	PROPN
ap-7723	196	6	)	)	PUNCT
ap-7723	196	7	on	on	ADP
ap-7723	196	8	λ	λ	NOUN
ap-7723	196	9	,	,	PUNCT
ap-7723	196	10	the	the	DET
ap-7723	196	11	classical	classical	ADJ
ap-7723	196	12	expectation	expectation	NOUN
ap-7723	196	13	value	value	NOUN
ap-7723	196	14	of	of	ADP
ap-7723	196	15	the	the	DET
ap-7723	196	16	product	product	NOUN
ap-7723	196	17	of	of	ADP
ap-7723	196	18	the	the	DET
ap-7723	196	19	two	two	NUM
ap-7723	196	20	components	component	NOUN
ap-7723	196	21	σa	σa	VERB
ap-7723	196	22	ϕa	ϕa	INTJ
ap-7723	197	1	and	and	CCONJ
ap-7723	197	2	σb	σb	ADP
ap-7723	197	3	ϕb	ϕb	ADV
ap-7723	197	4	is	be	AUX
ap-7723	197	5	given	give	VERB
ap-7723	197	6	by	by	ADP
ap-7723	197	7	p(ϕa	p(ϕa	PROPN
ap-7723	197	8	,	,	PUNCT
ap-7723	197	9	ϕb	ϕb	ADV
ap-7723	197	10	)	)	PUNCT
ap-7723	197	11	=	=	SYM
ap-7723	198	1	∫	∫	PUNCT
ap-7723	198	2	λ	λ	X
ap-7723	198	3	dλ	dλ	PROPN
ap-7723	198	4	ρ(λ	ρ(λ	PROPN
ap-7723	198	5	)	)	PUNCT
ap-7723	198	6	εa(ϕa	εa(ϕa	PROPN
ap-7723	198	7	,	,	PUNCT
ap-7723	198	8	λ	λ	NOUN
ap-7723	198	9	)	)	PUNCT
ap-7723	198	10	εb(ϕb	εb(ϕb	NOUN
ap-7723	198	11	,	,	PUNCT
ap-7723	198	12	λ	λ	NOUN
ap-7723	198	13	)	)	PUNCT
ap-7723	198	14	.	.	PUNCT
ap-7723	199	1	(	(	PUNCT
ap-7723	199	2	32	32	NUM
ap-7723	199	3	)	)	PUNCT
ap-7723	199	4	since	since	SCONJ
ap-7723	199	5	∫	∫	PROPN
ap-7723	199	6	λ	λ	X
ap-7723	199	7	dλ	dλ	PROPN
ap-7723	199	8	ρ(λ	ρ(λ	PROPN
ap-7723	199	9	)	)	PUNCT
ap-7723	199	10	=	=	SYM
ap-7723	199	11	1	1	NUM
ap-7723	199	12	and	and	CCONJ
ap-7723	199	13	εa	εa	NOUN
ap-7723	199	14	,	,	PUNCT
ap-7723	199	15	b	b	NOUN
ap-7723	199	16	=	=	PUNCT
ap-7723	199	17	±1	±1	VERB
ap-7723	199	18	,	,	PUNCT
ap-7723	199	19	(	(	PUNCT
ap-7723	199	20	33	33	NUM
ap-7723	199	21	)	)	PUNCT
ap-7723	199	22	we	we	PRON
ap-7723	199	23	have	have	AUX
ap-7723	199	24	−1	−1	NOUN
ap-7723	199	25	≤	≤	NOUN
ap-7723	199	26	p(ϕa	p(ϕa	PROPN
ap-7723	199	27	,	,	PUNCT
ap-7723	199	28	ϕb	ϕb	NOUN
ap-7723	199	29	)	)	PUNCT
ap-7723	199	30	≤	≤	NUM
ap-7723	200	1	1	1	NUM
ap-7723	200	2	.	.	PUNCT
ap-7723	201	1	equivalent	equivalent	ADJ
ap-7723	201	2	predictions	prediction	NOUN
ap-7723	201	3	within	within	ADP
ap-7723	201	4	the	the	DET
ap-7723	201	5	quantum	quantum	NOUN
ap-7723	201	6	setting	setting	NOUN
ap-7723	201	7	then	then	ADV
ap-7723	201	8	imposes	impose	VERB
ap-7723	201	9	the	the	DET
ap-7723	201	10	equality	equality	NOUN
ap-7723	201	11	between	between	ADP
ap-7723	201	12	the	the	DET
ap-7723	201	13	classical	classical	ADJ
ap-7723	201	14	and	and	CCONJ
ap-7723	201	15	quantum	quantum	ADJ
ap-7723	201	16	expectation	expectation	NOUN
ap-7723	201	17	values	value	NOUN
ap-7723	201	18	:	:	PUNCT
ap-7723	201	19	p(ϕa	p(ϕa	VERB
ap-7723	201	20	,	,	PUNCT
ap-7723	201	21	ϕb	ϕb	NOUN
ap-7723	201	22	)	)	PUNCT
ap-7723	202	1	=	=	PUNCT
ap-7723	202	2	〈	〈	PROPN
ap-7723	202	3	ψ−∣∣σa	ψ−∣∣σa	NOUN
ap-7723	202	4	ϕa	ϕa	ADP
ap-7723	203	1	⊗	⊗	PROPN
ap-7723	203	2	σb	σb	ADP
ap-7723	203	3	ϕb	ϕb	ADP
ap-7723	203	4	∣∣ψ−	∣∣ψ−	NOUN
ap-7723	203	5	〉	〉	NOUN
ap-7723	203	6	=	=	SYM
ap-7723	203	7	−ûϕa	−ûϕa	X
ap-7723	203	8	·	·	PUNCT
ap-7723	203	9	ûϕb	ûϕb	PROPN
ap-7723	203	10	=	=	SYM
ap-7723	203	11	−	−	PROPN
ap-7723	203	12	cos(ϕa	cos(ϕa	VERB
ap-7723	203	13	−	−	PROPN
ap-7723	203	14	ϕb	ϕb	ADP
ap-7723	203	15	)	)	PUNCT
ap-7723	203	16	.	.	PUNCT
ap-7723	204	1	(	(	PUNCT
ap-7723	204	2	34	34	NUM
ap-7723	204	3	)	)	PUNCT
ap-7723	204	4	in	in	ADP
ap-7723	204	5	the	the	DET
ap-7723	204	6	above	above	ADJ
ap-7723	204	7	equation	equation	NOUN
ap-7723	204	8	,	,	PUNCT
ap-7723	204	9	the	the	DET
ap-7723	204	10	value	value	NOUN
ap-7723	204	11	−1	−1	NOUN
ap-7723	204	12	is	be	AUX
ap-7723	204	13	reached	reach	VERB
ap-7723	204	14	at	at	ADP
ap-7723	204	15	ϕa	ϕa	PROPN
ap-7723	204	16	=	=	SYM
ap-7723	204	17	ϕb	ϕb	PROPN
ap-7723	204	18	.	.	PUNCT
ap-7723	205	1	this	this	PRON
ap-7723	205	2	is	be	AUX
ap-7723	205	3	possible	possible	ADJ
ap-7723	205	4	for	for	ADP
ap-7723	205	5	p(ϕa	p(ϕa	PROPN
ap-7723	205	6	,	,	PUNCT
ap-7723	205	7	ϕa	ϕa	NOUN
ap-7723	205	8	)	)	PUNCT
ap-7723	205	9	only	only	ADV
ap-7723	205	10	if	if	SCONJ
ap-7723	205	11	εa(ϕa	εa(ϕa	PROPN
ap-7723	205	12	,	,	PUNCT
ap-7723	205	13	λ	λ	NOUN
ap-7723	205	14	)	)	PUNCT
ap-7723	205	15	=	=	SYM
ap-7723	205	16	−εb(ϕa	−εb(ϕa	PROPN
ap-7723	205	17	,	,	PUNCT
ap-7723	205	18	λ	λ	NOUN
ap-7723	205	19	)	)	PUNCT
ap-7723	205	20	.	.	PUNCT
ap-7723	206	1	hence	hence	ADV
ap-7723	206	2	,	,	PUNCT
ap-7723	206	3	we	we	PRON
ap-7723	206	4	can	can	AUX
ap-7723	206	5	write	write	VERB
ap-7723	206	6	p(ϕa	p(ϕa	PROPN
ap-7723	206	7	,	,	PUNCT
ap-7723	206	8	ϕb	ϕb	ADV
ap-7723	206	9	)	)	PUNCT
ap-7723	206	10	as	as	ADP
ap-7723	206	11	p(ϕa	p(ϕa	PROPN
ap-7723	206	12	,	,	PUNCT
ap-7723	206	13	ϕb	ϕb	ADV
ap-7723	206	14	)	)	PUNCT
ap-7723	206	15	=	=	PUNCT
ap-7723	207	1	−	−	NOUN
ap-7723	207	2	∫	∫	INTJ
ap-7723	207	3	λ	λ	X
ap-7723	207	4	dλ	dλ	PROPN
ap-7723	207	5	ρ(λ	ρ(λ	PROPN
ap-7723	207	6	)	)	PUNCT
ap-7723	207	7	ε(ϕa	ε(ϕa	PROPN
ap-7723	207	8	,	,	PUNCT
ap-7723	207	9	λ	λ	NOUN
ap-7723	207	10	)	)	PUNCT
ap-7723	207	11	ε(ϕb	ε(ϕb	PROPN
ap-7723	207	12	,	,	PUNCT
ap-7723	207	13	λ	λ	NOUN
ap-7723	207	14	)	)	PUNCT
ap-7723	207	15	,	,	PUNCT
ap-7723	207	16	ε(ϕ	ε(ϕ	PROPN
ap-7723	207	17	,	,	PUNCT
ap-7723	207	18	λ	λ	NOUN
ap-7723	207	19	)	)	PUNCT
ap-7723	207	20	≡	≡	PROPN
ap-7723	207	21	εa(ϕ	εa(ϕ	PROPN
ap-7723	207	22	,	,	PUNCT
ap-7723	207	23	λ	λ	NOUN
ap-7723	207	24	)	)	PUNCT
ap-7723	207	25	=	=	VERB
ap-7723	207	26	±1	±1	VERB
ap-7723	207	27	.	.	PUNCT
ap-7723	208	1	(	(	PUNCT
ap-7723	208	2	35	35	NUM
ap-7723	208	3	)	)	PUNCT
ap-7723	208	4	let	let	VERB
ap-7723	208	5	us	we	PRON
ap-7723	208	6	now	now	ADV
ap-7723	208	7	introduce	introduce	VERB
ap-7723	208	8	a	a	DET
ap-7723	208	9	third	third	ADJ
ap-7723	208	10	unit	unit	NOUN
ap-7723	208	11	vector	vector	NOUN
ap-7723	208	12	ûϕc	ûϕc	ADJ
ap-7723	208	13	.	.	PUNCT
ap-7723	209	1	due	due	ADP
ap-7723	209	2	to	to	ADP
ap-7723	209	3	ε2	ε2	NOUN
ap-7723	209	4	=	=	SYM
ap-7723	209	5	1	1	NUM
ap-7723	209	6	,	,	PUNCT
ap-7723	209	7	we	we	PRON
ap-7723	209	8	have	have	VERB
ap-7723	209	9	p(ϕa	p(ϕa	VERB
ap-7723	209	10	,	,	PUNCT
ap-7723	209	11	ϕb	ϕb	ADJ
ap-7723	209	12	)	)	PUNCT
ap-7723	210	1	−	−	PROPN
ap-7723	210	2	p(ϕa	p(ϕa	PROPN
ap-7723	210	3	,	,	PUNCT
ap-7723	210	4	ϕc	ϕc	NOUN
ap-7723	210	5	)	)	PUNCT
ap-7723	210	6	=	=	SYM
ap-7723	211	1	∫	∫	PUNCT
ap-7723	211	2	λ	λ	X
ap-7723	211	3	dλ	dλ	PROPN
ap-7723	211	4	ρ(λ	ρ(λ	PROPN
ap-7723	211	5	)	)	PUNCT
ap-7723	211	6	ε(ϕa	ε(ϕa	PROPN
ap-7723	211	7	,	,	PUNCT
ap-7723	211	8	λ	λ	NOUN
ap-7723	211	9	)	)	PUNCT
ap-7723	211	10	ε(ϕb	ε(ϕb	PROPN
ap-7723	211	11	,	,	PUNCT
ap-7723	211	12	λ	λ	NOUN
ap-7723	211	13	)	)	PUNCT
ap-7723	211	14	×	×	NOUN
ap-7723	212	1	[	[	X
ap-7723	212	2	ε(ϕb	ε(ϕb	NOUN
ap-7723	212	3	,	,	PUNCT
ap-7723	212	4	λ	λ	NOUN
ap-7723	212	5	)	)	PUNCT
ap-7723	212	6	ε(ϕc	ε(ϕc	PROPN
ap-7723	212	7	,	,	PUNCT
ap-7723	212	8	λ	λ	NOUN
ap-7723	212	9	)	)	PUNCT
ap-7723	212	10	−	−	PROPN
ap-7723	212	11	1	1	NUM
ap-7723	212	12	]	]	PUNCT
ap-7723	212	13	.	.	PUNCT
ap-7723	213	1	(	(	PUNCT
ap-7723	213	2	36	36	NUM
ap-7723	213	3	)	)	PUNCT
ap-7723	213	4	12	12	NUM
ap-7723	213	5	vol	vol	NOUN
ap-7723	213	6	.	.	PUNCT
ap-7723	214	1	62	62	NUM
ap-7723	214	2	no	no	INTJ
ap-7723	214	3	.	.	PUNCT
ap-7723	215	1	1/2022	1/2022	NUM
ap-7723	215	2	quantum	quantum	NOUN
ap-7723	215	3	angles	angle	NOUN
ap-7723	215	4	from	from	ADP
ap-7723	215	5	this	this	DET
ap-7723	215	6	results	result	NOUN
ap-7723	215	7	the	the	DET
ap-7723	215	8	(	(	PUNCT
ap-7723	215	9	baby	baby	NOUN
ap-7723	215	10	)	)	PUNCT
ap-7723	215	11	bell	bell	NOUN
ap-7723	215	12	inequality	inequality	NOUN
ap-7723	215	13	:	:	PUNCT
ap-7723	215	14	|p(ϕa	|p(ϕa	PROPN
ap-7723	215	15	,	,	PUNCT
ap-7723	215	16	ϕb	ϕb	NOUN
ap-7723	215	17	)	)	PUNCT
ap-7723	216	1	−	−	PROPN
ap-7723	216	2	p(ϕa	p(ϕa	PROPN
ap-7723	216	3	,	,	PUNCT
ap-7723	216	4	ϕc)|	ϕc)|	ADP
ap-7723	216	5	≤	≤	NUM
ap-7723	216	6	∫	∫	PROPN
ap-7723	216	7	λ	λ	X
ap-7723	216	8	dλ	dλ	PROPN
ap-7723	216	9	ρ(λ	ρ(λ	PROPN
ap-7723	216	10	)	)	PUNCT
ap-7723	217	1	[	[	X
ap-7723	217	2	1	1	NUM
ap-7723	217	3	−	−	NOUN
ap-7723	217	4	ε(ϕb	ε(ϕb	ADJ
ap-7723	217	5	,	,	PUNCT
ap-7723	217	6	λ	λ	NOUN
ap-7723	217	7	)	)	PUNCT
ap-7723	217	8	ε(ϕc	ε(ϕc	PROPN
ap-7723	217	9	,	,	PUNCT
ap-7723	217	10	λ	λ	NOUN
ap-7723	217	11	)	)	PUNCT
ap-7723	217	12	]	]	PUNCT
ap-7723	217	13	=	=	SYM
ap-7723	217	14	1	1	NUM
ap-7723	217	15	+	+	CCONJ
ap-7723	217	16	p(ϕb	p(ϕb	NOUN
ap-7723	217	17	,	,	PUNCT
ap-7723	217	18	ϕc	ϕc	NOUN
ap-7723	217	19	)	)	PUNCT
ap-7723	217	20	.	.	PUNCT
ap-7723	218	1	hence	hence	ADV
ap-7723	218	2	,	,	PUNCT
ap-7723	218	3	the	the	DET
ap-7723	218	4	validity	validity	NOUN
ap-7723	218	5	of	of	ADP
ap-7723	218	6	the	the	DET
ap-7723	218	7	existence	existence	NOUN
ap-7723	218	8	of	of	ADP
ap-7723	218	9	hidden	hide	VERB
ap-7723	218	10	variable(s	variable(s	NOUN
ap-7723	218	11	)	)	PUNCT
ap-7723	218	12	for	for	ADP
ap-7723	218	13	justifying	justify	VERB
ap-7723	218	14	the	the	DET
ap-7723	218	15	quantum	quantum	ADJ
ap-7723	218	16	correlation	correlation	NOUN
ap-7723	218	17	in	in	ADP
ap-7723	218	18	the	the	DET
ap-7723	218	19	singlet	singlet	ADJ
ap-7723	218	20	state	state	NOUN
ap-7723	218	21	ψ−	ψ−	VERB
ap-7723	218	22	,	,	PUNCT
ap-7723	218	23	and	and	CCONJ
ap-7723	218	24	which	which	PRON
ap-7723	218	25	is	be	AUX
ap-7723	218	26	encapsulated	encapsulate	VERB
ap-7723	218	27	by	by	ADP
ap-7723	218	28	the	the	DET
ap-7723	218	29	above	above	ADJ
ap-7723	218	30	equation	equation	NOUN
ap-7723	218	31	,	,	PUNCT
ap-7723	218	32	has	have	VERB
ap-7723	218	33	the	the	DET
ap-7723	218	34	following	follow	VERB
ap-7723	218	35	consequence	consequence	NOUN
ap-7723	218	36	on	on	ADP
ap-7723	218	37	the	the	DET
ap-7723	218	38	arbitrary	arbitrary	ADJ
ap-7723	218	39	triple	triple	NOUN
ap-7723	218	40	(	(	PUNCT
ap-7723	218	41	ϕa	ϕa	NOUN
ap-7723	218	42	,	,	PUNCT
ap-7723	218	43	ϕb	ϕb	NOUN
ap-7723	218	44	,	,	PUNCT
ap-7723	218	45	ϕc	ϕc	ADJ
ap-7723	218	46	):	):	PUNCT
ap-7723	218	47	1	1	NUM
ap-7723	218	48	−	−	NOUN
ap-7723	218	49	cos(ϕb	cos(ϕb	X
ap-7723	218	50	−	−	PROPN
ap-7723	218	51	ϕc	ϕc	PROPN
ap-7723	218	52	)	)	PUNCT
ap-7723	218	53	≥	≥	NOUN
ap-7723	219	1	|cos(ϕb	|cos(ϕb	NOUN
ap-7723	219	2	−	−	PROPN
ap-7723	219	3	ϕa	ϕa	PROPN
ap-7723	219	4	)	)	PUNCT
ap-7723	220	1	−	−	PROPN
ap-7723	220	2	cos(ϕc	cos(ϕc	NOUN
ap-7723	220	3	−	−	PROPN
ap-7723	221	1	ϕa)|	ϕa)|	NOUN
ap-7723	221	2	.	.	PUNCT
ap-7723	222	1	equivalently	equivalently	ADV
ap-7723	222	2	,	,	PUNCT
ap-7723	222	3	in	in	ADP
ap-7723	222	4	terms	term	NOUN
ap-7723	222	5	of	of	ADP
ap-7723	222	6	the	the	DET
ap-7723	222	7	two	two	NUM
ap-7723	222	8	independent	independent	ADJ
ap-7723	222	9	angles	angle	NOUN
ap-7723	222	10	ζ	ζ	NOUN
ap-7723	222	11	and	and	CCONJ
ap-7723	222	12	η	η	PROPN
ap-7723	222	13	,	,	PUNCT
ap-7723	222	14	ζ	ζ	NOUN
ap-7723	222	15	=	=	SYM
ap-7723	222	16	ϕa	ϕa	PROPN
ap-7723	222	17	−	−	NOUN
ap-7723	223	1	ϕb	ϕb	ADV
ap-7723	223	2	2	2	NUM
ap-7723	223	3	,	,	PUNCT
ap-7723	223	4	η	η	PROPN
ap-7723	223	5	=	=	PROPN
ap-7723	223	6	ϕb	ϕb	ADP
ap-7723	223	7	−	−	PROPN
ap-7723	224	1	ϕc	ϕc	NOUN
ap-7723	224	2	2	2	NUM
ap-7723	224	3	,	,	PUNCT
ap-7723	224	4	we	we	PRON
ap-7723	224	5	have	have	VERB
ap-7723	224	6	∣∣sin2	∣∣sin2	X
ap-7723	225	1	ζ	ζ	NOUN
ap-7723	225	2	−	−	NOUN
ap-7723	225	3	sin2(η	sin2(η	X
ap-7723	225	4	+	+	CCONJ
ap-7723	225	5	ζ	ζ	NOUN
ap-7723	225	6	)	)	PUNCT
ap-7723	225	7	∣∣	∣∣	NUM
ap-7723	225	8	≤	≤	PROPN
ap-7723	225	9	sin2	sin2	PROPN
ap-7723	225	10	η	η	PROPN
ap-7723	225	11	.	.	PUNCT
ap-7723	226	1	(	(	PUNCT
ap-7723	226	2	37	37	NUM
ap-7723	226	3	)	)	PUNCT
ap-7723	226	4	it	it	PRON
ap-7723	226	5	is	be	AUX
ap-7723	226	6	easy	easy	ADJ
ap-7723	226	7	to	to	PART
ap-7723	226	8	find	find	VERB
ap-7723	226	9	pairs	pair	NOUN
ap-7723	226	10	(	(	PUNCT
ap-7723	226	11	ζ	ζ	NOUN
ap-7723	226	12	,	,	PUNCT
ap-7723	226	13	η	η	NOUN
ap-7723	226	14	)	)	PUNCT
ap-7723	226	15	for	for	ADP
ap-7723	226	16	which	which	PRON
ap-7723	226	17	the	the	DET
ap-7723	226	18	inequality	inequality	NOUN
ap-7723	226	19	(	(	PUNCT
ap-7723	226	20	37	37	NUM
ap-7723	226	21	)	)	PUNCT
ap-7723	226	22	does	do	AUX
ap-7723	226	23	not	not	PART
ap-7723	226	24	hold	hold	VERB
ap-7723	226	25	true	true	ADJ
ap-7723	226	26	.	.	PUNCT
ap-7723	227	1	for	for	ADP
ap-7723	227	2	instance	instance	NOUN
ap-7723	227	3	with	with	ADP
ap-7723	227	4	η	η	PROPN
ap-7723	227	5	=	=	PROPN
ap-7723	227	6	ζ	ζ	PROPN
ap-7723	227	7	̸=	̸=	PROPN
ap-7723	227	8	0	0	NUM
ap-7723	227	9	,	,	PUNCT
ap-7723	227	10	i.e.	i.e.	X
ap-7723	227	11	,	,	PUNCT
ap-7723	227	12	ϕb	ϕb	ADP
ap-7723	227	13	=	=	SYM
ap-7723	227	14	ϕa	ϕa	PROPN
ap-7723	228	1	+	+	CCONJ
ap-7723	228	2	ϕc	ϕc	PROPN
ap-7723	228	3	2	2	NUM
ap-7723	228	4	,	,	PUNCT
ap-7723	228	5	we	we	PRON
ap-7723	228	6	obtain	obtain	VERB
ap-7723	228	7	|4	|4	NUM
ap-7723	228	8	sin2	sin2	PROPN
ap-7723	228	9	η	η	PROPN
ap-7723	228	10	−	−	PROPN
ap-7723	228	11	3|	3|	NUM
ap-7723	228	12	≤	≤	NUM
ap-7723	228	13	1	1	NUM
ap-7723	228	14	,	,	PUNCT
ap-7723	228	15	(	(	PUNCT
ap-7723	228	16	38	38	NUM
ap-7723	228	17	)	)	PUNCT
ap-7723	228	18	which	which	PRON
ap-7723	228	19	does	do	AUX
ap-7723	228	20	not	not	PART
ap-7723	228	21	hold	hold	VERB
ap-7723	228	22	true	true	ADJ
ap-7723	228	23	for	for	ADP
ap-7723	228	24	all	all	DET
ap-7723	228	25	|η|	|η|	NOUN
ap-7723	228	26	<	<	X
ap-7723	228	27	π/4	π/4	PROPN
ap-7723	228	28	,	,	PUNCT
ap-7723	228	29	i.e.	i.e.	X
ap-7723	228	30	,	,	PUNCT
ap-7723	228	31	for	for	ADP
ap-7723	228	32	|ϕa	|ϕa	X
ap-7723	228	33	−	−	PROPN
ap-7723	228	34	ϕb|	ϕb|	NOUN
ap-7723	229	1	=	=	NOUN
ap-7723	230	1	|ϕb	|ϕb	NUM
ap-7723	230	2	−	−	PROPN
ap-7723	230	3	ϕc|	ϕc|	NOUN
ap-7723	230	4	<	<	X
ap-7723	230	5	π/2	π/2	NUM
ap-7723	230	6	.	.	PUNCT
ap-7723	231	1	actually	actually	ADV
ap-7723	231	2	,	,	PUNCT
ap-7723	231	3	we	we	PRON
ap-7723	231	4	did	do	AUX
ap-7723	231	5	not	not	PART
ap-7723	231	6	follow	follow	VERB
ap-7723	231	7	here	here	ADV
ap-7723	231	8	the	the	DET
ap-7723	231	9	proof	proof	NOUN
ap-7723	231	10	given	give	VERB
ap-7723	231	11	by	by	ADP
ap-7723	231	12	bell	bell	NOUN
ap-7723	231	13	,	,	PUNCT
ap-7723	231	14	which	which	PRON
ap-7723	231	15	is	be	AUX
ap-7723	231	16	a	a	DET
ap-7723	231	17	lot	lot	NOUN
ap-7723	231	18	more	more	ADV
ap-7723	231	19	elaborate	elaborate	ADJ
ap-7723	231	20	.	.	PUNCT
ap-7723	232	1	also	also	ADV
ap-7723	232	2	,	,	PUNCT
ap-7723	232	3	bell	bell	PROPN
ap-7723	232	4	considered	consider	VERB
ap-7723	232	5	unit	unit	NOUN
ap-7723	232	6	vectors	vector	NOUN
ap-7723	232	7	in	in	ADP
ap-7723	232	8	3	3	NUM
ap-7723	232	9	-	-	PUNCT
ap-7723	232	10	space	space	NOUN
ap-7723	232	11	.	.	PUNCT
ap-7723	233	1	restricting	restrict	VERB
ap-7723	233	2	his	his	PRON
ap-7723	233	3	proof	proof	NOUN
ap-7723	233	4	to	to	ADP
ap-7723	233	5	vectors	vector	NOUN
ap-7723	233	6	in	in	ADP
ap-7723	233	7	the	the	DET
ap-7723	233	8	plane	plane	NOUN
ap-7723	233	9	does	do	AUX
ap-7723	233	10	not	not	PART
ap-7723	233	11	make	make	VERB
ap-7723	233	12	any	any	DET
ap-7723	233	13	difference	difference	NOUN
ap-7723	233	14	,	,	PUNCT
ap-7723	233	15	as	as	SCONJ
ap-7723	233	16	it	it	PRON
ap-7723	233	17	is	be	AUX
ap-7723	233	18	actually	actually	ADV
ap-7723	233	19	the	the	DET
ap-7723	233	20	case	case	NOUN
ap-7723	233	21	in	in	ADP
ap-7723	233	22	many	many	ADJ
ap-7723	233	23	works	work	NOUN
ap-7723	233	24	devoted	devote	VERB
ap-7723	233	25	to	to	ADP
ap-7723	233	26	the	the	DET
ap-7723	233	27	foundations	foundation	NOUN
ap-7723	233	28	of	of	ADP
ap-7723	233	29	quantum	quantum	ADJ
ap-7723	233	30	mechanics	mechanic	NOUN
ap-7723	233	31	.	.	PUNCT
ap-7723	234	1	4.3	4.3	NUM
ap-7723	234	2	.	.	PUNCT
ap-7723	234	3	entanglement	entanglement	NOUN
ap-7723	234	4	of	of	ADP
ap-7723	234	5	two	two	NUM
ap-7723	234	6	angles	angle	NOUN
ap-7723	234	7	quantum	quantum	NOUN
ap-7723	234	8	entanglement	entanglement	NOUN
ap-7723	234	9	is	be	AUX
ap-7723	234	10	usually	usually	ADV
ap-7723	234	11	described	describe	VERB
ap-7723	234	12	by	by	ADP
ap-7723	234	13	the	the	DET
ap-7723	234	14	complex	complex	ADJ
ap-7723	234	15	two	two	NUM
ap-7723	234	16	-	-	PUNCT
ap-7723	234	17	dimensional	dimensional	ADJ
ap-7723	234	18	hilbert	hilbert	NOUN
ap-7723	234	19	space	space	NOUN
ap-7723	234	20	c2	c2	PROPN
ap-7723	234	21	.	.	PUNCT
ap-7723	235	1	as	as	ADP
ap-7723	235	2	a	a	DET
ap-7723	235	3	complex	complex	ADJ
ap-7723	235	4	vector	vector	NOUN
ap-7723	235	5	space	space	NOUN
ap-7723	235	6	,	,	PUNCT
ap-7723	235	7	c2	c2	PROPN
ap-7723	235	8	,	,	PUNCT
ap-7723	235	9	with	with	ADP
ap-7723	235	10	canonical	canonical	ADJ
ap-7723	235	11	basis	basis	NOUN
ap-7723	235	12	(	(	PUNCT
ap-7723	235	13	e1	e1	NOUN
ap-7723	235	14	,	,	PUNCT
ap-7723	235	15	e2	e2	PROPN
ap-7723	235	16	)	)	PUNCT
ap-7723	235	17	,	,	PUNCT
ap-7723	235	18	has	have	VERB
ap-7723	235	19	a	a	DET
ap-7723	235	20	real	real	ADJ
ap-7723	235	21	structure	structure	NOUN
ap-7723	235	22	,	,	PUNCT
ap-7723	235	23	i.e.	i.e.	X
ap-7723	235	24	,	,	PUNCT
ap-7723	235	25	is	be	AUX
ap-7723	235	26	isomorphic	isomorphic	ADJ
ap-7723	235	27	to	to	ADP
ap-7723	235	28	a	a	DET
ap-7723	235	29	real	real	ADJ
ap-7723	235	30	vector	vector	NOUN
ap-7723	235	31	space	space	NOUN
ap-7723	235	32	which	which	PRON
ap-7723	235	33	makes	make	VERB
ap-7723	235	34	it	it	PRON
ap-7723	235	35	isomorphic	isomorphic	ADJ
ap-7723	235	36	to	to	PART
ap-7723	235	37	r4	r4	VERB
ap-7723	235	38	,	,	PUNCT
ap-7723	235	39	itself	itself	PRON
ap-7723	235	40	isomorphic	isomorphic	ADJ
ap-7723	235	41	to	to	ADP
ap-7723	235	42	r2	r2	PROPN
ap-7723	235	43	⊗	⊗	PROPN
ap-7723	235	44	r2	r2	PROPN
ap-7723	235	45	.	.	PUNCT
ap-7723	236	1	a	a	DET
ap-7723	236	2	real	real	ADJ
ap-7723	236	3	structure	structure	NOUN
ap-7723	236	4	is	be	AUX
ap-7723	236	5	obtained	obtain	VERB
ap-7723	236	6	by	by	ADP
ap-7723	236	7	considering	consider	VERB
ap-7723	236	8	the	the	DET
ap-7723	236	9	vector	vector	NOUN
ap-7723	236	10	expansion	expansion	NOUN
ap-7723	236	11	c2	c2	PROPN
ap-7723	236	12	∈	∈	PROPN
ap-7723	236	13	v	v	ADP
ap-7723	236	14	=	=	SYM
ap-7723	236	15	z1e1	z1e1	X
ap-7723	236	16	+	+	CCONJ
ap-7723	236	17	z2e2	z2e2	PROPN
ap-7723	236	18	=	=	SYM
ap-7723	236	19	x1e1	x1e1	PROPN
ap-7723	237	1	+	+	CCONJ
ap-7723	237	2	y1	y1	INTJ
ap-7723	237	3	(	(	PUNCT
ap-7723	237	4	ie1	ie1	PROPN
ap-7723	237	5	)	)	PUNCT
ap-7723	237	6	+	+	NUM
ap-7723	237	7	x2e2	x2e2	PROPN
ap-7723	238	1	+	+	CCONJ
ap-7723	238	2	y2	y2	INTJ
ap-7723	238	3	(	(	PUNCT
ap-7723	238	4	ie2	ie2	PROPN
ap-7723	238	5	)	)	PUNCT
ap-7723	238	6	,	,	PUNCT
ap-7723	238	7	(	(	PUNCT
ap-7723	238	8	39	39	NUM
ap-7723	238	9	)	)	PUNCT
ap-7723	238	10	which	which	PRON
ap-7723	238	11	is	be	AUX
ap-7723	238	12	equivalent	equivalent	ADJ
ap-7723	238	13	to	to	ADP
ap-7723	238	14	writing	write	VERB
ap-7723	238	15	z1	z1	NOUN
ap-7723	238	16	=	=	PUNCT
ap-7723	238	17	x1	x1	PROPN
ap-7723	239	1	+	+	NUM
ap-7723	239	2	iy1	iy1	NOUN
ap-7723	239	3	,	,	PUNCT
ap-7723	239	4	z2	z2	NOUN
ap-7723	239	5	=	=	SYM
ap-7723	239	6	x2	x2	PROPN
ap-7723	240	1	+	+	CCONJ
ap-7723	240	2	iy2	iy2	NOUN
ap-7723	240	3	,	,	PUNCT
ap-7723	240	4	and	and	CCONJ
ap-7723	240	5	considering	consider	VERB
ap-7723	240	6	the	the	DET
ap-7723	240	7	set	set	NOUN
ap-7723	240	8	of	of	ADP
ap-7723	240	9	vectors	vector	NOUN
ap-7723	240	10	{	{	PUNCT
ap-7723	240	11	e1	e1	PROPN
ap-7723	240	12	,	,	PUNCT
ap-7723	240	13	e2	e2	PROPN
ap-7723	240	14	,	,	PUNCT
ap-7723	240	15	(	(	PUNCT
ap-7723	240	16	ie1	ie1	PROPN
ap-7723	240	17	)	)	PUNCT
ap-7723	240	18	,	,	PUNCT
ap-7723	240	19	(	(	PUNCT
ap-7723	240	20	ie2	ie2	ADV
ap-7723	240	21	)	)	PUNCT
ap-7723	240	22	}	}	PUNCT
ap-7723	240	23	(	(	PUNCT
ap-7723	240	24	40	40	NUM
ap-7723	240	25	)	)	PUNCT
ap-7723	240	26	as	as	ADP
ap-7723	240	27	forming	form	VERB
ap-7723	240	28	a	a	DET
ap-7723	240	29	basis	basis	NOUN
ap-7723	240	30	of	of	ADP
ap-7723	240	31	r4	r4	NOUN
ap-7723	240	32	.	.	PUNCT
ap-7723	241	1	forgetting	forget	VERB
ap-7723	241	2	about	about	ADP
ap-7723	241	3	the	the	DET
ap-7723	241	4	subscripts	subscript	NOUN
ap-7723	241	5	a	a	PRON
ap-7723	241	6	and	and	CCONJ
ap-7723	241	7	b	b	NOUN
ap-7723	241	8	in	in	ADP
ap-7723	241	9	(	(	PUNCT
ap-7723	241	10	29	29	NUM
ap-7723	241	11	)	)	PUNCT
ap-7723	241	12	,	,	PUNCT
ap-7723	241	13	we	we	PRON
ap-7723	241	14	can	can	AUX
ap-7723	241	15	map	map	VERB
ap-7723	241	16	vectors	vector	NOUN
ap-7723	241	17	in	in	ADP
ap-7723	241	18	the	the	DET
ap-7723	241	19	euclidean	euclidean	ADJ
ap-7723	241	20	plane	plane	NOUN
ap-7723	241	21	r2	r2	PROPN
ap-7723	241	22	to	to	ADP
ap-7723	241	23	the	the	DET
ap-7723	241	24	complex	complex	ADJ
ap-7723	241	25	“	"	PUNCT
ap-7723	241	26	plane	plane	NOUN
ap-7723	241	27	”	"	PUNCT
ap-7723	241	28	c	c	NOUN
ap-7723	241	29	by	by	ADP
ap-7723	241	30	|0⟩	|0⟩	PROPN
ap-7723	241	31	7→	7→	NUM
ap-7723	241	32	1	1	NUM
ap-7723	241	33	,	,	PUNCT
ap-7723	241	34	∣∣∣π2	∣∣∣π2	PROPN
ap-7723	241	35	〉	〉	NOUN
ap-7723	241	36	7→	7→	NUM
ap-7723	241	37	i	i	PRON
ap-7723	241	38	,	,	PUNCT
ap-7723	241	39	(	(	PUNCT
ap-7723	241	40	41	41	NUM
ap-7723	241	41	)	)	PUNCT
ap-7723	241	42	which	which	PRON
ap-7723	241	43	allows	allow	VERB
ap-7723	241	44	the	the	DET
ap-7723	241	45	correspondence	correspondence	NOUN
ap-7723	241	46	between	between	ADP
ap-7723	241	47	bases	basis	NOUN
ap-7723	241	48	as	as	ADP
ap-7723	241	49	|0⟩	|0⟩	PROPN
ap-7723	241	50	⊗	⊗	PROPN
ap-7723	241	51	|0⟩	|0⟩	PROPN
ap-7723	241	52	=	=	SYM
ap-7723	241	53	e1	e1	PROPN
ap-7723	241	54	,	,	PUNCT
ap-7723	241	55	∣∣∣π2〉⊗	∣∣∣π2〉⊗	NOUN
ap-7723	241	56	∣∣∣π2	∣∣∣π2	PROPN
ap-7723	241	57	〉	〉	NOUN
ap-7723	241	58	=	=	NOUN
ap-7723	241	59	−e2	−e2	NOUN
ap-7723	241	60	,	,	PUNCT
ap-7723	241	61	|0⟩	|0⟩	NOUN
ap-7723	241	62	⊗	⊗	VERB
ap-7723	241	63	∣∣∣π2	∣∣∣π2	PROPN
ap-7723	241	64	〉	〉	NOUN
ap-7723	241	65	=	=	SYM
ap-7723	241	66	(	(	PUNCT
ap-7723	241	67	ie1	ie1	PROPN
ap-7723	241	68	)	)	PUNCT
ap-7723	241	69	,	,	PUNCT
ap-7723	241	70	∣∣∣π2〉⊗	∣∣∣π2〉⊗	NOUN
ap-7723	241	71	|0⟩	|0⟩	NOUN
ap-7723	241	72	=	=	SYM
ap-7723	241	73	(	(	PUNCT
ap-7723	241	74	ie2	ie2	PROPN
ap-7723	241	75	)	)	PUNCT
ap-7723	241	76	.	.	PUNCT
ap-7723	242	1	(	(	PUNCT
ap-7723	242	2	42	42	NUM
ap-7723	242	3	)	)	PUNCT
ap-7723	242	4	also	also	ADV
ap-7723	242	5	,	,	PUNCT
ap-7723	242	6	the	the	DET
ap-7723	242	7	spin	spin	NOUN
ap-7723	242	8	of	of	ADP
ap-7723	242	9	a	a	DET
ap-7723	242	10	particle	particle	NOUN
ap-7723	242	11	in	in	ADP
ap-7723	242	12	a	a	DET
ap-7723	242	13	real	real	ADJ
ap-7723	242	14	basis	basis	NOUN
ap-7723	242	15	,	,	PUNCT
ap-7723	242	16	given	give	VERB
ap-7723	242	17	by	by	ADP
ap-7723	242	18	the	the	DET
ap-7723	242	19	“	"	PUNCT
ap-7723	242	20	up	up	ADV
ap-7723	242	21	”	"	PUNCT
ap-7723	242	22	and	and	CCONJ
ap-7723	242	23	“	"	PUNCT
ap-7723	242	24	down	down	ADJ
ap-7723	242	25	”	"	PUNCT
ap-7723	242	26	states	state	NOUN
ap-7723	242	27	,	,	PUNCT
ap-7723	242	28	are	be	AUX
ap-7723	242	29	defined	define	VERB
ap-7723	242	30	by	by	ADP
ap-7723	242	31	e1	e1	PROPN
ap-7723	242	32	≡	≡	PROPN
ap-7723	242	33	|	|	PROPN
ap-7723	242	34	↑	↑	PROPN
ap-7723	242	35	⟩	⟩	PROPN
ap-7723	242	36	≡	≡	PROPN
ap-7723	242	37	(	(	PUNCT
ap-7723	242	38	1	1	NUM
ap-7723	242	39	0	0	NUM
ap-7723	242	40	)	)	PUNCT
ap-7723	242	41	,	,	PUNCT
ap-7723	242	42	e2	e2	PROPN
ap-7723	242	43	≡	≡	PROPN
ap-7723	243	1	|	|	CCONJ
ap-7723	243	2	↓	↓	PROPN
ap-7723	243	3	⟩	⟩	PROPN
ap-7723	243	4	≡	≡	PROPN
ap-7723	243	5	(	(	PUNCT
ap-7723	243	6	0	0	NUM
ap-7723	243	7	1	1	NUM
ap-7723	243	8	)	)	PUNCT
ap-7723	243	9	.	.	PUNCT
ap-7723	244	1	(	(	PUNCT
ap-7723	244	2	43	43	NUM
ap-7723	244	3	)	)	PUNCT
ap-7723	244	4	finally	finally	ADV
ap-7723	244	5	,	,	PUNCT
ap-7723	244	6	we	we	PRON
ap-7723	244	7	obtain	obtain	VERB
ap-7723	244	8	an	an	DET
ap-7723	244	9	unitary	unitary	ADJ
ap-7723	244	10	map	map	NOUN
ap-7723	244	11	from	from	ADP
ap-7723	244	12	the	the	DET
ap-7723	244	13	bell	bell	PROPN
ap-7723	244	14	basis	basis	NOUN
ap-7723	244	15	to	to	ADP
ap-7723	244	16	the	the	DET
ap-7723	244	17	basis	basis	NOUN
ap-7723	244	18	of	of	ADP
ap-7723	244	19	real	real	ADJ
ap-7723	244	20	structure	structure	NOUN
ap-7723	244	21	of	of	ADP
ap-7723	244	22	c2	c2	PROPN
ap-7723	244	23	(	(	PUNCT
ap-7723	244	24	|φ+⟩	|φ+⟩	NUM
ap-7723	244	25	|φ−⟩	|φ−⟩	VERB
ap-7723	244	26	|ψ+⟩	|ψ+⟩	X
ap-7723	244	27	|ψ−⟩	|ψ−⟩	X
ap-7723	244	28	)	)	PUNCT
ap-7723	245	1	=	=	SYM
ap-7723	245	2	(	(	PUNCT
ap-7723	245	3	e1	e1	PROPN
ap-7723	245	4	e2	e2	PROPN
ap-7723	245	5	(	(	PUNCT
ap-7723	245	6	ie1	ie1	PROPN
ap-7723	245	7	)	)	PUNCT
ap-7723	245	8	(	(	PUNCT
ap-7723	245	9	ie2	ie2	PROPN
ap-7723	245	10	)	)	PUNCT
ap-7723	245	11	)	)	PUNCT
ap-7723	245	12	1√	1√	PROPN
ap-7723	245	13	2	2	NUM
ap-7723	245	14			NOUN
ap-7723	245	15	1	1	NUM
ap-7723	245	16	1	1	NUM
ap-7723	245	17	0	0	NUM
ap-7723	245	18	0	0	NUM
ap-7723	245	19	−1	−1	NOUN
ap-7723	245	20	1	1	NUM
ap-7723	245	21	0	0	NUM
ap-7723	245	22	0	0	NUM
ap-7723	245	23	0	0	NUM
ap-7723	245	24	0	0	NUM
ap-7723	245	25	1	1	NUM
ap-7723	245	26	−1	−1	NOUN
ap-7723	245	27	0	0	NUM
ap-7723	245	28	0	0	NUM
ap-7723	245	29	1	1	NUM
ap-7723	245	30	1	1	NUM
ap-7723	245	31			NOUN
ap-7723	245	32	.	.	PUNCT
ap-7723	246	1	in	in	ADP
ap-7723	246	2	terms	term	NOUN
ap-7723	246	3	of	of	ADP
ap-7723	246	4	respective	respective	ADJ
ap-7723	246	5	components	component	NOUN
ap-7723	246	6	of	of	ADP
ap-7723	246	7	vectors	vector	NOUN
ap-7723	246	8	in	in	ADP
ap-7723	246	9	their	their	PRON
ap-7723	246	10	respective	respective	ADJ
ap-7723	246	11	spaces	space	NOUN
ap-7723	246	12	,	,	PUNCT
ap-7723	246	13	we	we	PRON
ap-7723	246	14	have	have	VERB
ap-7723	247	1	x1	x1	NUM
ap-7723	247	2	x2	x2	PROPN
ap-7723	247	3	y1	y1	ADJ
ap-7723	247	4	y2	y2	NOUN
ap-7723	247	5			NOUN
ap-7723	248	1	=	=	SYM
ap-7723	248	2	1√	1√	PROPN
ap-7723	248	3	2	2	NUM
ap-7723	248	4			NOUN
ap-7723	248	5	1	1	NUM
ap-7723	248	6	1	1	NUM
ap-7723	248	7	0	0	NUM
ap-7723	248	8	0	0	NUM
ap-7723	248	9	−1	−1	NOUN
ap-7723	248	10	1	1	NUM
ap-7723	248	11	0	0	NUM
ap-7723	248	12	0	0	NUM
ap-7723	248	13	0	0	NUM
ap-7723	248	14	0	0	NUM
ap-7723	248	15	1	1	NUM
ap-7723	248	16	−1	−1	NOUN
ap-7723	248	17	0	0	NUM
ap-7723	248	18	0	0	NUM
ap-7723	248	19	1	1	NUM
ap-7723	248	20	1	1	NUM
ap-7723	248	21			NOUN
ap-7723	248	22			NOUN
ap-7723	248	23	x+	x+	PUNCT
ap-7723	248	24	x−	x−	PROPN
ap-7723	248	25	y+	y+	NUM
ap-7723	248	26	y−	y−	PROPN
ap-7723	248	27			NOUN
ap-7723	248	28	.	.	PUNCT
ap-7723	249	1	(	(	PUNCT
ap-7723	249	2	44	44	NUM
ap-7723	249	3	)	)	PUNCT
ap-7723	249	4	in	in	ADP
ap-7723	249	5	complex	complex	ADJ
ap-7723	249	6	notations	notation	NOUN
ap-7723	249	7	,	,	PUNCT
ap-7723	249	8	with	with	ADP
ap-7723	249	9	z±	z±	PROPN
ap-7723	249	10	=	=	SYM
ap-7723	249	11	x±	x±	PROPN
ap-7723	250	1	+	+	CCONJ
ap-7723	250	2	iy±	iy±	NUM
ap-7723	250	3	,	,	PUNCT
ap-7723	250	4	this	this	PRON
ap-7723	250	5	is	be	AUX
ap-7723	250	6	equivalent	equivalent	ADJ
ap-7723	250	7	to	to	ADP
ap-7723	250	8	(	(	PUNCT
ap-7723	250	9	z+	z+	NUM
ap-7723	250	10	z−	z−	X
ap-7723	250	11	)	)	PUNCT
ap-7723	251	1	=	=	SYM
ap-7723	251	2	1√	1√	NUM
ap-7723	251	3	2	2	NUM
ap-7723	251	4	(	(	PUNCT
ap-7723	251	5	1	1	NUM
ap-7723	251	6	−c	−c	NOUN
ap-7723	251	7	c	c	NOUN
ap-7723	251	8	1	1	NUM
ap-7723	251	9	)	)	PUNCT
ap-7723	251	10	(	(	PUNCT
ap-7723	251	11	z1	z1	PROPN
ap-7723	251	12	z2	z2	PROPN
ap-7723	251	13	)	)	PUNCT
ap-7723	251	14	≡	≡	PROPN
ap-7723	251	15	c@	c@	PROPN
ap-7723	251	16	(	(	PUNCT
ap-7723	251	17	z1	z1	PROPN
ap-7723	251	18	z2	z2	PROPN
ap-7723	251	19	)	)	PUNCT
ap-7723	251	20	,	,	PUNCT
ap-7723	251	21	(	(	PUNCT
ap-7723	251	22	45	45	NUM
ap-7723	251	23	)	)	PUNCT
ap-7723	251	24	in	in	ADP
ap-7723	251	25	which	which	PRON
ap-7723	251	26	we	we	PRON
ap-7723	251	27	have	have	AUX
ap-7723	251	28	introduced	introduce	VERB
ap-7723	251	29	the	the	DET
ap-7723	251	30	conjugation	conjugation	NOUN
ap-7723	251	31	operator	operator	NOUN
ap-7723	251	32	cz	cz	NOUN
ap-7723	251	33	=	=	PUNCT
ap-7723	251	34	z̄	z̄	NOUN
ap-7723	251	35	,	,	PUNCT
ap-7723	251	36	i.e.	i.e.	X
ap-7723	251	37	,	,	PUNCT
ap-7723	251	38	the	the	DET
ap-7723	251	39	mirror	mirror	NOUN
ap-7723	251	40	symmetry	symmetry	NOUN
ap-7723	251	41	with	with	ADP
ap-7723	251	42	respect	respect	NOUN
ap-7723	251	43	to	to	ADP
ap-7723	251	44	the	the	DET
ap-7723	251	45	real	real	ADJ
ap-7723	251	46	axis	axis	NOUN
ap-7723	251	47	,	,	PUNCT
ap-7723	251	48	−c	−c	NOUN
ap-7723	251	49	being	be	AUX
ap-7723	251	50	the	the	DET
ap-7723	251	51	mirror	mirror	NOUN
ap-7723	251	52	symmetry	symmetry	NOUN
ap-7723	251	53	with	with	ADP
ap-7723	251	54	respect	respect	NOUN
ap-7723	251	55	to	to	ADP
ap-7723	251	56	the	the	DET
ap-7723	251	57	imaginary	imaginary	ADJ
ap-7723	251	58	axis	axis	NOUN
ap-7723	251	59	.	.	PUNCT
ap-7723	252	1	let	let	VERB
ap-7723	252	2	us	we	PRON
ap-7723	252	3	now	now	ADV
ap-7723	252	4	see	see	VERB
ap-7723	252	5	what	what	PRON
ap-7723	252	6	is	be	AUX
ap-7723	252	7	the	the	DET
ap-7723	252	8	influence	influence	NOUN
ap-7723	252	9	of	of	ADP
ap-7723	252	10	having	have	VERB
ap-7723	252	11	real	real	ADJ
ap-7723	252	12	bell	bell	NOUN
ap-7723	252	13	states	state	NOUN
ap-7723	252	14	on	on	ADP
ap-7723	252	15	schrödinger	schrödinger	ADJ
ap-7723	252	16	cat	cat	NOUN
ap-7723	252	17	states	state	NOUN
ap-7723	252	18	.	.	PUNCT
ap-7723	253	1	the	the	DET
ap-7723	253	2	operator	operator	NOUN
ap-7723	253	3	“	"	PUNCT
ap-7723	253	4	cat	cat	NOUN
ap-7723	253	5	”	"	PUNCT
ap-7723	253	6	c@	c@	NOUN
ap-7723	253	7	can	can	AUX
ap-7723	253	8	be	be	AUX
ap-7723	253	9	expressed	express	VERB
ap-7723	253	10	as	as	ADP
ap-7723	253	11	c@	c@	PROPN
ap-7723	253	12	=	=	SYM
ap-7723	253	13	1√	1√	NUM
ap-7723	253	14	2	2	NUM
ap-7723	253	15	(	(	PUNCT
ap-7723	253	16	1	1	NUM
ap-7723	253	17	+	+	CCONJ
ap-7723	253	18	f	f	X
ap-7723	253	19	)	)	PUNCT
ap-7723	253	20	,	,	PUNCT
ap-7723	253	21	f	f	X
ap-7723	253	22	:	:	PUNCT
ap-7723	254	1	=	=	SYM
ap-7723	254	2	cτ2	cτ2	NOUN
ap-7723	254	3	=	=	SYM
ap-7723	254	4	(	(	PUNCT
ap-7723	254	5	0	0	NUM
ap-7723	254	6	−c	−c	NOUN
ap-7723	254	7	c	c	NOUN
ap-7723	254	8	0	0	NUM
ap-7723	254	9	)	)	PUNCT
ap-7723	254	10	.	.	PUNCT
ap-7723	255	1	(	(	PUNCT
ap-7723	255	2	46	46	NUM
ap-7723	255	3	)	)	PUNCT
ap-7723	255	4	therefore	therefore	ADV
ap-7723	255	5	,	,	PUNCT
ap-7723	255	6	with	with	SCONJ
ap-7723	255	7	the	the	DET
ap-7723	255	8	above	above	ADJ
ap-7723	255	9	choice	choice	NOUN
ap-7723	255	10	of	of	ADP
ap-7723	255	11	isomorphisms	isomorphism	NOUN
ap-7723	255	12	,	,	PUNCT
ap-7723	255	13	bell	bell	NOUN
ap-7723	255	14	entanglement	entanglement	NOUN
ap-7723	255	15	in	in	ADP
ap-7723	255	16	r2	r2	PROPN
ap-7723	255	17	⊗	⊗	PROPN
ap-7723	255	18	r2	r2	PROPN
ap-7723	255	19	is	be	AUX
ap-7723	255	20	not	not	PART
ap-7723	255	21	represented	represent	VERB
ap-7723	255	22	by	by	ADP
ap-7723	255	23	a	a	DET
ap-7723	255	24	simple	simple	ADJ
ap-7723	255	25	linear	linear	NOUN
ap-7723	255	26	superposition	superposition	NOUN
ap-7723	255	27	in	in	ADP
ap-7723	255	28	c2	c2	PROPN
ap-7723	255	29	.	.	PUNCT
ap-7723	256	1	it	it	PRON
ap-7723	256	2	involves	involve	VERB
ap-7723	256	3	also	also	ADV
ap-7723	256	4	the	the	DET
ap-7723	256	5	two	two	NUM
ap-7723	256	6	mirror	mirror	NOUN
ap-7723	256	7	symmetries	symmetry	NOUN
ap-7723	256	8	±c	±c	PROPN
ap-7723	256	9	.	.	PUNCT
ap-7723	257	1	the	the	DET
ap-7723	257	2	operator	operator	NOUN
ap-7723	257	3	f	f	PROPN
ap-7723	257	4	is	be	AUX
ap-7723	257	5	a	a	DET
ap-7723	257	6	kind	kind	NOUN
ap-7723	257	7	of	of	ADP
ap-7723	257	8	“	"	PUNCT
ap-7723	257	9	flip	flip	NOUN
ap-7723	257	10	”	"	PUNCT
ap-7723	257	11	whereas	whereas	SCONJ
ap-7723	257	12	the	the	DET
ap-7723	257	13	“	"	PUNCT
ap-7723	257	14	cat	cat	NOUN
ap-7723	257	15	”	"	PUNCT
ap-7723	257	16	or	or	CCONJ
ap-7723	257	17	“	"	PUNCT
ap-7723	257	18	beam	beam	NOUN
ap-7723	257	19	splitter	splitter	NOUN
ap-7723	257	20	”	"	PUNCT
ap-7723	257	21	operator	operator	NOUN
ap-7723	257	22	c@	c@	PROPN
ap-7723	257	23	builds	build	VERB
ap-7723	257	24	,	,	PUNCT
ap-7723	257	25	using	use	VERB
ap-7723	257	26	the	the	DET
ap-7723	257	27	up	up	ADJ
ap-7723	257	28	and	and	CCONJ
ap-7723	257	29	down	down	ADJ
ap-7723	257	30	basic	basic	ADJ
ap-7723	257	31	states	state	NOUN
ap-7723	257	32	,	,	PUNCT
ap-7723	257	33	the	the	DET
ap-7723	257	34	two	two	NUM
ap-7723	257	35	elementary	elementary	ADJ
ap-7723	257	36	schrödinger	schrödinger	ADJ
ap-7723	257	37	cats	cat	NOUN
ap-7723	258	1	f	f	PROPN
ap-7723	258	2	|	|	ADV
ap-7723	258	3	↑	↑	PROPN
ap-7723	258	4	⟩	⟩	NOUN
ap-7723	258	5	=	=	SYM
ap-7723	259	1	|	|	ADV
ap-7723	259	2	↓	↓	PROPN
ap-7723	259	3	⟩	⟩	PROPN
ap-7723	259	4	,	,	PUNCT
ap-7723	259	5	c@	c@	PROPN
ap-7723	259	6	|	|	ADV
ap-7723	259	7	↑	↑	PROPN
ap-7723	260	1	⟩	⟩	PROPN
ap-7723	260	2	=	=	SYM
ap-7723	260	3	1√	1√	PROPN
ap-7723	260	4	2	2	NUM
ap-7723	260	5	(	(	PUNCT
ap-7723	260	6	|	|	ADV
ap-7723	260	7	↑	↑	NOUN
ap-7723	260	8	⟩	⟩	PROPN
ap-7723	261	1	+	+	CCONJ
ap-7723	261	2	|	|	ADV
ap-7723	261	3	↓	↓	PROPN
ap-7723	261	4	⟩	⟩	PROPN
ap-7723	261	5	)	)	PUNCT
ap-7723	261	6	,	,	PUNCT
ap-7723	261	7	(	(	PUNCT
ap-7723	261	8	47	47	NUM
ap-7723	261	9	)	)	PUNCT
ap-7723	261	10	f	f	NOUN
ap-7723	262	1	|	|	ADV
ap-7723	262	2	↓	↓	PROPN
ap-7723	262	3	⟩	⟩	NOUN
ap-7723	262	4	=	=	SYM
ap-7723	262	5	−|	−|	NOUN
ap-7723	262	6	↑	↑	NOUN
ap-7723	262	7	⟩	⟩	PROPN
ap-7723	262	8	,	,	PUNCT
ap-7723	262	9	c@	c@	PROPN
ap-7723	262	10	|	|	ADV
ap-7723	262	11	↓	↓	PROPN
ap-7723	262	12	⟩	⟩	PROPN
ap-7723	262	13	=	=	SYM
ap-7723	262	14	1√	1√	PROPN
ap-7723	262	15	2	2	NUM
ap-7723	262	16	(	(	PUNCT
ap-7723	262	17	−|	−|	NOUN
ap-7723	262	18	↑	↑	NOUN
ap-7723	262	19	⟩	⟩	PROPN
ap-7723	263	1	+	+	CCONJ
ap-7723	263	2	|	|	ADV
ap-7723	263	3	↓	↓	PROPN
ap-7723	263	4	⟩	⟩	PROPN
ap-7723	263	5	)	)	PUNCT
ap-7723	263	6	.	.	PUNCT
ap-7723	264	1	(	(	PUNCT
ap-7723	264	2	48	48	NUM
ap-7723	264	3	)	)	PUNCT
ap-7723	264	4	the	the	DET
ap-7723	264	5	flip	flip	ADJ
ap-7723	264	6	operator	operator	NOUN
ap-7723	264	7	also	also	ADV
ap-7723	264	8	appears	appear	VERB
ap-7723	264	9	in	in	ADP
ap-7723	264	10	the	the	DET
ap-7723	264	11	construction	construction	NOUN
ap-7723	264	12	of	of	ADP
ap-7723	264	13	the	the	DET
ap-7723	264	14	spin	spin	NOUN
ap-7723	264	15	one	one	NUM
ap-7723	264	16	-	-	PUNCT
ap-7723	264	17	half	half	NOUN
ap-7723	264	18	coherent	coherent	ADJ
ap-7723	264	19	states	state	NOUN
ap-7723	264	20	|θ	|θ	NOUN
ap-7723	264	21	,	,	PUNCT
ap-7723	264	22	ϕ⟩	ϕ⟩	ADP
ap-7723	264	23	,	,	PUNCT
ap-7723	264	24	defined	define	VERB
ap-7723	264	25	in	in	ADP
ap-7723	264	26	13	13	NUM
ap-7723	264	27	r.	r.	PROPN
ap-7723	264	28	beneduci	beneduci	PROPN
ap-7723	264	29	,	,	PUNCT
ap-7723	264	30	e.	e.	PROPN
ap-7723	264	31	frion	frion	PROPN
ap-7723	264	32	,	,	PUNCT
ap-7723	264	33	j.-p	j.-p	PROPN
ap-7723	264	34	.	.	PUNCT
ap-7723	265	1	gazeau	gazeau	PROPN
ap-7723	265	2	acta	acta	PROPN
ap-7723	265	3	polytechnica	polytechnica	PROPN
ap-7723	265	4	terms	term	NOUN
ap-7723	265	5	of	of	ADP
ap-7723	265	6	spherical	spherical	ADJ
ap-7723	265	7	coordinates	coordinate	NOUN
ap-7723	265	8	(	(	PUNCT
ap-7723	265	9	θ	θ	PROPN
ap-7723	265	10	,	,	PUNCT
ap-7723	265	11	ϕ	ϕ	NOUN
ap-7723	265	12	)	)	PUNCT
ap-7723	265	13	as	as	ADP
ap-7723	265	14	the	the	DET
ap-7723	265	15	quantum	quantum	ADJ
ap-7723	265	16	counterpart	counterpart	NOUN
ap-7723	265	17	of	of	ADP
ap-7723	265	18	the	the	DET
ap-7723	265	19	classical	classical	ADJ
ap-7723	265	20	state	state	NOUN
ap-7723	265	21	n̂(θ	n̂(θ	NOUN
ap-7723	265	22	,	,	PUNCT
ap-7723	265	23	ϕ	ϕ	NOUN
ap-7723	265	24	)	)	PUNCT
ap-7723	265	25	in	in	ADP
ap-7723	265	26	the	the	DET
ap-7723	265	27	sphere	sphere	NOUN
ap-7723	265	28	s2	s2	NOUN
ap-7723	265	29	by	by	ADP
ap-7723	265	30	|θ	|θ	PRON
ap-7723	265	31	,	,	PUNCT
ap-7723	265	32	ϕ⟩	ϕ⟩	PUNCT
ap-7723	265	33	=	=	SYM
ap-7723	265	34	(	(	PUNCT
ap-7723	265	35	cos	cos	ADP
ap-7723	265	36	θ	θ	PROPN
ap-7723	265	37	2	2	NUM
ap-7723	265	38	|	|	ADV
ap-7723	265	39	↑	↑	PROPN
ap-7723	265	40	⟩	⟩	PROPN
ap-7723	266	1	+	+	CCONJ
ap-7723	266	2	eiϕ	eiϕ	PROPN
ap-7723	266	3	sin	sin	NOUN
ap-7723	266	4	θ	θ	NOUN
ap-7723	266	5	2	2	NUM
ap-7723	266	6	|	|	ADV
ap-7723	266	7	↓	↓	PROPN
ap-7723	266	8	⟩	⟩	PROPN
ap-7723	266	9	)	)	PUNCT
ap-7723	267	1	≡	≡	PROPN
ap-7723	267	2	(	(	PUNCT
ap-7723	267	3	cos	cos	ADP
ap-7723	267	4	θ	θ	PROPN
ap-7723	267	5	2	2	NUM
ap-7723	267	6	eiϕ	eiϕ	PRON
ap-7723	267	7	sin	sin	NOUN
ap-7723	267	8	θ	θ	NOUN
ap-7723	267	9	2	2	NUM
ap-7723	267	10	)	)	PUNCT
ap-7723	267	11	=	=	SYM
ap-7723	267	12	(	(	PUNCT
ap-7723	267	13	cos	cos	ADP
ap-7723	267	14	θ	θ	PROPN
ap-7723	267	15	2	2	NUM
ap-7723	267	16	−	−	NOUN
ap-7723	267	17	sin	sin	NOUN
ap-7723	267	18	θ	θ	NOUN
ap-7723	267	19	2	2	NUM
ap-7723	267	20	e−iϕ	e−iϕ	NOUN
ap-7723	267	21	sin	sin	NOUN
ap-7723	267	22	θ	θ	PROPN
ap-7723	267	23	2	2	NUM
ap-7723	267	24	eiϕ	eiϕ	NOUN
ap-7723	267	25	cos	cos	PROPN
ap-7723	267	26	θ	θ	PROPN
ap-7723	267	27	2	2	NUM
ap-7723	267	28	)	)	PUNCT
ap-7723	267	29	(	(	PUNCT
ap-7723	267	30	1	1	NUM
ap-7723	267	31	0	0	NUM
ap-7723	267	32	)	)	PUNCT
ap-7723	267	33	≡	≡	PROPN
ap-7723	268	1	d	d	ADP
ap-7723	268	2	1	1	NUM
ap-7723	268	3	2	2	NUM
ap-7723	268	4	(	(	PUNCT
ap-7723	268	5	ξ−1	ξ−1	PROPN
ap-7723	268	6	n̂	n̂	NUM
ap-7723	268	7	)	)	PUNCT
ap-7723	269	1	|	|	ADV
ap-7723	269	2	↑	↑	PROPN
ap-7723	269	3	⟩	⟩	PROPN
ap-7723	269	4	.	.	PUNCT
ap-7723	270	1	(	(	PUNCT
ap-7723	270	2	49	49	NUM
ap-7723	270	3	)	)	PUNCT
ap-7723	270	4	here	here	ADV
ap-7723	270	5	,	,	PUNCT
ap-7723	270	6	ξn̂	ξn̂	PROPN
ap-7723	270	7	corresponds	correspond	VERB
ap-7723	270	8	,	,	PUNCT
ap-7723	270	9	through	through	ADP
ap-7723	270	10	the	the	DET
ap-7723	270	11	homomorphism	homomorphism	NOUN
ap-7723	270	12	so(3	so(3	NOUN
ap-7723	270	13	)	)	PUNCT
ap-7723	270	14	7→	7→	NUM
ap-7723	270	15	su(2	su(2	NOUN
ap-7723	270	16	)	)	PUNCT
ap-7723	270	17	,	,	PUNCT
ap-7723	270	18	to	to	ADP
ap-7723	270	19	the	the	DET
ap-7723	270	20	specific	specific	ADJ
ap-7723	270	21	rotation	rotation	NOUN
ap-7723	270	22	rn̂	rn̂	PROPN
ap-7723	270	23	mapping	map	VERB
ap-7723	270	24	the	the	DET
ap-7723	270	25	unit	unit	NOUN
ap-7723	270	26	vector	vector	NOUN
ap-7723	270	27	pointing	pointing	NOUN
ap-7723	270	28	to	to	ADP
ap-7723	270	29	the	the	DET
ap-7723	270	30	north	north	NOUN
ap-7723	270	31	pole	pole	NOUN
ap-7723	270	32	,	,	PUNCT
ap-7723	270	33	k̂	k̂	X
ap-7723	270	34	=	=	SYM
ap-7723	270	35	(	(	PUNCT
ap-7723	270	36	0	0	NUM
ap-7723	270	37	,	,	PUNCT
ap-7723	270	38	0	0	NUM
ap-7723	270	39	,	,	PUNCT
ap-7723	270	40	1	1	NUM
ap-7723	270	41	)	)	PUNCT
ap-7723	270	42	,	,	PUNCT
ap-7723	270	43	to	to	PART
ap-7723	270	44	n̂.	n̂.	VERB
ap-7723	270	45	the	the	DET
ap-7723	270	46	operator	operator	NOUN
ap-7723	270	47	d	d	NOUN
ap-7723	270	48	1	1	NUM
ap-7723	270	49	2	2	NUM
ap-7723	270	50	(	(	PUNCT
ap-7723	270	51	ξ−1	ξ−1	PROPN
ap-7723	270	52	n̂	n̂	PUNCT
ap-7723	270	53	)	)	PUNCT
ap-7723	270	54	represents	represent	VERB
ap-7723	270	55	the	the	DET
ap-7723	270	56	element	element	NOUN
ap-7723	270	57	ξ−1	ξ−1	PROPN
ap-7723	270	58	n̂	n̂	NUM
ap-7723	270	59	of	of	ADP
ap-7723	270	60	su(2	su(2	NOUN
ap-7723	270	61	)	)	PUNCT
ap-7723	270	62	in	in	ADP
ap-7723	270	63	its	its	PRON
ap-7723	270	64	complex	complex	ADJ
ap-7723	270	65	two	two	NUM
ap-7723	270	66	-	-	PUNCT
ap-7723	270	67	dimensional	dimensional	ADJ
ap-7723	270	68	unitary	unitary	ADJ
ap-7723	270	69	irreducible	irreducible	ADJ
ap-7723	270	70	representation	representation	NOUN
ap-7723	270	71	.	.	PUNCT
ap-7723	271	1	as	as	SCONJ
ap-7723	271	2	we	we	PRON
ap-7723	271	3	can	can	AUX
ap-7723	271	4	see	see	VERB
ap-7723	271	5	in	in	ADP
ap-7723	271	6	matrix	matrix	NOUN
ap-7723	271	7	(	(	PUNCT
ap-7723	271	8	49	49	NUM
ap-7723	271	9	)	)	PUNCT
ap-7723	271	10	,	,	PUNCT
ap-7723	271	11	the	the	DET
ap-7723	271	12	second	second	ADJ
ap-7723	271	13	column	column	NOUN
ap-7723	271	14	of	of	ADP
ap-7723	271	15	d	d	PROPN
ap-7723	271	16	1	1	NUM
ap-7723	271	17	2	2	NUM
ap-7723	271	18	(	(	PUNCT
ap-7723	271	19	ξ−1	ξ−1	PROPN
ap-7723	271	20	n̂	n̂	NUM
ap-7723	271	21	)	)	PUNCT
ap-7723	271	22	is	be	AUX
ap-7723	271	23	precisely	precisely	ADV
ap-7723	271	24	the	the	DET
ap-7723	271	25	flip	flip	NOUN
ap-7723	271	26	of	of	ADP
ap-7723	271	27	the	the	DET
ap-7723	271	28	first	first	ADJ
ap-7723	271	29	one	one	NUM
ap-7723	271	30	,	,	PUNCT
ap-7723	271	31	d	d	NOUN
ap-7723	271	32	1	1	NUM
ap-7723	271	33	2	2	NUM
ap-7723	271	34	(	(	PUNCT
ap-7723	271	35	ξ−1	ξ−1	PROPN
ap-7723	271	36	n̂	n̂	NUM
ap-7723	271	37	)	)	PUNCT
ap-7723	272	1	=	=	PRON
ap-7723	272	2	(	(	PUNCT
ap-7723	272	3	|θ	|θ	NOUN
ap-7723	272	4	,	,	PUNCT
ap-7723	272	5	ϕ⟩	ϕ⟩	ADJ
ap-7723	272	6	f|θ	f|θ	NOUN
ap-7723	272	7	,	,	PUNCT
ap-7723	272	8	ϕ⟩	ϕ⟩	PUNCT
ap-7723	272	9	)	)	PUNCT
ap-7723	272	10	.	.	PUNCT
ap-7723	273	1	(	(	PUNCT
ap-7723	273	2	50	50	NUM
ap-7723	273	3	)	)	PUNCT
ap-7723	273	4	actually	actually	ADV
ap-7723	273	5	,	,	PUNCT
ap-7723	273	6	we	we	PRON
ap-7723	273	7	can	can	AUX
ap-7723	273	8	learn	learn	VERB
ap-7723	273	9	more	more	ADJ
ap-7723	273	10	about	about	ADP
ap-7723	273	11	the	the	DET
ap-7723	273	12	isomorphisms	isomorphisms	PROPN
ap-7723	273	13	c2	c2	PROPN
ap-7723	273	14	∼=	∼=	PROPN
ap-7723	273	15	h	h	NOUN
ap-7723	273	16	∼=	∼=	PROPN
ap-7723	273	17	r+	r+	NOUN
ap-7723	273	18	×	×	PROPN
ap-7723	273	19	su(2	su(2	NOUN
ap-7723	273	20	)	)	PUNCT
ap-7723	273	21	through	through	ADP
ap-7723	273	22	the	the	DET
ap-7723	273	23	flip	flip	NOUN
ap-7723	273	24	and	and	CCONJ
ap-7723	273	25	matrix	matrix	NOUN
ap-7723	273	26	representations	representation	NOUN
ap-7723	273	27	of	of	ADP
ap-7723	273	28	quaternions	quaternion	NOUN
ap-7723	273	29	.	.	PUNCT
ap-7723	274	1	in	in	ADP
ap-7723	274	2	quaternionic	quaternionic	ADJ
ap-7723	274	3	algebra	algebra	NOUN
ap-7723	274	4	,	,	PUNCT
ap-7723	274	5	we	we	PRON
ap-7723	274	6	have	have	VERB
ap-7723	274	7	the	the	DET
ap-7723	274	8	property	property	NOUN
ap-7723	274	9	ı̂	ı̂	PUNCT
ap-7723	274	10	=	=	PUNCT
ap-7723	274	11	ȷ̂k̂	ȷ̂k̂	X
ap-7723	275	1	+	+	PUNCT
ap-7723	275	2	even	even	ADV
ap-7723	275	3	permutations	permutation	NOUN
ap-7723	275	4	,	,	PUNCT
ap-7723	275	5	and	and	CCONJ
ap-7723	275	6	a	a	DET
ap-7723	275	7	quaternion	quaternion	NOUN
ap-7723	275	8	q	q	NOUN
ap-7723	275	9	is	be	AUX
ap-7723	275	10	represented	represent	VERB
ap-7723	275	11	by	by	ADP
ap-7723	275	12	h	h	PROPN
ap-7723	275	13	∋	∋	NOUN
ap-7723	275	14	q	q	NOUN
ap-7723	275	15	=	=	PUNCT
ap-7723	275	16	q0	q0	NOUN
ap-7723	275	17	+	+	CCONJ
ap-7723	275	18	q1ı̂	q1ı̂	PROPN
ap-7723	275	19	+	+	NUM
ap-7723	275	20	q2ȷ̂	q2ȷ̂	NOUN
ap-7723	275	21	+	+	CCONJ
ap-7723	275	22	q3k̂	q3k̂	NOUN
ap-7723	275	23	=	=	SYM
ap-7723	275	24	q0	q0	PROPN
ap-7723	275	25	+	+	CCONJ
ap-7723	275	26	q3k̂	q3k̂	PROPN
ap-7723	276	1	+	+	CCONJ
ap-7723	276	2	ȷ̂	ȷ̂	NUM
ap-7723	276	3	(	(	PUNCT
ap-7723	276	4	q1k̂	q1k̂	NOUN
ap-7723	276	5	+	+	CCONJ
ap-7723	276	6	q2	q2	NOUN
ap-7723	276	7	)	)	PUNCT
ap-7723	276	8	≡	≡	PROPN
ap-7723	276	9	(	(	PUNCT
ap-7723	276	10	q0	q0	PROPN
ap-7723	276	11	+	+	CCONJ
ap-7723	276	12	iq3	iq3	NOUN
ap-7723	276	13	q2	q2	NOUN
ap-7723	276	14	+	+	CCONJ
ap-7723	276	15	iq1	iq1	ADJ
ap-7723	276	16	)	)	PUNCT
ap-7723	276	17	≡	≡	PROPN
ap-7723	276	18	zq	zq	PROPN
ap-7723	276	19	∈	∈	PROPN
ap-7723	276	20	c2	c2	PROPN
ap-7723	276	21	,	,	PUNCT
ap-7723	276	22	(	(	PUNCT
ap-7723	276	23	51	51	NUM
ap-7723	276	24	)	)	PUNCT
ap-7723	276	25	after	after	ADP
ap-7723	276	26	identifying	identify	VERB
ap-7723	276	27	k̂	k̂	PROPN
ap-7723	276	28	≡	≡	PROPN
ap-7723	276	29	i	i	PRON
ap-7723	276	30	as	as	SCONJ
ap-7723	276	31	both	both	PRON
ap-7723	276	32	are	be	AUX
ap-7723	276	33	roots	root	NOUN
ap-7723	276	34	of	of	ADP
ap-7723	276	35	−1	−1	NOUN
ap-7723	276	36	.	.	PUNCT
ap-7723	277	1	then	then	ADV
ap-7723	277	2	the	the	DET
ap-7723	277	3	flip	flip	NOUN
ap-7723	277	4	appears	appear	VERB
ap-7723	277	5	naturally	naturally	ADV
ap-7723	277	6	in	in	ADP
ap-7723	277	7	the	the	DET
ap-7723	277	8	final	final	ADJ
ap-7723	277	9	identification	identification	NOUN
ap-7723	277	10	h	h	NOUN
ap-7723	277	11	∼=	∼=	PROPN
ap-7723	277	12	r+	r+	PUNCT
ap-7723	277	13	×	×	PROPN
ap-7723	277	14	su(2	su(2	NOUN
ap-7723	277	15	)	)	PUNCT
ap-7723	277	16	as	as	ADP
ap-7723	277	17	q	q	PROPN
ap-7723	277	18	≡	≡	PROPN
ap-7723	277	19	(	(	PUNCT
ap-7723	277	20	q0	q0	PROPN
ap-7723	277	21	+	+	CCONJ
ap-7723	277	22	iq3	iq3	NOUN
ap-7723	277	23	−q2	−q2	PROPN
ap-7723	277	24	+	+	CCONJ
ap-7723	277	25	iq1	iq1	PROPN
ap-7723	277	26	q2	q2	NOUN
ap-7723	277	27	+	+	CCONJ
ap-7723	277	28	iq1	iq1	PROPN
ap-7723	277	29	q0	q0	PROPN
ap-7723	277	30	−	−	PROPN
ap-7723	277	31	iq3	iq3	NOUN
ap-7723	277	32	)	)	PUNCT
ap-7723	278	1	=	=	SYM
ap-7723	278	2	(	(	PUNCT
ap-7723	278	3	zq	zq	PROPN
ap-7723	278	4	fzq	fzq	NOUN
ap-7723	278	5	)	)	PUNCT
ap-7723	278	6	.	.	PUNCT
ap-7723	279	1	(	(	PUNCT
ap-7723	279	2	52	52	NUM
ap-7723	279	3	)	)	PUNCT
ap-7723	279	4	let	let	VERB
ap-7723	279	5	us	we	PRON
ap-7723	279	6	close	close	VERB
ap-7723	279	7	this	this	DET
ap-7723	279	8	article	article	NOUN
ap-7723	279	9	with	with	ADP
ap-7723	279	10	a	a	DET
ap-7723	279	11	final	final	ADJ
ap-7723	279	12	remark	remark	NOUN
ap-7723	279	13	on	on	ADP
ap-7723	279	14	spin1/2	spin1/2	ADJ
ap-7723	279	15	coherent	coherent	ADJ
ap-7723	279	16	states	state	NOUN
ap-7723	279	17	as	as	ADP
ap-7723	279	18	vectors	vector	NOUN
ap-7723	279	19	in	in	ADP
ap-7723	279	20	r2	r2	PROPN
ap-7723	279	21	a	a	DET
ap-7723	279	22	⊗	⊗	PROPN
ap-7723	279	23	r2	r2	PROPN
ap-7723	279	24	b	b	PROPN
ap-7723	279	25	.	.	PUNCT
ap-7723	280	1	the	the	DET
ap-7723	280	2	“	"	PUNCT
ap-7723	280	3	cat	cat	NOUN
ap-7723	280	4	states	state	NOUN
ap-7723	280	5	”	"	PUNCT
ap-7723	280	6	in	in	ADP
ap-7723	280	7	c2	c2	PROPN
ap-7723	280	8	given	give	VERB
ap-7723	280	9	by	by	ADP
ap-7723	280	10	(	(	PUNCT
ap-7723	280	11	49	49	NUM
ap-7723	280	12	)	)	PUNCT
ap-7723	280	13	and	and	CCONJ
ap-7723	280	14	equivalently	equivalently	ADV
ap-7723	280	15	viewed	view	VERB
ap-7723	280	16	as	as	ADP
ap-7723	280	17	4	4	NUM
ap-7723	280	18	-	-	PUNCT
ap-7723	280	19	vectors	vector	NOUN
ap-7723	280	20	in	in	ADP
ap-7723	280	21	h	h	NOUN
ap-7723	280	22	∼	∼	NOUN
ap-7723	280	23	r4	r4	NOUN
ap-7723	280	24	as	as	ADP
ap-7723	280	25	|θ	|θ	PRON
ap-7723	280	26	,	,	PUNCT
ap-7723	280	27	ϕ⟩	ϕ⟩	DET
ap-7723	280	28	7→	7→	NUM
ap-7723	280	29			ADJ
ap-7723	280	30	cos	cos	ADP
ap-7723	280	31	θ	θ	PROPN
ap-7723	280	32	2	2	NUM
ap-7723	280	33	−	−	NOUN
ap-7723	280	34	sin	sin	NOUN
ap-7723	280	35	θ	θ	PROPN
ap-7723	280	36	2	2	NUM
ap-7723	280	37	cos	cos	ADP
ap-7723	280	38	ϕ	ϕ	NOUN
ap-7723	280	39	sin	sin	NOUN
ap-7723	280	40	θ	θ	PROPN
ap-7723	280	41	2	2	NUM
ap-7723	280	42	sin	sin	NOUN
ap-7723	280	43	ϕ	ϕ	PROPN
ap-7723	280	44	0	0	NUM
ap-7723	280	45			NOUN
ap-7723	280	46	,	,	PUNCT
ap-7723	280	47	(	(	PUNCT
ap-7723	280	48	53	53	NUM
ap-7723	280	49	)	)	PUNCT
ap-7723	280	50	are	be	AUX
ap-7723	280	51	represented	represent	VERB
ap-7723	280	52	as	as	ADP
ap-7723	280	53	entangled	entangle	VERB
ap-7723	280	54	states	state	NOUN
ap-7723	280	55	in	in	ADP
ap-7723	280	56	r2	r2	PROPN
ap-7723	280	57	a	a	DET
ap-7723	280	58	⊗	⊗	PROPN
ap-7723	280	59	r2	r2	PROPN
ap-7723	280	60	b	b	PROPN
ap-7723	280	61	by	by	ADP
ap-7723	280	62	|θ	|θ	PRON
ap-7723	280	63	,	,	PUNCT
ap-7723	280	64	ϕ⟩	ϕ⟩	PUNCT
ap-7723	280	65	=	=	PUNCT
ap-7723	280	66	cos	cos	ADP
ap-7723	280	67	θ	θ	PROPN
ap-7723	280	68	2	2	NUM
ap-7723	280	69	|0⟩a	|0⟩a	ADJ
ap-7723	280	70	⊗	⊗	NOUN
ap-7723	280	71	|0⟩b	|0⟩b	NOUN
ap-7723	280	72	−	−	NOUN
ap-7723	280	73	sin	sin	NOUN
ap-7723	280	74	θ	θ	PROPN
ap-7723	280	75	2	2	NUM
ap-7723	280	76	cos	cos	ADP
ap-7723	280	77	ϕ	ϕ	PROPN
ap-7723	280	78	∣∣∣π2〉a	∣∣∣π2〉a	PROPN
ap-7723	280	79	⊗	⊗	PROPN
ap-7723	280	80	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	281	1	+	+	CCONJ
ap-7723	281	2	sin	sin	NOUN
ap-7723	281	3	θ	θ	PROPN
ap-7723	281	4	2	2	NUM
ap-7723	281	5	sin	sin	NOUN
ap-7723	281	6	ϕ|0⟩a	ϕ|0⟩a	NOUN
ap-7723	281	7	⊗	⊗	PROPN
ap-7723	281	8	∣∣∣π2〉b	∣∣∣π2〉b	PROPN
ap-7723	282	1	+	+	CCONJ
ap-7723	282	2	0	0	NUM
ap-7723	282	3	∣∣∣π2〉a	∣∣∣π2〉a	ADJ
ap-7723	282	4	⊗	⊗	PROPN
ap-7723	282	5	|0⟩b	|0⟩b	PROPN
ap-7723	282	6	.	.	PUNCT
ap-7723	283	1	therefore	therefore	ADV
ap-7723	283	2	,	,	PUNCT
ap-7723	283	3	we	we	PRON
ap-7723	283	4	can	can	AUX
ap-7723	283	5	say	say	VERB
ap-7723	283	6	that	that	SCONJ
ap-7723	283	7	two	two	NUM
ap-7723	283	8	entangled	entangle	VERB
ap-7723	283	9	angles	angle	NOUN
ap-7723	283	10	in	in	ADP
ap-7723	283	11	the	the	DET
ap-7723	283	12	plane	plane	NOUN
ap-7723	283	13	can	can	AUX
ap-7723	283	14	be	be	AUX
ap-7723	283	15	viewed	view	VERB
ap-7723	283	16	as	as	ADP
ap-7723	283	17	a	a	DET
ap-7723	283	18	point	point	NOUN
ap-7723	283	19	in	in	ADP
ap-7723	283	20	the	the	DET
ap-7723	283	21	upper	upper	ADJ
ap-7723	283	22	half	half	ADJ
ap-7723	283	23	-	-	PUNCT
ap-7723	283	24	sphere	sphere	NOUN
ap-7723	283	25	s2	s2	PROPN
ap-7723	283	26	/	/	SYM
ap-7723	283	27	z2	z2	PROPN
ap-7723	283	28	in	in	ADP
ap-7723	283	29	r3	r3	PROPN
ap-7723	283	30	shown	show	VERB
ap-7723	283	31	in	in	ADP
ap-7723	283	32	figure	figure	NOUN
ap-7723	283	33	2	2	NUM
ap-7723	283	34	.	.	PUNCT
ap-7723	283	35	figure	figure	NOUN
ap-7723	283	36	2	2	NUM
ap-7723	283	37	.	.	PUNCT
ap-7723	283	38	each	each	DET
ap-7723	283	39	point	point	NOUN
ap-7723	283	40	in	in	ADP
ap-7723	283	41	the	the	DET
ap-7723	283	42	upper	upper	ADJ
ap-7723	283	43	half	half	ADJ
ap-7723	283	44	-	-	PUNCT
ap-7723	283	45	sphere	sphere	NOUN
ap-7723	283	46	is	be	AUX
ap-7723	283	47	in	in	ADP
ap-7723	283	48	one	one	NUM
ap-7723	283	49	-	-	PUNCT
ap-7723	283	50	to	to	ADP
ap-7723	283	51	-	-	PUNCT
ap-7723	283	52	one	one	NUM
ap-7723	283	53	correspondence	correspondence	NOUN
ap-7723	283	54	with	with	ADP
ap-7723	283	55	two	two	NUM
ap-7723	283	56	entangled	entangled	ADJ
ap-7723	283	57	angles	angle	NOUN
ap-7723	283	58	in	in	ADP
ap-7723	283	59	the	the	DET
ap-7723	283	60	plane	plane	NOUN
ap-7723	283	61	.	.	PUNCT
ap-7723	284	1	5	5	X
ap-7723	284	2	.	.	PUNCT
ap-7723	284	3	conclusions	conclusion	NOUN
ap-7723	284	4	integral	integral	ADJ
ap-7723	284	5	quantization	quantization	NOUN
ap-7723	284	6	is	be	AUX
ap-7723	284	7	a	a	DET
ap-7723	284	8	quantization	quantization	NOUN
ap-7723	284	9	scheme	scheme	NOUN
ap-7723	284	10	constructed	construct	VERB
ap-7723	284	11	on	on	ADP
ap-7723	284	12	positive	positive	ADJ
ap-7723	284	13	operator	operator	NOUN
ap-7723	284	14	-	-	PUNCT
ap-7723	284	15	value	value	NOUN
ap-7723	284	16	measures	measure	NOUN
ap-7723	284	17	.	.	PUNCT
ap-7723	285	1	when	when	SCONJ
ap-7723	285	2	applied	apply	VERB
ap-7723	285	3	to	to	ADP
ap-7723	285	4	a	a	DET
ap-7723	285	5	two	two	NUM
ap-7723	285	6	-	-	PUNCT
ap-7723	285	7	dimensional	dimensional	ADJ
ap-7723	285	8	real	real	ADJ
ap-7723	285	9	space	space	NOUN
ap-7723	285	10	,	,	PUNCT
ap-7723	285	11	it	it	PRON
ap-7723	285	12	allows	allow	VERB
ap-7723	285	13	for	for	ADP
ap-7723	285	14	a	a	DET
ap-7723	285	15	description	description	NOUN
ap-7723	285	16	of	of	ADP
ap-7723	285	17	quantum	quantum	ADJ
ap-7723	285	18	states	state	NOUN
ap-7723	285	19	as	as	ADP
ap-7723	285	20	pointers	pointer	NOUN
ap-7723	285	21	in	in	ADP
ap-7723	285	22	the	the	DET
ap-7723	285	23	real	real	ADJ
ap-7723	285	24	unit	unit	NOUN
ap-7723	285	25	half	half	ADJ
ap-7723	285	26	-	-	PUNCT
ap-7723	285	27	plane	plane	NOUN
ap-7723	285	28	.	.	PUNCT
ap-7723	286	1	we	we	PRON
ap-7723	286	2	recalled	recall	VERB
ap-7723	286	3	in	in	ADP
ap-7723	286	4	this	this	DET
ap-7723	286	5	paper	paper	NOUN
ap-7723	286	6	that	that	SCONJ
ap-7723	286	7	in	in	ADP
ap-7723	286	8	this	this	DET
ap-7723	286	9	case	case	NOUN
ap-7723	286	10	,	,	PUNCT
ap-7723	286	11	a	a	DET
ap-7723	286	12	family	family	NOUN
ap-7723	286	13	of	of	ADP
ap-7723	286	14	density	density	NOUN
ap-7723	286	15	matrices	matrix	NOUN
ap-7723	286	16	is	be	AUX
ap-7723	286	17	sufficient	sufficient	ADJ
ap-7723	286	18	to	to	PART
ap-7723	286	19	perform	perform	VERB
ap-7723	286	20	this	this	DET
ap-7723	286	21	kind	kind	NOUN
ap-7723	286	22	of	of	ADP
ap-7723	286	23	quantization	quantization	NOUN
ap-7723	286	24	as	as	SCONJ
ap-7723	286	25	it	it	PRON
ap-7723	286	26	describes	describe	VERB
ap-7723	286	27	all	all	DET
ap-7723	286	28	the	the	DET
ap-7723	286	29	mixed	mixed	ADJ
ap-7723	286	30	states	state	NOUN
ap-7723	286	31	in	in	ADP
ap-7723	286	32	this	this	DET
ap-7723	286	33	space	space	NOUN
ap-7723	286	34	.	.	PUNCT
ap-7723	287	1	furthermore	furthermore	ADV
ap-7723	287	2	,	,	PUNCT
ap-7723	287	3	a	a	DET
ap-7723	287	4	density	density	NOUN
ap-7723	287	5	matrix	matrix	NOUN
ap-7723	287	6	in	in	ADP
ap-7723	287	7	a	a	DET
ap-7723	287	8	two	two	NUM
ap-7723	287	9	-	-	PUNCT
ap-7723	287	10	dimensional	dimensional	ADJ
ap-7723	287	11	real	real	ADJ
ap-7723	287	12	space	space	NOUN
ap-7723	287	13	depends	depend	VERB
ap-7723	287	14	on	on	ADP
ap-7723	287	15	the	the	DET
ap-7723	287	16	usual	usual	ADJ
ap-7723	287	17	observable	observable	ADJ
ap-7723	287	18	σϕ	σϕ	NOUN
ap-7723	287	19	=	=	X
ap-7723	287	20	(	(	PUNCT
ap-7723	287	21	cos	cos	ADP
ap-7723	287	22	ϕ	ϕ	PROPN
ap-7723	287	23	sin	sin	PROPN
ap-7723	287	24	ϕ	ϕ	PROPN
ap-7723	287	25	sin	sin	NOUN
ap-7723	287	26	ϕ	ϕ	PROPN
ap-7723	287	27	−	−	PROPN
ap-7723	287	28	cos	cos	PROPN
ap-7723	287	29	ϕ	ϕ	PROPN
ap-7723	287	30	)	)	PUNCT
ap-7723	287	31	,	,	PUNCT
ap-7723	287	32	which	which	PRON
ap-7723	287	33	captures	capture	VERB
ap-7723	287	34	the	the	DET
ap-7723	287	35	essence	essence	NOUN
ap-7723	287	36	of	of	ADP
ap-7723	287	37	non	non	NOUN
ap-7723	287	38	-	-	NOUN
ap-7723	287	39	commutativity	commutativity	NOUN
ap-7723	287	40	in	in	ADP
ap-7723	287	41	real	real	ADJ
ap-7723	287	42	space	space	NOUN
ap-7723	287	43	.	.	PUNCT
ap-7723	288	1	as	as	ADP
ap-7723	288	2	a	a	DET
ap-7723	288	3	consequence	consequence	NOUN
ap-7723	288	4	,	,	PUNCT
ap-7723	288	5	commutation	commutation	NOUN
ap-7723	288	6	relations	relation	NOUN
ap-7723	288	7	are	be	AUX
ap-7723	288	8	expressed	express	VERB
ap-7723	288	9	in	in	ADP
ap-7723	288	10	terms	term	NOUN
ap-7723	288	11	of	of	ADP
ap-7723	288	12	the	the	DET
ap-7723	288	13	real	real	ADJ
ap-7723	288	14	matrix	matrix	NOUN
ap-7723	288	15	τ2	τ2	NOUN
ap-7723	288	16	,	,	PUNCT
ap-7723	288	17	which	which	PRON
ap-7723	288	18	serves	serve	VERB
ap-7723	288	19	as	as	ADP
ap-7723	288	20	the	the	DET
ap-7723	288	21	basis	basis	NOUN
ap-7723	288	22	to	to	ADP
ap-7723	288	23	the	the	DET
ap-7723	288	24	description	description	NOUN
ap-7723	288	25	of	of	ADP
ap-7723	288	26	quantum	quantum	ADJ
ap-7723	288	27	measurement	measurement	NOUN
ap-7723	288	28	.	.	PUNCT
ap-7723	289	1	we	we	PRON
ap-7723	289	2	provide	provide	VERB
ap-7723	289	3	an	an	DET
ap-7723	289	4	illustration	illustration	NOUN
ap-7723	289	5	considering	consider	VERB
ap-7723	289	6	linearlypolarized	linearlypolarize	VERB
ap-7723	289	7	light	light	NOUN
ap-7723	289	8	passing	pass	VERB
ap-7723	289	9	through	through	ADP
ap-7723	289	10	a	a	DET
ap-7723	289	11	polarizer	polarizer	NOUN
ap-7723	289	12	.	.	PUNCT
ap-7723	290	1	the	the	DET
ap-7723	290	2	pointer	pointer	NOUN
ap-7723	290	3	,	,	PUNCT
ap-7723	290	4	associated	associate	VERB
ap-7723	290	5	with	with	ADP
ap-7723	290	6	τ2	τ2	PROPN
ap-7723	290	7	,	,	PUNCT
ap-7723	290	8	can	can	AUX
ap-7723	290	9	rotate	rotate	VERB
ap-7723	290	10	by	by	ADP
ap-7723	290	11	an	an	DET
ap-7723	290	12	angle	angle	NOUN
ap-7723	290	13	(	(	PUNCT
ap-7723	290	14	1±r)/2	1±r)/2	NUM
ap-7723	290	15	with	with	ADP
ap-7723	290	16	r	r	NOUN
ap-7723	290	17	the	the	DET
ap-7723	290	18	degree	degree	NOUN
ap-7723	290	19	of	of	ADP
ap-7723	290	20	mixing	mixing	NOUN
ap-7723	290	21	of	of	ADP
ap-7723	290	22	the	the	DET
ap-7723	290	23	density	density	NOUN
ap-7723	290	24	matrix	matrix	NOUN
ap-7723	290	25	,	,	PUNCT
ap-7723	290	26	with	with	ADP
ap-7723	290	27	a	a	DET
ap-7723	290	28	probability	probability	NOUN
ap-7723	290	29	given	give	VERB
ap-7723	290	30	by	by	ADP
ap-7723	290	31	the	the	DET
ap-7723	290	32	usual	usual	ADJ
ap-7723	290	33	malus	malus	NOUN
ap-7723	290	34	’	'	PUNCT
ap-7723	290	35	laws	law	NOUN
ap-7723	290	36	(	(	PUNCT
ap-7723	290	37	26	26	NUM
ap-7723	290	38	)	)	PUNCT
ap-7723	290	39	and	and	CCONJ
ap-7723	290	40	(	(	PUNCT
ap-7723	290	41	27	27	NUM
ap-7723	290	42	)	)	PUNCT
ap-7723	290	43	.	.	PUNCT
ap-7723	291	1	we	we	PRON
ap-7723	291	2	extended	extend	VERB
ap-7723	291	3	the	the	DET
ap-7723	291	4	analysis	analysis	NOUN
ap-7723	291	5	by	by	ADP
ap-7723	291	6	showing	show	VERB
ap-7723	291	7	that	that	SCONJ
ap-7723	291	8	the	the	DET
ap-7723	291	9	interaction	interaction	NOUN
ap-7723	291	10	between	between	ADP
ap-7723	291	11	a	a	DET
ap-7723	291	12	polarizer	polarizer	NOUN
ap-7723	291	13	and	and	CCONJ
ap-7723	291	14	a	a	DET
ap-7723	291	15	light	light	ADJ
ap-7723	291	16	ray	ray	NOUN
ap-7723	291	17	is	be	AUX
ap-7723	291	18	equivalent	equivalent	ADJ
ap-7723	291	19	to	to	ADP
ap-7723	291	20	the	the	DET
ap-7723	291	21	quantum	quantum	ADJ
ap-7723	291	22	entanglement	entanglement	NOUN
ap-7723	291	23	of	of	ADP
ap-7723	291	24	two	two	NUM
ap-7723	291	25	hilbert	hilbert	NOUN
ap-7723	291	26	spaces	space	NOUN
ap-7723	291	27	.	.	PUNCT
ap-7723	292	1	orientations	orientation	NOUN
ap-7723	292	2	in	in	ADP
ap-7723	292	3	the	the	DET
ap-7723	292	4	plane	plane	NOUN
ap-7723	292	5	have	have	VERB
ap-7723	292	6	only	only	ADV
ap-7723	292	7	two	two	NUM
ap-7723	292	8	outcomes	outcome	NOUN
ap-7723	292	9	(	(	PUNCT
ap-7723	292	10	±1	±1	PROPN
ap-7723	292	11	)	)	PUNCT
ap-7723	292	12	,	,	PUNCT
ap-7723	292	13	which	which	PRON
ap-7723	292	14	are	be	AUX
ap-7723	292	15	the	the	DET
ap-7723	292	16	possible	possible	ADJ
ap-7723	292	17	issues	issue	NOUN
ap-7723	292	18	of	of	ADP
ap-7723	292	19	σϕ.	σϕ.	NOUN
ap-7723	292	20	we	we	PRON
ap-7723	292	21	showed	show	VERB
ap-7723	292	22	that	that	SCONJ
ap-7723	292	23	for	for	ADP
ap-7723	292	24	a	a	DET
ap-7723	292	25	general	general	ADJ
ap-7723	292	26	bipartite	bipartite	PROPN
ap-7723	292	27	system	system	NOUN
ap-7723	292	28	,	,	PUNCT
ap-7723	292	29	the	the	DET
ap-7723	292	30	classical	classical	ADJ
ap-7723	292	31	and	and	CCONJ
ap-7723	292	32	quantum	quantum	ADJ
ap-7723	292	33	measurement	measurement	NOUN
ap-7723	292	34	of	of	ADP
ap-7723	292	35	σϕ	σϕ	INTJ
ap-7723	292	36	deny	deny	VERB
ap-7723	292	37	the	the	DET
ap-7723	292	38	existence	existence	NOUN
ap-7723	292	39	of	of	ADP
ap-7723	292	40	local	local	ADJ
ap-7723	292	41	hidden	hidden	ADJ
ap-7723	292	42	variables	variable	NOUN
ap-7723	292	43	,	,	PUNCT
ap-7723	292	44	resulting	result	VERB
ap-7723	292	45	in	in	ADP
ap-7723	292	46	the	the	DET
ap-7723	292	47	well	well	ADV
ap-7723	292	48	-	-	PUNCT
ap-7723	292	49	known	know	VERB
ap-7723	292	50	violation	violation	NOUN
ap-7723	292	51	of	of	ADP
ap-7723	292	52	bell	bell	NOUN
ap-7723	292	53	inequalities	inequality	NOUN
ap-7723	292	54	,	,	PUNCT
ap-7723	292	55	here	here	ADV
ap-7723	292	56	given	give	VERB
ap-7723	292	57	by	by	ADP
ap-7723	292	58	(	(	PUNCT
ap-7723	292	59	37	37	NUM
ap-7723	292	60	)	)	PUNCT
ap-7723	292	61	.	.	PUNCT
ap-7723	293	1	finally	finally	ADV
ap-7723	293	2	,	,	PUNCT
ap-7723	293	3	we	we	PRON
ap-7723	293	4	demonstrated	demonstrate	VERB
ap-7723	293	5	that	that	SCONJ
ap-7723	293	6	the	the	DET
ap-7723	293	7	isomorphism	isomorphism	NOUN
ap-7723	293	8	c2	c2	PROPN
ap-7723	293	9	≃	≃	PROPN
ap-7723	293	10	r4	r4	PROPN
ap-7723	293	11	allows	allow	VERB
ap-7723	293	12	to	to	PART
ap-7723	293	13	write	write	VERB
ap-7723	293	14	bell	bell	NOUN
ap-7723	293	15	states	state	NOUN
ap-7723	293	16	in	in	ADP
ap-7723	293	17	real	real	ADJ
ap-7723	293	18	space	space	NOUN
ap-7723	293	19	,	,	PUNCT
ap-7723	293	20	with	with	ADP
ap-7723	293	21	the	the	DET
ap-7723	293	22	introduction	introduction	NOUN
ap-7723	293	23	of	of	ADP
ap-7723	293	24	the	the	DET
ap-7723	293	25	“	"	PUNCT
ap-7723	293	26	flip	flip	NOUN
ap-7723	293	27	”	"	PUNCT
ap-7723	293	28	operator	operator	NOUN
ap-7723	293	29	(	(	PUNCT
ap-7723	293	30	46	46	NUM
ap-7723	293	31	)	)	PUNCT
ap-7723	293	32	.	.	PUNCT
ap-7723	294	1	this	this	DET
ap-7723	294	2	operator	operator	NOUN
ap-7723	294	3	is	be	AUX
ap-7723	294	4	necessary	necessary	ADJ
ap-7723	294	5	for	for	ADP
ap-7723	294	6	constructing	construct	VERB
ap-7723	294	7	spin	spin	NOUN
ap-7723	294	8	one	one	NUM
ap-7723	294	9	-	-	PUNCT
ap-7723	294	10	half	half	NOUN
ap-7723	294	11	coherent	coherent	ADJ
ap-7723	294	12	states	state	NOUN
ap-7723	294	13	,	,	PUNCT
ap-7723	294	14	that	that	SCONJ
ap-7723	294	15	we	we	PRON
ap-7723	294	16	can	can	AUX
ap-7723	294	17	fully	fully	ADV
ap-7723	294	18	describe	describe	VERB
ap-7723	294	19	by	by	ADP
ap-7723	294	20	a	a	DET
ap-7723	294	21	set	set	NOUN
ap-7723	294	22	of	of	ADP
ap-7723	294	23	orientations	orientation	NOUN
ap-7723	294	24	in	in	ADP
ap-7723	294	25	r3	r3	PROPN
ap-7723	294	26	,	,	PUNCT
ap-7723	294	27	as	as	SCONJ
ap-7723	294	28	shown	show	VERB
ap-7723	294	29	in	in	ADP
ap-7723	294	30	(	(	PUNCT
ap-7723	294	31	53	53	NUM
ap-7723	294	32	)	)	PUNCT
ap-7723	294	33	.	.	PUNCT
ap-7723	295	1	acknowledgements	acknowledgement	NOUN
ap-7723	295	2	r.b	r.b	PROPN
ap-7723	295	3	.	.	PUNCT
ap-7723	296	1	the	the	DET
ap-7723	296	2	present	present	ADJ
ap-7723	296	3	work	work	NOUN
ap-7723	296	4	was	be	AUX
ap-7723	296	5	performed	perform	VERB
ap-7723	296	6	under	under	ADP
ap-7723	296	7	the	the	DET
ap-7723	296	8	auspices	auspex	NOUN
ap-7723	296	9	of	of	ADP
ap-7723	296	10	the	the	DET
ap-7723	296	11	gnfm	gnfm	NOUN
ap-7723	296	12	(	(	PUNCT
ap-7723	296	13	gruppo	gruppo	PROPN
ap-7723	296	14	nazionale	nazionale	PROPN
ap-7723	296	15	di	di	PROPN
ap-7723	296	16	fisica	fisica	PROPN
ap-7723	296	17	matematica	matematica	PROPN
ap-7723	296	18	)	)	PUNCT
ap-7723	296	19	.	.	PUNCT
ap-7723	297	1	14	14	NUM
ap-7723	297	2	vol	vol	NOUN
ap-7723	297	3	.	.	PUNCT
ap-7723	298	1	62	62	NUM
ap-7723	298	2	no	no	INTJ
ap-7723	298	3	.	.	PUNCT
ap-7723	299	1	1/2022	1/2022	NUM
ap-7723	299	2	quantum	quantum	NOUN
ap-7723	299	3	angles	angle	NOUN
ap-7723	299	4	ef	ef	VERB
ap-7723	299	5	thanks	thank	NOUN
ap-7723	299	6	the	the	DET
ap-7723	299	7	helsinki	helsinki	PROPN
ap-7723	299	8	institute	institute	PROPN
ap-7723	299	9	of	of	ADP
ap-7723	299	10	physics	physics	PROPN
ap-7723	299	11	(	(	PUNCT
ap-7723	299	12	hip	hip	NOUN
ap-7723	299	13	)	)	PUNCT
ap-7723	299	14	for	for	ADP
ap-7723	299	15	their	their	PRON
ap-7723	299	16	hospitality	hospitality	NOUN
ap-7723	299	17	.	.	PUNCT
ap-7723	300	1	references	reference	NOUN
ap-7723	300	2	[	[	X
ap-7723	300	3	1	1	NUM
ap-7723	300	4	]	]	PUNCT
ap-7723	300	5	e.	e.	PROPN
ap-7723	300	6	c.	c.	PROPN
ap-7723	300	7	g.	g.	PROPN
ap-7723	300	8	stueckelberg	stueckelberg	PROPN
ap-7723	300	9	.	.	PUNCT
ap-7723	301	1	quantum	quantum	PROPN
ap-7723	301	2	theory	theory	NOUN
ap-7723	301	3	in	in	ADP
ap-7723	301	4	real	real	ADJ
ap-7723	301	5	hilbert	hilbert	NOUN
ap-7723	301	6	space	space	NOUN
ap-7723	301	7	.	.	PUNCT
ap-7723	302	1	helvetica	helvetica	PROPN
ap-7723	302	2	physica	physica	PROPN
ap-7723	302	3	acta	acta	PROPN
ap-7723	302	4	33(8):727–752	33(8):727–752	PROPN
ap-7723	302	5	,	,	PUNCT
ap-7723	302	6	1960	1960	NUM
ap-7723	302	7	.	.	PUNCT
ap-7723	303	1	[	[	X
ap-7723	303	2	2	2	NUM
ap-7723	303	3	]	]	PUNCT
ap-7723	303	4	m.	m.	NOUN
ap-7723	303	5	p.	p.	NOUN
ap-7723	303	6	solèr	solèr	PROPN
ap-7723	303	7	.	.	PUNCT
ap-7723	304	1	characterization	characterization	NOUN
ap-7723	304	2	of	of	ADP
ap-7723	304	3	hilbert	hilbert	NOUN
ap-7723	304	4	spaces	space	NOUN
ap-7723	304	5	by	by	ADP
ap-7723	304	6	orthomodular	orthomodular	ADJ
ap-7723	304	7	spaces	space	NOUN
ap-7723	304	8	.	.	PUNCT
ap-7723	305	1	communications	communication	NOUN
ap-7723	305	2	in	in	ADP
ap-7723	305	3	algebra	algebra	PROPN
ap-7723	305	4	23(1):219–243	23(1):219–243	PROPN
ap-7723	305	5	,	,	PUNCT
ap-7723	305	6	1995	1995	NUM
ap-7723	305	7	.	.	PUNCT
ap-7723	306	1	https://doi.org/10.1080/00927879508825218	https://doi.org/10.1080/00927879508825218	NOUN
ap-7723	306	2	.	.	PUNCT
ap-7723	307	1	[	[	X
ap-7723	307	2	3	3	X
ap-7723	307	3	]	]	PUNCT
ap-7723	307	4	v.	v.	X
ap-7723	307	5	moretti	moretti	PROPN
ap-7723	307	6	,	,	PUNCT
ap-7723	307	7	m.	m.	NOUN
ap-7723	307	8	oppio	oppio	ADJ
ap-7723	307	9	.	.	PUNCT
ap-7723	307	10	quantum	quantum	PROPN
ap-7723	307	11	theory	theory	NOUN
ap-7723	307	12	in	in	ADP
ap-7723	307	13	quaternionic	quaternionic	ADJ
ap-7723	307	14	hilbert	hilbert	NOUN
ap-7723	307	15	space	space	NOUN
ap-7723	307	16	:	:	PUNCT
ap-7723	307	17	how	how	SCONJ
ap-7723	307	18	poincaré	poincaré	PROPN
ap-7723	307	19	symmetry	symmetry	NOUN
ap-7723	307	20	reduces	reduce	VERB
ap-7723	307	21	the	the	DET
ap-7723	307	22	theory	theory	NOUN
ap-7723	307	23	to	to	ADP
ap-7723	307	24	the	the	DET
ap-7723	307	25	standard	standard	ADJ
ap-7723	307	26	complex	complex	ADJ
ap-7723	307	27	one	one	NUM
ap-7723	307	28	.	.	PUNCT
ap-7723	308	1	reviews	review	NOUN
ap-7723	308	2	in	in	ADP
ap-7723	308	3	mathematical	mathematical	ADJ
ap-7723	308	4	physics	physics	NOUN
ap-7723	308	5	31(04):1950013	31(04):1950013	NUM
ap-7723	308	6	,	,	PUNCT
ap-7723	308	7	2019	2019	NUM
ap-7723	308	8	.	.	PUNCT
ap-7723	309	1	https://doi.org/10.1142/s0129055x19500132	https://doi.org/10.1142/s0129055x19500132	X
ap-7723	309	2	.	.	PUNCT
ap-7723	310	1	[	[	X
ap-7723	310	2	4	4	NUM
ap-7723	310	3	]	]	PUNCT
ap-7723	310	4	a.	a.	NOUN
ap-7723	310	5	peres	peres	PROPN
ap-7723	310	6	.	.	PUNCT
ap-7723	311	1	neumark	neumark	PROPN
ap-7723	311	2	’s	’s	PART
ap-7723	311	3	theorem	theorem	NOUN
ap-7723	311	4	and	and	CCONJ
ap-7723	311	5	quantum	quantum	NOUN
ap-7723	311	6	inseparability	inseparability	NOUN
ap-7723	311	7	.	.	PUNCT
ap-7723	312	1	foundations	foundation	NOUN
ap-7723	312	2	of	of	ADP
ap-7723	312	3	physics	physics	NOUN
ap-7723	312	4	20:1441–1453	20:1441–1453	NUM
ap-7723	312	5	,	,	PUNCT
ap-7723	312	6	1990	1990	NUM
ap-7723	312	7	.	.	PUNCT
ap-7723	313	1	https://doi.org/10.1007/bf01883517	https://doi.org/10.1007/bf01883517	X
ap-7723	313	2	.	.	PUNCT
ap-7723	314	1	[	[	X
ap-7723	314	2	5	5	X
ap-7723	314	3	]	]	X
ap-7723	314	4	h.	h.	PROPN
ap-7723	314	5	bergeron	bergeron	PROPN
ap-7723	314	6	,	,	PUNCT
ap-7723	314	7	e.	e.	PROPN
ap-7723	314	8	m.	m.	PROPN
ap-7723	314	9	f.	f.	PROPN
ap-7723	314	10	curado	curado	PROPN
ap-7723	314	11	,	,	PUNCT
ap-7723	314	12	j.-p	j.-p	PROPN
ap-7723	314	13	.	.	PUNCT
ap-7723	315	1	gazeau	gazeau	PROPN
ap-7723	315	2	,	,	PUNCT
ap-7723	315	3	l.	l.	PROPN
ap-7723	315	4	m.	m.	PROPN
ap-7723	315	5	c.	c.	PROPN
ap-7723	315	6	s.	s.	PROPN
ap-7723	315	7	rodrigues	rodrigues	PROPN
ap-7723	315	8	.	.	PUNCT
ap-7723	316	1	orientations	orientation	NOUN
ap-7723	316	2	in	in	ADP
ap-7723	316	3	the	the	DET
ap-7723	316	4	plane	plane	NOUN
ap-7723	316	5	as	as	ADP
ap-7723	316	6	quantum	quantum	NOUN
ap-7723	316	7	states	state	NOUN
ap-7723	316	8	.	.	PUNCT
ap-7723	317	1	brazilian	brazilian	ADJ
ap-7723	317	2	journal	journal	PROPN
ap-7723	317	3	of	of	ADP
ap-7723	317	4	physics	physics	PROPN
ap-7723	317	5	49(3):391–401	49(3):391–401	PROPN
ap-7723	317	6	,	,	PUNCT
ap-7723	317	7	2019	2019	NUM
ap-7723	317	8	.	.	PUNCT
ap-7723	318	1	https://doi.org/10.1007/s13538-019-00652-x	https://doi.org/10.1007/s13538-019-00652-x	PROPN
ap-7723	318	2	.	.	PUNCT
ap-7723	319	1	[	[	X
ap-7723	319	2	6	6	NUM
ap-7723	319	3	]	]	PUNCT
ap-7723	319	4	r.	r.	PROPN
ap-7723	319	5	beneduci	beneduci	PROPN
ap-7723	319	6	,	,	PUNCT
ap-7723	319	7	e.	e.	PROPN
ap-7723	319	8	frion	frion	PROPN
ap-7723	319	9	,	,	PUNCT
ap-7723	319	10	j.-p	j.-p	PROPN
ap-7723	319	11	.	.	PUNCT
ap-7723	320	1	gazeau	gazeau	PROPN
ap-7723	320	2	,	,	PUNCT
ap-7723	320	3	a.	a.	NOUN
ap-7723	320	4	perri	perri	NOUN
ap-7723	320	5	.	.	PUNCT
ap-7723	321	1	real	real	ADJ
ap-7723	321	2	povms	povms	NOUN
ap-7723	321	3	on	on	ADP
ap-7723	321	4	the	the	DET
ap-7723	321	5	plane	plane	NOUN
ap-7723	321	6	:	:	PUNCT
ap-7723	321	7	integral	integral	ADJ
ap-7723	321	8	quantization	quantization	NOUN
ap-7723	321	9	,	,	PUNCT
ap-7723	321	10	naimark	naimark	PROPN
ap-7723	321	11	theorem	theorem	ADJ
ap-7723	321	12	and	and	CCONJ
ap-7723	321	13	linear	linear	ADJ
ap-7723	321	14	polarization	polarization	NOUN
ap-7723	321	15	of	of	ADP
ap-7723	321	16	the	the	DET
ap-7723	321	17	light	light	NOUN
ap-7723	321	18	.	.	PUNCT
ap-7723	322	1	quantum	quantum	ADJ
ap-7723	322	2	physics	physics	NOUN
ap-7723	322	3	2021	2021	NUM
ap-7723	322	4	.	.	PUNCT
ap-7723	323	1	arxiv:2108.04086	arxiv:2108.04086	NUM
ap-7723	323	2	.	.	PUNCT
ap-7723	324	1	[	[	X
ap-7723	324	2	7	7	X
ap-7723	324	3	]	]	X
ap-7723	324	4	r.	r.	PROPN
ap-7723	324	5	beneduci	beneduci	PROPN
ap-7723	324	6	.	.	PUNCT
ap-7723	325	1	joint	joint	ADJ
ap-7723	325	2	measurability	measurability	NOUN
ap-7723	325	3	through	through	ADP
ap-7723	325	4	naimark	naimark	PROPN
ap-7723	325	5	’s	’s	PART
ap-7723	325	6	dilation	dilation	NOUN
ap-7723	325	7	theorem	theorem	VERB
ap-7723	325	8	.	.	PUNCT
ap-7723	326	1	reports	report	NOUN
ap-7723	326	2	on	on	ADP
ap-7723	326	3	mathematical	mathematical	ADJ
ap-7723	326	4	physics	physics	NOUN
ap-7723	326	5	79(2):197–214	79(2):197–214	NOUN
ap-7723	326	6	,	,	PUNCT
ap-7723	326	7	2017	2017	NUM
ap-7723	326	8	.	.	PUNCT
ap-7723	327	1	https://doi.org/10.1016/s0034-4877(17)30035-6	https://doi.org/10.1016/s0034-4877(17)30035-6	PROPN
ap-7723	327	2	.	.	PUNCT
ap-7723	328	1	[	[	X
ap-7723	328	2	8	8	NUM
ap-7723	328	3	]	]	PUNCT
ap-7723	328	4	a.	a.	NOUN
ap-7723	328	5	holevo	holevo	PROPN
ap-7723	328	6	.	.	PUNCT
ap-7723	329	1	probabilistic	probabilistic	ADJ
ap-7723	329	2	and	and	CCONJ
ap-7723	329	3	statistical	statistical	ADJ
ap-7723	329	4	aspects	aspect	NOUN
ap-7723	329	5	of	of	ADP
ap-7723	329	6	quantum	quantum	NOUN
ap-7723	329	7	theory	theory	NOUN
ap-7723	329	8	.	.	PUNCT
ap-7723	330	1	springer	springer	NOUN
ap-7723	330	2	science	science	PROPN
ap-7723	330	3	&	&	CCONJ
ap-7723	330	4	business	business	NOUN
ap-7723	330	5	media	medium	NOUN
ap-7723	330	6	,	,	PUNCT
ap-7723	330	7	2011	2011	NUM
ap-7723	330	8	.	.	PUNCT
ap-7723	331	1	https://doi.org/10.1007/978-88-7642-378-9	https://doi.org/10.1007/978-88-7642-378-9	X
ap-7723	331	2	.	.	PUNCT
ap-7723	332	1	[	[	X
ap-7723	332	2	9	9	NUM
ap-7723	332	3	]	]	X
ap-7723	332	4	h.	h.	PROPN
ap-7723	332	5	bergeron	bergeron	PROPN
ap-7723	332	6	,	,	PUNCT
ap-7723	332	7	j.-p	j.-p	PROPN
ap-7723	332	8	.	.	PUNCT
ap-7723	333	1	gazeau	gazeau	PROPN
ap-7723	333	2	.	.	PUNCT
ap-7723	334	1	integral	integral	ADJ
ap-7723	334	2	quantizations	quantization	NOUN
ap-7723	334	3	with	with	ADP
ap-7723	334	4	two	two	NUM
ap-7723	334	5	basic	basic	ADJ
ap-7723	334	6	examples	example	NOUN
ap-7723	334	7	.	.	PUNCT
ap-7723	335	1	annals	annal	NOUN
ap-7723	335	2	of	of	ADP
ap-7723	335	3	physics	physics	PROPN
ap-7723	335	4	344:43–68	344:43–68	NUM
ap-7723	335	5	,	,	PUNCT
ap-7723	335	6	2014	2014	NUM
ap-7723	335	7	.	.	PUNCT
ap-7723	336	1	https://doi.org/10.1016/j.aop.2014.02.008	https://doi.org/10.1016/j.aop.2014.02.008	NOUN
ap-7723	336	2	.	.	PUNCT
ap-7723	337	1	[	[	X
ap-7723	337	2	10	10	NUM
ap-7723	337	3	]	]	X
ap-7723	337	4	w.	w.	PROPN
ap-7723	337	5	h.	h.	PROPN
ap-7723	337	6	mcmaster	mcmaster	PROPN
ap-7723	337	7	.	.	PUNCT
ap-7723	337	8	polarization	polarization	NOUN
ap-7723	337	9	and	and	CCONJ
ap-7723	337	10	the	the	DET
ap-7723	337	11	stokes	stoke	NOUN
ap-7723	337	12	parameters	parameter	NOUN
ap-7723	337	13	.	.	PUNCT
ap-7723	338	1	american	american	PROPN
ap-7723	338	2	journal	journal	PROPN
ap-7723	338	3	of	of	ADP
ap-7723	338	4	physics	physics	PROPN
ap-7723	338	5	22(6):351	22(6):351	PROPN
ap-7723	338	6	–	–	PUNCT
ap-7723	338	7	362	362	NUM
ap-7723	338	8	,	,	PUNCT
ap-7723	338	9	1954	1954	NUM
ap-7723	338	10	.	.	PUNCT
ap-7723	339	1	https://doi.org/10.1119/1.1933744	https://doi.org/10.1119/1.1933744	X
ap-7723	339	2	.	.	PUNCT
ap-7723	340	1	[	[	X
ap-7723	340	2	11	11	NUM
ap-7723	340	3	]	]	X
ap-7723	340	4	b.	b.	PROPN
ap-7723	340	5	schaefer	schaefer	PROPN
ap-7723	340	6	,	,	PUNCT
ap-7723	340	7	e.	e.	PROPN
ap-7723	340	8	collett	collett	PROPN
ap-7723	340	9	,	,	PUNCT
ap-7723	340	10	r.	r.	PROPN
ap-7723	340	11	smyth	smyth	PROPN
ap-7723	340	12	,	,	PUNCT
ap-7723	340	13	et	et	PROPN
ap-7723	340	14	al	al	PROPN
ap-7723	340	15	.	.	PROPN
ap-7723	340	16	measuring	measure	VERB
ap-7723	340	17	the	the	DET
ap-7723	340	18	stokes	stoke	NOUN
ap-7723	340	19	polarization	polarization	NOUN
ap-7723	340	20	parameters	parameter	NOUN
ap-7723	340	21	.	.	PUNCT
ap-7723	341	1	american	american	PROPN
ap-7723	341	2	journal	journal	PROPN
ap-7723	341	3	of	of	ADP
ap-7723	341	4	physics	physics	PROPN
ap-7723	341	5	75(2):163–168	75(2):163–168	PROPN
ap-7723	341	6	,	,	PUNCT
ap-7723	341	7	2007	2007	NUM
ap-7723	341	8	.	.	PUNCT
ap-7723	342	1	https://doi.org/10.1119/1.2386162	https://doi.org/10.1119/1.2386162	X
ap-7723	342	2	.	.	PUNCT
ap-7723	343	1	[	[	X
ap-7723	343	2	12	12	NUM
ap-7723	343	3	]	]	X
ap-7723	343	4	l.	l.	PROPN
ap-7723	343	5	d.	d.	PROPN
ap-7723	343	6	landau	landau	PROPN
ap-7723	343	7	,	,	PUNCT
ap-7723	343	8	e.	e.	PROPN
ap-7723	343	9	m.	m.	PROPN
ap-7723	343	10	lifshitz	lifshitz	PROPN
ap-7723	343	11	.	.	PUNCT
ap-7723	344	1	the	the	DET
ap-7723	344	2	classical	classical	ADJ
ap-7723	344	3	theory	theory	NOUN
ap-7723	344	4	of	of	ADP
ap-7723	344	5	fields	field	NOUN
ap-7723	344	6	.	.	PUNCT
ap-7723	345	1	vol	vol	NOUN
ap-7723	345	2	.	.	PROPN
ap-7723	346	1	2	2	NUM
ap-7723	346	2	.	.	PUNCT
ap-7723	346	3	(	(	PUNCT
ap-7723	346	4	4th	4th	ADJ
ap-7723	346	5	ed	ed	NOUN
ap-7723	346	6	.	.	PUNCT
ap-7723	346	7	)	)	PUNCT
ap-7723	346	8	.	.	PUNCT
ap-7723	347	1	butterworth	butterworth	PROPN
ap-7723	347	2	-	-	PUNCT
ap-7723	347	3	heinemann	heinemann	PROPN
ap-7723	347	4	,	,	PUNCT
ap-7723	347	5	1975	1975	NUM
ap-7723	347	6	.	.	PUNCT
ap-7723	348	1	isbn	isbn	ADJ
ap-7723	348	2	978	978	NUM
ap-7723	348	3	-	-	SYM
ap-7723	348	4	0	0	NUM
ap-7723	348	5	-	-	PUNCT
ap-7723	348	6	7506	7506	NUM
ap-7723	348	7	-	-	PUNCT
ap-7723	348	8	2768	2768	NUM
ap-7723	348	9	-	-	SYM
ap-7723	348	10	9	9	NUM
ap-7723	348	11	.	.	PUNCT
ap-7723	349	1	[	[	X
ap-7723	349	2	13	13	NUM
ap-7723	349	3	]	]	PUNCT
ap-7723	349	4	j.	j.	PROPN
ap-7723	349	5	s.	s.	PROPN
ap-7723	349	6	bell	bell	PROPN
ap-7723	349	7	.	.	PUNCT
ap-7723	350	1	on	on	ADP
ap-7723	350	2	the	the	DET
ap-7723	350	3	einstein	einstein	NOUN
ap-7723	350	4	-	-	PUNCT
ap-7723	350	5	podolsky	podolsky	NOUN
ap-7723	350	6	-	-	PUNCT
ap-7723	350	7	rosen	rosen	PROPN
ap-7723	350	8	paradox	paradox	NOUN
ap-7723	350	9	.	.	PUNCT
ap-7723	351	1	physics	physics	NOUN
ap-7723	351	2	1(3):195–200	1(3):195–200	NUM
ap-7723	351	3	,	,	PUNCT
ap-7723	351	4	1964	1964	NUM
ap-7723	351	5	.	.	PUNCT
ap-7723	352	1	https	https	NOUN
ap-7723	352	2	:	:	PUNCT
ap-7723	352	3	//doi.org/10.1103	//doi.org/10.1103	X
ap-7723	352	4	/	/	SYM
ap-7723	352	5	physicsphysiquefizika.1.195	physicsphysiquefizika.1.195	NOUN
ap-7723	352	6	.	.	PUNCT
ap-7723	353	1	[	[	X
ap-7723	353	2	14	14	NUM
ap-7723	353	3	]	]	X
ap-7723	353	4	d.	d.	PROPN
ap-7723	353	5	bohm	bohm	PROPN
ap-7723	353	6	.	.	PUNCT
ap-7723	354	1	a	a	DET
ap-7723	354	2	suggested	suggest	VERB
ap-7723	354	3	interpretation	interpretation	NOUN
ap-7723	354	4	of	of	ADP
ap-7723	354	5	the	the	DET
ap-7723	354	6	quantum	quantum	NOUN
ap-7723	354	7	theory	theory	NOUN
ap-7723	354	8	in	in	ADP
ap-7723	354	9	terms	term	NOUN
ap-7723	354	10	of	of	ADP
ap-7723	354	11	“	"	PUNCT
ap-7723	354	12	hidden	hidden	ADJ
ap-7723	354	13	”	"	PUNCT
ap-7723	354	14	variables	variable	NOUN
ap-7723	354	15	.	.	PUNCT
ap-7723	355	1	i.	i.	PROPN
ap-7723	355	2	physical	physical	PROPN
ap-7723	355	3	review	review	PROPN
ap-7723	355	4	85(2):166–179	85(2):166–179	PROPN
ap-7723	355	5	,	,	PUNCT
ap-7723	355	6	1952	1952	NUM
ap-7723	355	7	.	.	PUNCT
ap-7723	356	1	https://doi.org/10.1103/physrev.85.166	https://doi.org/10.1103/physrev.85.166	PROPN
ap-7723	356	2	.	.	PROPN
ap-7723	356	3	15	15	NUM
ap-7723	356	4	https://doi.org/10.1080/00927879508825218	https://doi.org/10.1080/00927879508825218	NOUN
ap-7723	356	5	https://doi.org/10.1142/s0129055x19500132	https://doi.org/10.1142/s0129055x19500132	NUM
ap-7723	356	6	https://doi.org/10.1007/bf01883517	https://doi.org/10.1007/bf01883517	PROPN
ap-7723	356	7	https://doi.org/10.1007/s13538-019-00652-x	https://doi.org/10.1007/s13538-019-00652-x	PROPN
ap-7723	356	8	https://arxiv.org/abs/2108.04086	https://arxiv.org/abs/2108.04086	VERB
ap-7723	356	9	https://doi.org/10.1016/s0034-4877(17)30035-6	https://doi.org/10.1016/s0034-4877(17)30035-6	ADP
ap-7723	356	10	https://doi.org/10.1007/978-88-7642-378-9	https://doi.org/10.1007/978-88-7642-378-9	PROPN
ap-7723	356	11	https://doi.org/10.1016/j.aop.2014.02.008	https://doi.org/10.1016/j.aop.2014.02.008	PROPN
ap-7723	356	12	https://doi.org/10.1119/1.1933744	https://doi.org/10.1119/1.1933744	PROPN
ap-7723	356	13	https://doi.org/10.1119/1.2386162	https://doi.org/10.1119/1.2386162	PROPN
ap-7723	356	14	https://doi.org/10.1103/physicsphysiquefizika.1.195	https://doi.org/10.1103/physicsphysiquefizika.1.195	PROPN
ap-7723	356	15	https://doi.org/10.1103/physicsphysiquefizika.1.195	https://doi.org/10.1103/physicsphysiquefizika.1.195	PROPN
ap-7723	356	16	https://doi.org/10.1103/physrev.85.166	https://doi.org/10.1103/physrev.85.166	PROPN
ap-7723	356	17	acta	acta	PROPN
ap-7723	356	18	polytechnica	polytechnica	PROPN
ap-7723	356	19	62(1):8–15	62(1):8–15	PROPN
ap-7723	356	20	,	,	PUNCT
ap-7723	356	21	2022	2022	NUM
ap-7723	356	22	1	1	NUM
ap-7723	356	23	introduction	introduction	NOUN
ap-7723	356	24	2	2	NUM
ap-7723	356	25	background	background	NOUN
ap-7723	356	26	2.1	2.1	NUM
ap-7723	356	27	definition	definition	NOUN
ap-7723	356	28	of	of	ADP
ap-7723	356	29	povms	povms	NOUN
ap-7723	356	30	2.2	2.2	NUM
ap-7723	356	31	integral	integral	ADJ
ap-7723	356	32	quantization	quantization	NOUN
ap-7723	356	33	3	3	NUM
ap-7723	356	34	euclidean	euclidean	ADJ
ap-7723	356	35	plane	plane	NOUN
ap-7723	356	36	as	as	ADP
ap-7723	356	37	hilbert	hilbert	NOUN
ap-7723	356	38	space	space	NOUN
ap-7723	356	39	of	of	ADP
ap-7723	356	40	quantum	quantum	ADJ
ap-7723	356	41	states	state	NOUN
ap-7723	356	42	3.1	3.1	NUM
ap-7723	356	43	mixed	mix	VERB
ap-7723	356	44	states	state	NOUN
ap-7723	356	45	as	as	SCONJ
ap-7723	356	46	density	density	NOUN
ap-7723	356	47	matrices	matrix	NOUN
ap-7723	356	48	3.2	3.2	NUM
ap-7723	356	49	describing	describe	VERB
ap-7723	356	50	non	non	ADJ
ap-7723	356	51	-	-	ADJ
ap-7723	356	52	commutativity	commutativity	ADJ
ap-7723	356	53	and	and	CCONJ
ap-7723	356	54	finding	find	VERB
ap-7723	356	55	naimark	naimark	ADJ
ap-7723	356	56	extensions	extension	NOUN
ap-7723	356	57	through	through	ADP
ap-7723	356	58	rotations	rotation	NOUN
ap-7723	356	59	3.3	3.3	NUM
ap-7723	356	60	linear	linear	ADJ
ap-7723	356	61	polarization	polarization	NOUN
ap-7723	356	62	of	of	ADP
ap-7723	356	63	light	light	NOUN
ap-7723	356	64	as	as	ADP
ap-7723	356	65	a	a	DET
ap-7723	356	66	quantum	quantum	ADJ
ap-7723	356	67	phenomenon	phenomenon	NOUN
ap-7723	356	68	4	4	NUM
ap-7723	356	69	entanglement	entanglement	NOUN
ap-7723	356	70	and	and	CCONJ
ap-7723	356	71	isomorphisms	isomorphism	VERB
ap-7723	356	72	4.1	4.1	NUM
ap-7723	356	73	bell	bell	PROPN
ap-7723	356	74	states	state	NOUN
ap-7723	356	75	and	and	CCONJ
ap-7723	356	76	quantum	quantum	NOUN
ap-7723	356	77	correlations	correlation	NOUN
ap-7723	356	78	4.2	4.2	NUM
ap-7723	356	79	bell	bell	NOUN
ap-7723	356	80	inequality	inequality	NOUN
ap-7723	356	81	and	and	CCONJ
ap-7723	356	82	its	its	PRON
ap-7723	356	83	violation	violation	NOUN
ap-7723	356	84	4.3	4.3	NUM
ap-7723	356	85	entanglement	entanglement	NOUN
ap-7723	356	86	of	of	ADP
ap-7723	356	87	two	two	NUM
ap-7723	356	88	angles	angle	NOUN
ap-7723	356	89	5	5	NUM
ap-7723	356	90	conclusions	conclusion	NOUN
ap-7723	356	91	acknowledgements	acknowledgement	NOUN
ap-7723	356	92	references	reference	NOUN