id	sid	tid	token	lemma	pos
ap-1874	1	1	acta	acta	PROPN
ap-1874	1	2	polytechnica	polytechnica	PROPN
ap-1874	1	3	doi:10.14311	doi:10.14311	PROPN
ap-1874	1	4	/	/	SYM
ap-1874	1	5	ap.2013.53.0470	ap.2013.53.0470	PROPN
ap-1874	1	6	acta	acta	PROPN
ap-1874	1	7	polytechnica	polytechnica	PROPN
ap-1874	1	8	53(5):470–472	53(5):470–472	PROPN
ap-1874	1	9	,	,	PUNCT
ap-1874	1	10	2013	2013	NUM
ap-1874	1	11	©	©	PROPN
ap-1874	1	12	czech	czech	PROPN
ap-1874	1	13	technical	technical	PROPN
ap-1874	1	14	university	university	PROPN
ap-1874	1	15	in	in	ADP
ap-1874	1	16	prague	prague	PROPN
ap-1874	1	17	,	,	PUNCT
ap-1874	1	18	2013	2013	NUM
ap-1874	1	19	available	available	ADJ
ap-1874	1	20	online	online	ADV
ap-1874	1	21	at	at	ADP
ap-1874	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1874	1	23	the	the	DET
ap-1874	1	24	number	number	NOUN
ap-1874	1	25	of	of	ADP
ap-1874	1	26	orthogonal	orthogonal	ADJ
ap-1874	1	27	conjugations	conjugation	NOUN
ap-1874	1	28	armin	armin	PROPN
ap-1874	1	29	uhlmann∗	uhlmann∗	PROPN
ap-1874	1	30	university	university	PROPN
ap-1874	1	31	of	of	ADP
ap-1874	1	32	leipzig	leipzig	PROPN
ap-1874	1	33	,	,	PUNCT
ap-1874	1	34	institute	institute	NOUN
ap-1874	1	35	for	for	ADP
ap-1874	1	36	theoretical	theoretical	ADJ
ap-1874	1	37	physics	physics	NOUN
ap-1874	1	38	,	,	PUNCT
ap-1874	1	39	pb	pb	ADP
ap-1874	1	40	:	:	PUNCT
ap-1874	1	41	100920	100920	NUM
ap-1874	1	42	,	,	PUNCT
ap-1874	1	43	d-04009	d-04009	PROPN
ap-1874	1	44	leipzig	leipzig	PROPN
ap-1874	1	45	,	,	PUNCT
ap-1874	1	46	germany	germany	PROPN
ap-1874	1	47	.	.	PUNCT
ap-1874	2	1	∗	∗	NOUN
ap-1874	2	2	corresponding	correspond	VERB
ap-1874	2	3	author	author	NOUN
ap-1874	2	4	:	:	PUNCT
ap-1874	2	5	armin.uhlmann@t-online.de	armin.uhlmann@t-online.de	ADJ
ap-1874	2	6	abstract	abstract	NOUN
ap-1874	2	7	.	.	PUNCT
ap-1874	3	1	after	after	ADP
ap-1874	3	2	a	a	DET
ap-1874	3	3	short	short	ADJ
ap-1874	3	4	introduction	introduction	NOUN
ap-1874	3	5	to	to	ADP
ap-1874	3	6	anti	anti	ADJ
ap-1874	3	7	-	-	ADJ
ap-1874	3	8	linearity	linearity	ADJ
ap-1874	3	9	,	,	PUNCT
ap-1874	3	10	bounds	bound	VERB
ap-1874	3	11	for	for	ADP
ap-1874	3	12	the	the	DET
ap-1874	3	13	number	number	NOUN
ap-1874	3	14	of	of	ADP
ap-1874	3	15	orthogonal	orthogonal	ADJ
ap-1874	3	16	(	(	PUNCT
ap-1874	3	17	skew	skew	NOUN
ap-1874	3	18	)	)	PUNCT
ap-1874	3	19	conjugations	conjugation	NOUN
ap-1874	3	20	are	be	AUX
ap-1874	3	21	proved	prove	VERB
ap-1874	3	22	.	.	PUNCT
ap-1874	4	1	they	they	PRON
ap-1874	4	2	are	be	AUX
ap-1874	4	3	saturated	saturate	VERB
ap-1874	4	4	if	if	SCONJ
ap-1874	4	5	the	the	DET
ap-1874	4	6	dimension	dimension	NOUN
ap-1874	4	7	of	of	ADP
ap-1874	4	8	the	the	DET
ap-1874	4	9	hilbert	hilbert	NOUN
ap-1874	4	10	space	space	NOUN
ap-1874	4	11	is	be	AUX
ap-1874	4	12	a	a	DET
ap-1874	4	13	power	power	NOUN
ap-1874	4	14	of	of	ADP
ap-1874	4	15	two	two	NUM
ap-1874	4	16	.	.	PUNCT
ap-1874	5	1	for	for	ADP
ap-1874	5	2	other	other	ADJ
ap-1874	5	3	dimensions	dimension	NOUN
ap-1874	5	4	this	this	PRON
ap-1874	5	5	is	be	AUX
ap-1874	5	6	an	an	DET
ap-1874	5	7	open	open	ADJ
ap-1874	5	8	problem	problem	NOUN
ap-1874	5	9	.	.	PUNCT
ap-1874	6	1	keywords	keyword	NOUN
ap-1874	6	2	:	:	PUNCT
ap-1874	6	3	anti(conjugate	anti(conjugate	PROPN
ap-1874	6	4	)	)	PUNCT
ap-1874	6	5	linearity	linearity	NOUN
ap-1874	6	6	,	,	PUNCT
ap-1874	6	7	canonical	canonical	ADJ
ap-1874	6	8	hermitian	hermitian	ADJ
ap-1874	6	9	form	form	NOUN
ap-1874	6	10	,	,	PUNCT
ap-1874	6	11	(	(	PUNCT
ap-1874	6	12	skew	skew	NOUN
ap-1874	6	13	)	)	PUNCT
ap-1874	6	14	conjugations	conjugation	NOUN
ap-1874	6	15	.	.	PUNCT
ap-1874	7	1	submitted	submit	VERB
ap-1874	7	2	:	:	PUNCT
ap-1874	7	3	31	31	NUM
ap-1874	7	4	march	march	NOUN
ap-1874	7	5	2013	2013	NUM
ap-1874	7	6	.	.	PUNCT
ap-1874	8	1	accepted	accept	VERB
ap-1874	8	2	:	:	PUNCT
ap-1874	8	3	1	1	NUM
ap-1874	8	4	may	may	PROPN
ap-1874	8	5	2013	2013	NUM
ap-1874	8	6	.	.	PUNCT
ap-1874	9	1	1	1	X
ap-1874	9	2	.	.	X
ap-1874	9	3	introduction	introduction	NOUN
ap-1874	9	4	the	the	DET
ap-1874	9	5	use	use	NOUN
ap-1874	9	6	of	of	ADP
ap-1874	9	7	anti	anti	ADJ
ap-1874	9	8	-	-	ADJ
ap-1874	9	9	linear	linear	ADJ
ap-1874	9	10	or	or	CCONJ
ap-1874	9	11	,	,	PUNCT
ap-1874	9	12	as	as	SCONJ
ap-1874	9	13	mathematicians	mathematician	NOUN
ap-1874	9	14	call	call	VERB
ap-1874	9	15	it	it	PRON
ap-1874	9	16	,	,	PUNCT
ap-1874	9	17	conjugate	conjugate	ADJ
ap-1874	9	18	linear	linear	ADJ
ap-1874	9	19	operators	operator	NOUN
ap-1874	9	20	in	in	ADP
ap-1874	9	21	physics	physics	NOUN
ap-1874	9	22	goes	go	VERB
ap-1874	9	23	back	back	ADV
ap-1874	9	24	to	to	ADP
ap-1874	9	25	e.	e.	PROPN
ap-1874	9	26	p.	p.	PROPN
ap-1874	9	27	wigner	wigner	NOUN
ap-1874	9	28	,	,	PUNCT
ap-1874	9	29	[	[	X
ap-1874	9	30	11	11	NUM
ap-1874	9	31	]	]	PUNCT
ap-1874	9	32	.	.	PUNCT
ap-1874	10	1	wigner	wigner	NOUN
ap-1874	10	2	also	also	ADV
ap-1874	10	3	discovered	discover	VERB
ap-1874	10	4	the	the	DET
ap-1874	10	5	structure	structure	NOUN
ap-1874	10	6	of	of	ADP
ap-1874	10	7	anti	anti	ADJ
ap-1874	10	8	-	-	ADJ
ap-1874	10	9	unitary	unitary	ADJ
ap-1874	10	10	operators	operator	NOUN
ap-1874	10	11	,	,	PUNCT
ap-1874	10	12	[	[	X
ap-1874	10	13	12	12	NUM
ap-1874	10	14	]	]	PUNCT
ap-1874	10	15	,	,	PUNCT
ap-1874	10	16	in	in	ADP
ap-1874	10	17	finite	finite	ADJ
ap-1874	10	18	dimensional	dimensional	ADJ
ap-1874	10	19	hilbert	hilbert	NOUN
ap-1874	10	20	spaces	space	NOUN
ap-1874	10	21	.	.	PUNCT
ap-1874	11	1	the	the	DET
ap-1874	11	2	essential	essential	ADJ
ap-1874	11	3	difference	difference	NOUN
ap-1874	11	4	from	from	ADP
ap-1874	11	5	the	the	DET
ap-1874	11	6	linear	linear	ADJ
ap-1874	11	7	case	case	NOUN
ap-1874	11	8	is	be	AUX
ap-1874	11	9	the	the	DET
ap-1874	11	10	existence	existence	NOUN
ap-1874	11	11	of	of	ADP
ap-1874	11	12	2	2	NUM
ap-1874	11	13	-	-	PUNCT
ap-1874	11	14	dimensional	dimensional	ADJ
ap-1874	11	15	irreducible	irreducible	ADJ
ap-1874	11	16	subspaces	subspace	NOUN
ap-1874	11	17	so	so	SCONJ
ap-1874	11	18	that	that	SCONJ
ap-1874	11	19	the	the	DET
ap-1874	11	20	hilbert	hilbert	PROPN
ap-1874	11	21	space	space	NOUN
ap-1874	11	22	decomposes	decompose	VERB
ap-1874	11	23	into	into	ADP
ap-1874	11	24	a	a	DET
ap-1874	11	25	direct	direct	ADJ
ap-1874	11	26	sum	sum	NOUN
ap-1874	11	27	of	of	ADP
ap-1874	11	28	1and	1and	NUM
ap-1874	11	29	2	2	NUM
ap-1874	11	30	-	-	PUNCT
ap-1874	11	31	dimensional	dimensional	ADJ
ap-1874	11	32	invariant	invariant	ADJ
ap-1874	11	33	spaces	space	NOUN
ap-1874	11	34	in	in	ADP
ap-1874	11	35	general	general	ADJ
ap-1874	11	36	.	.	PUNCT
ap-1874	12	1	later	later	ADV
ap-1874	12	2	on	on	ADV
ap-1874	12	3	,	,	PUNCT
ap-1874	12	4	f.	f.	PROPN
ap-1874	12	5	herbut	herbut	PROPN
ap-1874	12	6	and	and	CCONJ
ap-1874	12	7	m.	m.	NOUN
ap-1874	12	8	vujičić	vujičić	PROPN
ap-1874	12	9	were	be	AUX
ap-1874	12	10	able	able	ADJ
ap-1874	12	11	to	to	PART
ap-1874	12	12	clarify	clarify	VERB
ap-1874	12	13	the	the	DET
ap-1874	12	14	structure	structure	NOUN
ap-1874	12	15	of	of	ADP
ap-1874	12	16	anti	anti	ADJ
ap-1874	12	17	-	-	ADJ
ap-1874	12	18	linear	linear	ADJ
ap-1874	12	19	normal	normal	ADJ
ap-1874	12	20	operators	operator	NOUN
ap-1874	12	21	,	,	PUNCT
ap-1874	12	22	[	[	X
ap-1874	12	23	4	4	NUM
ap-1874	12	24	]	]	PUNCT
ap-1874	12	25	,	,	PUNCT
ap-1874	12	26	by	by	ADP
ap-1874	12	27	proving	prove	VERB
ap-1874	12	28	that	that	SCONJ
ap-1874	12	29	such	such	DET
ap-1874	12	30	a	a	DET
ap-1874	12	31	decomposition	decomposition	NOUN
ap-1874	12	32	also	also	ADV
ap-1874	12	33	exists	exist	VERB
ap-1874	12	34	for	for	ADP
ap-1874	12	35	anti	anti	ADJ
ap-1874	12	36	-	-	ADJ
ap-1874	12	37	linear	linear	ADJ
ap-1874	12	38	normal	normal	ADJ
ap-1874	12	39	operators	operator	NOUN
ap-1874	12	40	.	.	PUNCT
ap-1874	13	1	while	while	SCONJ
ap-1874	13	2	any	any	DET
ap-1874	13	3	linear	linear	ADJ
ap-1874	13	4	operator	operator	NOUN
ap-1874	13	5	allows	allow	VERB
ap-1874	13	6	for	for	ADP
ap-1874	13	7	a	a	DET
ap-1874	13	8	jordan	jordan	PROPN
ap-1874	13	9	decomposition	decomposition	NOUN
ap-1874	13	10	,	,	PUNCT
ap-1874	13	11	i	i	PRON
ap-1874	13	12	do	do	AUX
ap-1874	13	13	not	not	PART
ap-1874	13	14	know	know	VERB
ap-1874	13	15	a	a	DET
ap-1874	13	16	similar	similar	ADJ
ap-1874	13	17	decomposition	decomposition	NOUN
ap-1874	13	18	of	of	ADP
ap-1874	13	19	an	an	DET
ap-1874	13	20	arbitrary	arbitrary	ADJ
ap-1874	13	21	anti	anti	ADJ
ap-1874	13	22	-	-	ADJ
ap-1874	13	23	linear	linear	ADJ
ap-1874	13	24	operator	operator	NOUN
ap-1874	13	25	.	.	PUNCT
ap-1874	14	1	in	in	ADP
ap-1874	14	2	the	the	DET
ap-1874	14	3	main	main	ADJ
ap-1874	14	4	part	part	NOUN
ap-1874	14	5	of	of	ADP
ap-1874	14	6	the	the	DET
ap-1874	14	7	paper	paper	NOUN
ap-1874	14	8	there	there	PRON
ap-1874	14	9	is	be	VERB
ap-1874	14	10	no	no	DET
ap-1874	14	11	discussion	discussion	NOUN
ap-1874	14	12	of	of	ADP
ap-1874	14	13	what	what	PRON
ap-1874	14	14	is	be	AUX
ap-1874	14	15	happening	happen	VERB
ap-1874	14	16	in	in	ADP
ap-1874	14	17	case	case	NOUN
ap-1874	14	18	of	of	ADP
ap-1874	14	19	an	an	DET
ap-1874	14	20	infinite	infinite	ADJ
ap-1874	14	21	dimensional	dimensional	ADJ
ap-1874	14	22	hilbert	hilbert	NOUN
ap-1874	14	23	space	space	NOUN
ap-1874	14	24	.	.	PUNCT
ap-1874	15	1	there	there	PRON
ap-1874	15	2	are	be	VERB
ap-1874	15	3	,	,	PUNCT
ap-1874	15	4	however	however	ADV
ap-1874	15	5	,	,	PUNCT
ap-1874	15	6	several	several	ADJ
ap-1874	15	7	important	important	ADJ
ap-1874	15	8	issues	issue	NOUN
ap-1874	15	9	both	both	PRON
ap-1874	15	10	in	in	ADP
ap-1874	15	11	physics	physics	NOUN
ap-1874	15	12	and	and	CCONJ
ap-1874	15	13	in	in	ADP
ap-1874	15	14	mathematics	mathematic	NOUN
ap-1874	15	15	:	:	PUNCT
ap-1874	15	16	a	a	DET
ap-1874	15	17	motivation	motivation	NOUN
ap-1874	15	18	of	of	ADP
ap-1874	15	19	wigner	wigner	NOUN
ap-1874	15	20	was	be	AUX
ap-1874	15	21	in	in	ADP
ap-1874	15	22	the	the	DET
ap-1874	15	23	prominent	prominent	ADJ
ap-1874	15	24	application	application	NOUN
ap-1874	15	25	of	of	ADP
ap-1874	15	26	(	(	PUNCT
ap-1874	15	27	skew	skew	NOUN
ap-1874	15	28	)	)	PUNCT
ap-1874	15	29	conjugations	conjugation	NOUN
ap-1874	15	30	,	,	PUNCT
ap-1874	15	31	(	(	PUNCT
ap-1874	15	32	see	see	VERB
ap-1874	15	33	the	the	DET
ap-1874	15	34	next	next	ADJ
ap-1874	15	35	section	section	NOUN
ap-1874	15	36	for	for	ADP
ap-1874	15	37	definitions	definition	NOUN
ap-1874	15	38	)	)	PUNCT
ap-1874	15	39	,	,	PUNCT
ap-1874	15	40	to	to	ADP
ap-1874	15	41	time	time	NOUN
ap-1874	15	42	reversal	reversal	NOUN
ap-1874	15	43	symmetry	symmetry	NOUN
ap-1874	15	44	and	and	CCONJ
ap-1874	15	45	related	relate	VERB
ap-1874	15	46	inexecutable	inexecutable	ADJ
ap-1874	15	47	symmetries	symmetry	NOUN
ap-1874	15	48	.	.	PUNCT
ap-1874	16	1	it	it	PRON
ap-1874	16	2	is	be	AUX
ap-1874	16	3	impossible	impossible	ADJ
ap-1874	16	4	to	to	PART
ap-1874	16	5	give	give	VERB
ap-1874	16	6	credit	credit	NOUN
ap-1874	16	7	to	to	ADP
ap-1874	16	8	the	the	DET
ap-1874	16	9	many	many	ADJ
ap-1874	16	10	beautiful	beautiful	ADJ
ap-1874	16	11	results	result	NOUN
ap-1874	16	12	in	in	ADP
ap-1874	16	13	elementary	elementary	ADJ
ap-1874	16	14	particle	particle	NOUN
ap-1874	16	15	physics	physics	PROPN
ap-1874	16	16	and	and	CCONJ
ap-1874	16	17	in	in	ADP
ap-1874	16	18	minkowski	minkowski	ADJ
ap-1874	16	19	quantum	quantum	NOUN
ap-1874	16	20	field	field	NOUN
ap-1874	16	21	theory	theory	NOUN
ap-1874	16	22	in	in	ADP
ap-1874	16	23	this	this	DET
ap-1874	16	24	domain	domain	NOUN
ap-1874	16	25	.	.	PUNCT
ap-1874	17	1	however	however	ADV
ap-1874	17	2	,	,	PUNCT
ap-1874	17	3	it	it	PRON
ap-1874	17	4	is	be	AUX
ap-1874	17	5	perhaps	perhaps	ADV
ap-1874	17	6	worthwhile	worthwhile	ADJ
ap-1874	17	7	to	to	PART
ap-1874	17	8	note	note	VERB
ap-1874	17	9	the	the	DET
ap-1874	17	10	following	following	NOUN
ap-1874	17	11	:	:	PUNCT
ap-1874	17	12	the	the	DET
ap-1874	17	13	cpt	cpt	NOUN
ap-1874	17	14	-	-	NOUN
ap-1874	17	15	operator	operator	NOUN
ap-1874	17	16	,	,	PUNCT
ap-1874	17	17	the	the	DET
ap-1874	17	18	combination	combination	NOUN
ap-1874	17	19	of	of	ADP
ap-1874	17	20	particle	particle	NOUN
ap-1874	17	21	conjugation	conjugation	NOUN
ap-1874	17	22	c	c	NOUN
ap-1874	17	23	,	,	PUNCT
ap-1874	17	24	parity	parity	NOUN
ap-1874	17	25	operator	operator	NOUN
ap-1874	17	26	p	p	NOUN
ap-1874	17	27	,	,	PUNCT
ap-1874	17	28	and	and	CCONJ
ap-1874	17	29	time	time	NOUN
ap-1874	17	30	-	-	PUNCT
ap-1874	17	31	reversal	reversal	NOUN
ap-1874	17	32	t	t	PROPN
ap-1874	17	33	,	,	PUNCT
ap-1874	17	34	is	be	AUX
ap-1874	17	35	an	an	DET
ap-1874	17	36	anti	anti	ADJ
ap-1874	17	37	-	-	ADJ
ap-1874	17	38	unitary	unitary	ADJ
ap-1874	17	39	operator	operator	NOUN
ap-1874	17	40	acting	act	VERB
ap-1874	17	41	on	on	ADP
ap-1874	17	42	bosons	boson	NOUN
ap-1874	17	43	as	as	ADP
ap-1874	17	44	a	a	DET
ap-1874	17	45	conjugation	conjugation	NOUN
ap-1874	17	46	and	and	CCONJ
ap-1874	17	47	on	on	ADP
ap-1874	17	48	fermions	fermion	NOUN
ap-1874	17	49	as	as	ADP
ap-1874	17	50	a	a	DET
ap-1874	17	51	skew	skew	ADJ
ap-1874	17	52	conjugation	conjugation	NOUN
ap-1874	17	53	.	.	PUNCT
ap-1874	18	1	it	it	PRON
ap-1874	18	2	is	be	AUX
ap-1874	18	3	a	a	DET
ap-1874	18	4	genuine	genuine	ADJ
ap-1874	18	5	symmetry	symmetry	NOUN
ap-1874	18	6	of	of	ADP
ap-1874	18	7	any	any	DET
ap-1874	18	8	relativistic	relativistic	ADJ
ap-1874	18	9	quantum	quantum	NOUN
ap-1874	18	10	field	field	NOUN
ap-1874	18	11	theory	theory	NOUN
ap-1874	18	12	in	in	ADP
ap-1874	18	13	minkowski	minkowski	ADJ
ap-1874	18	14	space	space	NOUN
ap-1874	18	15	.	.	PUNCT
ap-1874	19	1	the	the	DET
ap-1874	19	2	proof	proof	NOUN
ap-1874	19	3	is	be	AUX
ap-1874	19	4	a	a	DET
ap-1874	19	5	masterpiece	masterpiece	NOUN
ap-1874	19	6	of	of	ADP
ap-1874	19	7	r.	r.	PROPN
ap-1874	19	8	jost	jost	PROPN
ap-1874	19	9	,	,	PUNCT
ap-1874	19	10	[	[	X
ap-1874	19	11	7	7	NUM
ap-1874	19	12	]	]	PUNCT
ap-1874	19	13	.	.	PUNCT
ap-1874	20	1	a	a	DET
ap-1874	20	2	further	further	ADJ
ap-1874	20	3	remarkable	remarkable	ADJ
ap-1874	20	4	feature	feature	NOUN
ap-1874	20	5	of	of	ADP
ap-1874	20	6	anti	anti	ADJ
ap-1874	20	7	-	-	ADJ
ap-1874	20	8	linearity	linearity	NOUN
ap-1874	20	9	is	be	AUX
ap-1874	20	10	shown	show	VERB
ap-1874	20	11	by	by	ADP
ap-1874	20	12	cpt	cpt	PROPN
ap-1874	20	13	.	.	PUNCT
ap-1874	21	1	this	this	DET
ap-1874	21	2	operator	operator	NOUN
ap-1874	21	3	is	be	AUX
ap-1874	21	4	defined	define	VERB
ap-1874	21	5	up	up	ADP
ap-1874	21	6	to	to	ADP
ap-1874	21	7	the	the	DET
ap-1874	21	8	choice	choice	NOUN
ap-1874	21	9	of	of	ADP
ap-1874	21	10	the	the	DET
ap-1874	21	11	point	point	NOUN
ap-1874	21	12	x	x	PUNCT
ap-1874	21	13	in	in	ADP
ap-1874	21	14	minkowski	minkowski	ADJ
ap-1874	21	15	space	space	NOUN
ap-1874	21	16	on	on	ADP
ap-1874	21	17	which	which	PRON
ap-1874	21	18	pt	pt	NOUN
ap-1874	21	19	acts	act	VERB
ap-1874	21	20	as	as	ADP
ap-1874	21	21	x→	x→	PROPN
ap-1874	21	22	−x	−x	NOUN
ap-1874	21	23	.	.	PUNCT
ap-1874	22	1	calling	call	VERB
ap-1874	22	2	this	this	DET
ap-1874	22	3	specific	specific	ADJ
ap-1874	22	4	form	form	NOUN
ap-1874	22	5	cptx	cptx	NOUN
ap-1874	22	6	,	,	PUNCT
ap-1874	22	7	one	one	NUM
ap-1874	22	8	quite	quite	ADV
ap-1874	22	9	forwardly	forwardly	ADV
ap-1874	22	10	shows	show	VERB
ap-1874	22	11	that	that	SCONJ
ap-1874	22	12	the	the	DET
ap-1874	22	13	linear	linear	ADJ
ap-1874	22	14	operator	operator	NOUN
ap-1874	22	15	cptxcpty	cptxcpty	NOUN
ap-1874	22	16	is	be	AUX
ap-1874	22	17	representing	represent	VERB
ap-1874	22	18	the	the	DET
ap-1874	22	19	translation	translation	NOUN
ap-1874	22	20	by	by	ADP
ap-1874	22	21	the	the	DET
ap-1874	22	22	vector	vector	NOUN
ap-1874	22	23	2(x−	2(x−	PROPN
ap-1874	22	24	y	y	NOUN
ap-1874	22	25	)	)	PUNCT
ap-1874	22	26	.	.	PUNCT
ap-1874	23	1	the	the	DET
ap-1874	23	2	particular	particular	ADJ
ap-1874	23	3	feature	feature	NOUN
ap-1874	23	4	in	in	ADP
ap-1874	23	5	the	the	DET
ap-1874	23	6	example	example	NOUN
ap-1874	23	7	at	at	ADP
ap-1874	23	8	hand	hand	NOUN
ap-1874	23	9	is	be	AUX
ap-1874	23	10	the	the	DET
ap-1874	23	11	splitting	splitting	NOUN
ap-1874	23	12	of	of	ADP
ap-1874	23	13	an	an	DET
ap-1874	23	14	executable	executable	ADJ
ap-1874	23	15	symmetry	symmetry	NOUN
ap-1874	23	16	operation	operation	NOUN
ap-1874	23	17	into	into	ADP
ap-1874	23	18	the	the	DET
ap-1874	23	19	product	product	NOUN
ap-1874	23	20	of	of	ADP
ap-1874	23	21	two	two	NUM
ap-1874	23	22	anti	anti	ADJ
ap-1874	23	23	-	-	ADJ
ap-1874	23	24	linear	linear	ADJ
ap-1874	23	25	ones	one	NOUN
ap-1874	23	26	.	.	PUNCT
ap-1874	24	1	this	this	DET
ap-1874	24	2	feature	feature	NOUN
ap-1874	24	3	can	can	AUX
ap-1874	24	4	be	be	AUX
ap-1874	24	5	observed	observe	VERB
ap-1874	24	6	also	also	ADV
ap-1874	24	7	in	in	ADP
ap-1874	24	8	some	some	DET
ap-1874	24	9	completely	completely	ADV
ap-1874	24	10	different	different	ADJ
ap-1874	24	11	situations	situation	NOUN
ap-1874	24	12	.	.	PUNCT
ap-1874	25	1	an	an	DET
ap-1874	25	2	example	example	NOUN
ap-1874	25	3	is	be	AUX
ap-1874	25	4	the	the	DET
ap-1874	25	5	possibility	possibility	NOUN
ap-1874	25	6	to	to	PART
ap-1874	25	7	write	write	VERB
ap-1874	25	8	the	the	DET
ap-1874	25	9	output	output	NOUN
ap-1874	25	10	of	of	ADP
ap-1874	25	11	quantum	quantum	NOUN
ap-1874	25	12	teleportation	teleportation	NOUN
ap-1874	25	13	,	,	PUNCT
ap-1874	25	14	as	as	SCONJ
ap-1874	25	15	introduced	introduce	VERB
ap-1874	25	16	by	by	ADP
ap-1874	25	17	bennett	bennett	PROPN
ap-1874	25	18	et	et	PROPN
ap-1874	25	19	al	al	PROPN
ap-1874	25	20	.	.	PUNCT
ap-1874	26	1	[	[	X
ap-1874	26	2	1	1	NUM
ap-1874	26	3	]	]	PUNCT
ap-1874	26	4	,	,	PUNCT
ap-1874	26	5	[	[	X
ap-1874	26	6	2	2	NUM
ap-1874	26	7	,	,	PUNCT
ap-1874	26	8	8	8	NUM
ap-1874	26	9	]	]	PUNCT
ap-1874	26	10	,	,	PUNCT
ap-1874	26	11	as	as	ADP
ap-1874	26	12	the	the	DET
ap-1874	26	13	action	action	NOUN
ap-1874	26	14	of	of	ADP
ap-1874	26	15	the	the	DET
ap-1874	26	16	product	product	NOUN
ap-1874	26	17	of	of	ADP
ap-1874	26	18	two	two	NUM
ap-1874	26	19	anti	anti	ADJ
ap-1874	26	20	-	-	ADJ
ap-1874	26	21	linear	linear	ADJ
ap-1874	26	22	ones	one	NOUN
ap-1874	26	23	on	on	ADP
ap-1874	26	24	the	the	DET
ap-1874	26	25	input	input	NOUN
ap-1874	26	26	state	state	NOUN
ap-1874	26	27	vector	vector	NOUN
ap-1874	26	28	,	,	PUNCT
ap-1874	26	29	see	see	VERB
ap-1874	26	30	[	[	X
ap-1874	26	31	3	3	NUM
ap-1874	26	32	,	,	PUNCT
ap-1874	26	33	9	9	NUM
ap-1874	26	34	,	,	PUNCT
ap-1874	26	35	10	10	NUM
ap-1874	26	36	]	]	PUNCT
ap-1874	26	37	.	.	PUNCT
ap-1874	27	1	these	these	DET
ap-1874	27	2	few	few	ADJ
ap-1874	27	3	sketched	sketched	ADJ
ap-1874	27	4	examples	example	NOUN
ap-1874	27	5	may	may	AUX
ap-1874	27	6	hopefully	hopefully	ADV
ap-1874	27	7	convince	convince	VERB
ap-1874	27	8	the	the	DET
ap-1874	27	9	reader	reader	NOUN
ap-1874	27	10	that	that	SCONJ
ap-1874	27	11	studying	study	VERB
ap-1874	27	12	anti	anti	ADJ
ap-1874	27	13	-	-	ADJ
ap-1874	27	14	linearity	linearity	NOUN
ap-1874	27	15	is	be	AUX
ap-1874	27	16	quite	quite	ADV
ap-1874	27	17	reasonable	reasonable	ADJ
ap-1874	27	18	—	—	PUNCT
ap-1874	27	19	though	though	SCONJ
ap-1874	27	20	the	the	DET
ap-1874	27	21	topic	topic	NOUN
ap-1874	27	22	of	of	ADP
ap-1874	27	23	the	the	DET
ap-1874	27	24	present	present	ADJ
ap-1874	27	25	paper	paper	NOUN
ap-1874	27	26	is	be	AUX
ap-1874	27	27	by	by	ADP
ap-1874	27	28	far	far	ADV
ap-1874	27	29	not	not	PART
ap-1874	27	30	so	so	ADV
ap-1874	27	31	spectacular	spectacular	ADJ
ap-1874	27	32	.	.	PUNCT
ap-1874	28	1	the	the	DET
ap-1874	28	2	next	next	ADJ
ap-1874	28	3	two	two	NUM
ap-1874	28	4	sections	section	NOUN
ap-1874	28	5	provide	provide	VERB
ap-1874	28	6	a	a	DET
ap-1874	28	7	mini	mini	NOUN
ap-1874	28	8	-	-	NOUN
ap-1874	28	9	introduction	introduction	NOUN
ap-1874	28	10	to	to	ADP
ap-1874	28	11	anti	anti	ADJ
ap-1874	28	12	-	-	ADJ
ap-1874	28	13	linearity	linearity	ADJ
ap-1874	28	14	.	.	PUNCT
ap-1874	29	1	in	in	ADP
ap-1874	29	2	the	the	DET
ap-1874	29	3	last	last	ADJ
ap-1874	29	4	one	one	NOUN
ap-1874	29	5	it	it	PRON
ap-1874	29	6	is	be	AUX
ap-1874	29	7	proved	prove	VERB
ap-1874	29	8	that	that	SCONJ
ap-1874	29	9	the	the	DET
ap-1874	29	10	number	number	NOUN
ap-1874	29	11	of	of	ADP
ap-1874	29	12	mutually	mutually	ADV
ap-1874	29	13	orthogonal	orthogonal	ADJ
ap-1874	29	14	(	(	PUNCT
ap-1874	29	15	skew	skew	NOUN
ap-1874	29	16	)	)	PUNCT
ap-1874	29	17	conjugations	conjugation	NOUN
ap-1874	29	18	is	be	AUX
ap-1874	29	19	maximal	maximal	ADJ
ap-1874	29	20	if	if	SCONJ
ap-1874	29	21	the	the	DET
ap-1874	29	22	dimension	dimension	NOUN
ap-1874	29	23	of	of	ADP
ap-1874	29	24	the	the	DET
ap-1874	29	25	hilbert	hilbert	NOUN
ap-1874	29	26	space	space	NOUN
ap-1874	29	27	is	be	AUX
ap-1874	29	28	a	a	DET
ap-1874	29	29	power	power	NOUN
ap-1874	29	30	of	of	ADP
ap-1874	29	31	two	two	NUM
ap-1874	29	32	.	.	PUNCT
ap-1874	30	1	it	it	PRON
ap-1874	30	2	is	be	AUX
ap-1874	30	3	conjectured	conjecture	VERB
ap-1874	30	4	that	that	SCONJ
ap-1874	30	5	there	there	PRON
ap-1874	30	6	are	be	VERB
ap-1874	30	7	no	no	DET
ap-1874	30	8	other	other	ADJ
ap-1874	30	9	dimensions	dimension	NOUN
ap-1874	30	10	for	for	ADP
ap-1874	30	11	which	which	PRON
ap-1874	30	12	this	this	DET
ap-1874	30	13	number	number	NOUN
ap-1874	30	14	reaches	reach	VERB
ap-1874	30	15	its	its	PRON
ap-1874	30	16	natural	natural	ADJ
ap-1874	30	17	upper	upper	ADJ
ap-1874	30	18	bound	bind	VERB
ap-1874	30	19	.	.	PUNCT
ap-1874	31	1	2	2	X
ap-1874	31	2	.	.	X
ap-1874	31	3	anti(or	anti(or	ADP
ap-1874	31	4	conjugate	conjugate	NOUN
ap-1874	31	5	)	)	PUNCT
ap-1874	31	6	linearity	linearity	NOUN
ap-1874	31	7	let	let	VERB
ap-1874	31	8	h	h	PRON
ap-1874	31	9	be	be	AUX
ap-1874	31	10	a	a	DET
ap-1874	31	11	complex	complex	ADJ
ap-1874	31	12	hilbert	hilbert	NOUN
ap-1874	31	13	space	space	NOUN
ap-1874	31	14	of	of	ADP
ap-1874	31	15	dimension	dimension	NOUN
ap-1874	32	1	d	d	X
ap-1874	32	2	<	<	X
ap-1874	32	3	∞.	∞.	PROPN
ap-1874	32	4	its	its	PRON
ap-1874	32	5	scalar	scalar	ADJ
ap-1874	32	6	product	product	NOUN
ap-1874	32	7	is	be	AUX
ap-1874	32	8	denoted	denote	VERB
ap-1874	32	9	by	by	ADP
ap-1874	32	10	〈	〈	PROPN
ap-1874	32	11	φb	φb	NOUN
ap-1874	32	12	,	,	PUNCT
ap-1874	32	13	φa	φa	ADP
ap-1874	32	14	〉	〉	NOUN
ap-1874	32	15	for	for	ADP
ap-1874	32	16	all	all	DET
ap-1874	32	17	φa	φa	ADP
ap-1874	32	18	,	,	PUNCT
ap-1874	32	19	φb	φb	PROPN
ap-1874	32	20	∈	∈	PROPN
ap-1874	32	21	h.	h.	NOUN
ap-1874	32	22	the	the	DET
ap-1874	32	23	scalar	scalar	ADJ
ap-1874	32	24	product	product	NOUN
ap-1874	32	25	is	be	AUX
ap-1874	32	26	assumed	assume	VERB
ap-1874	32	27	linear	linear	PROPN
ap-1874	32	28	in	in	ADP
ap-1874	32	29	φa	φa	PROPN
ap-1874	32	30	.	.	PUNCT
ap-1874	33	1	this	this	PRON
ap-1874	33	2	is	be	AUX
ap-1874	33	3	the	the	DET
ap-1874	33	4	“	"	PUNCT
ap-1874	33	5	physical	physical	ADJ
ap-1874	33	6	”	"	PUNCT
ap-1874	33	7	convention	convention	NOUN
ap-1874	33	8	going	go	VERB
ap-1874	33	9	back	back	ADV
ap-1874	33	10	to	to	ADP
ap-1874	33	11	e.	e.	PROPN
ap-1874	33	12	schrödinger	schrödinger	PROPN
ap-1874	33	13	.	.	PUNCT
ap-1874	34	1	1	1	NUM
ap-1874	34	2	is	be	AUX
ap-1874	34	3	the	the	DET
ap-1874	34	4	identity	identity	NOUN
ap-1874	34	5	operator	operator	NOUN
ap-1874	34	6	.	.	PUNCT
ap-1874	35	1	definition	definition	NOUN
ap-1874	35	2	1	1	NUM
ap-1874	35	3	.	.	PUNCT
ap-1874	36	1	an	an	DET
ap-1874	36	2	operator	operator	NOUN
ap-1874	36	3	ϑ	ϑ	VERB
ap-1874	36	4	acting	act	VERB
ap-1874	36	5	on	on	ADP
ap-1874	36	6	a	a	DET
ap-1874	36	7	complex	complex	ADJ
ap-1874	36	8	linear	linear	ADJ
ap-1874	36	9	space	space	NOUN
ap-1874	36	10	is	be	AUX
ap-1874	36	11	called	call	VERB
ap-1874	36	12	anti	anti	ADJ
ap-1874	36	13	-	-	ADJ
ap-1874	36	14	linear	linear	ADJ
ap-1874	36	15	or	or	CCONJ
ap-1874	36	16	,	,	PUNCT
ap-1874	36	17	equivalently	equivalently	ADV
ap-1874	36	18	,	,	PUNCT
ap-1874	36	19	conjugate	conjugate	ADJ
ap-1874	36	20	linear	linear	NOUN
ap-1874	36	21	if	if	SCONJ
ap-1874	36	22	it	it	PRON
ap-1874	36	23	obeys	obey	VERB
ap-1874	36	24	the	the	DET
ap-1874	36	25	relation	relation	NOUN
ap-1874	36	26	ϑ	ϑ	X
ap-1874	36	27	(	(	PUNCT
ap-1874	36	28	c1φ1	c1φ1	X
ap-1874	36	29	+	+	NUM
ap-1874	36	30	c2φ2	c2φ2	NOUN
ap-1874	36	31	)	)	PUNCT
ap-1874	37	1	=	=	SYM
ap-1874	37	2	c∗1ϑφ1	c∗1ϑφ1	NOUN
ap-1874	38	1	+	+	CCONJ
ap-1874	38	2	c∗2ϑφ2	c∗2ϑφ2	PROPN
ap-1874	38	3	,	,	PUNCT
ap-1874	38	4	cj	cj	PROPN
ap-1874	38	5	∈	∈	PROPN
ap-1874	38	6	c.	c.	PROPN
ap-1874	38	7	(	(	PUNCT
ap-1874	38	8	1	1	X
ap-1874	38	9	)	)	PUNCT
ap-1874	38	10	as	as	SCONJ
ap-1874	38	11	is	be	AUX
ap-1874	38	12	common	common	ADJ
ap-1874	38	13	use	use	NOUN
ap-1874	38	14	,	,	PUNCT
ap-1874	38	15	b(h	b(h	PROPN
ap-1874	38	16	)	)	PUNCT
ap-1874	38	17	denotes	denote	VERB
ap-1874	38	18	the	the	DET
ap-1874	38	19	set	set	NOUN
ap-1874	38	20	(	(	PUNCT
ap-1874	38	21	algebra	algebra	NOUN
ap-1874	38	22	)	)	PUNCT
ap-1874	38	23	of	of	ADP
ap-1874	38	24	all	all	DET
ap-1874	38	25	linear	linear	PROPN
ap-1874	38	26	operators	operator	NOUN
ap-1874	38	27	from	from	ADP
ap-1874	38	28	h	h	NOUN
ap-1874	38	29	into	into	ADP
ap-1874	38	30	itself	itself	PRON
ap-1874	38	31	.	.	PUNCT
ap-1874	39	1	the	the	DET
ap-1874	39	2	set	set	NOUN
ap-1874	39	3	(	(	PUNCT
ap-1874	39	4	linear	linear	ADJ
ap-1874	39	5	space	space	NOUN
ap-1874	39	6	)	)	PUNCT
ap-1874	39	7	of	of	ADP
ap-1874	39	8	all	all	DET
ap-1874	39	9	anti	anti	ADJ
ap-1874	39	10	-	-	ADJ
ap-1874	39	11	linear	linear	ADJ
ap-1874	39	12	operators	operator	NOUN
ap-1874	39	13	is	be	AUX
ap-1874	39	14	called	call	VERB
ap-1874	39	15	b(h)anti	b(h)anti	ADJ
ap-1874	39	16	.	.	PUNCT
ap-1874	40	1	anti	anti	ADJ
ap-1874	40	2	-	-	ADJ
ap-1874	40	3	linearity	linearity	ADJ
ap-1874	40	4	requires	require	VERB
ap-1874	40	5	a	a	DET
ap-1874	40	6	special	special	ADJ
ap-1874	40	7	definition	definition	NOUN
ap-1874	40	8	of	of	ADP
ap-1874	40	9	the	the	DET
ap-1874	40	10	hermitian	hermitian	ADJ
ap-1874	40	11	adjoint	adjoint	PROPN
ap-1874	40	12	.	.	PUNCT
ap-1874	41	1	definition	definition	NOUN
ap-1874	41	2	2	2	NUM
ap-1874	41	3	(	(	PUNCT
ap-1874	41	4	wigner	wigner	NOUN
ap-1874	41	5	)	)	PUNCT
ap-1874	41	6	.	.	PUNCT
ap-1874	42	1	the	the	DET
ap-1874	42	2	hermitian	hermitian	PROPN
ap-1874	42	3	adjoint	adjoint	PROPN
ap-1874	42	4	,	,	PUNCT
ap-1874	42	5	ϑ†	ϑ†	NOUN
ap-1874	42	6	,	,	PUNCT
ap-1874	42	7	of	of	ADP
ap-1874	42	8	ϑ	ϑ	X
ap-1874	42	9	∈	∈	NOUN
ap-1874	42	10	b(h)anti	b(h)anti	NOUN
ap-1874	42	11	is	be	AUX
ap-1874	42	12	defined	define	VERB
ap-1874	42	13	by	by	ADP
ap-1874	42	14	〈	〈	PROPN
ap-1874	42	15	φ1	φ1	PROPN
ap-1874	42	16	,	,	PUNCT
ap-1874	42	17	ϑ	ϑ	PROPN
ap-1874	42	18	†	†	PROPN
ap-1874	42	19	φ2	φ2	PROPN
ap-1874	42	20	〉	〉	PROPN
ap-1874	42	21	=	=	SYM
ap-1874	42	22	〈	〈	PROPN
ap-1874	42	23	φ2	φ2	PROPN
ap-1874	42	24	,	,	PUNCT
ap-1874	42	25	ϑ	ϑ	PROPN
ap-1874	42	26	φ1	φ1	PROPN
ap-1874	42	27	〉	〉	PROPN
ap-1874	42	28	,	,	PUNCT
ap-1874	42	29	φ1	φ1	PROPN
ap-1874	42	30	,	,	PUNCT
ap-1874	42	31	φ2	φ2	PROPN
ap-1874	42	32	∈	∈	PROPN
ap-1874	42	33	h.	h.	PROPN
ap-1874	42	34	(	(	PUNCT
ap-1874	42	35	2	2	NUM
ap-1874	42	36	)	)	PUNCT
ap-1874	42	37	470	470	NUM
ap-1874	42	38	http://dx.doi.org/10.14311/ap.2013.53.0470	http://dx.doi.org/10.14311/ap.2013.53.0470	NOUN
ap-1874	42	39	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-1874	42	40	vol	vol	NOUN
ap-1874	42	41	.	.	PUNCT
ap-1874	43	1	53	53	NUM
ap-1874	43	2	no	no	NOUN
ap-1874	43	3	.	.	PUNCT
ap-1874	44	1	5/2013	5/2013	NUM
ap-1874	44	2	the	the	DET
ap-1874	44	3	number	number	NOUN
ap-1874	44	4	of	of	ADP
ap-1874	44	5	orthogonal	orthogonal	ADJ
ap-1874	44	6	conjugations	conjugation	NOUN
ap-1874	44	7	a	a	DET
ap-1874	44	8	simple	simple	ADJ
ap-1874	44	9	but	but	CCONJ
ap-1874	44	10	important	important	ADJ
ap-1874	44	11	fact	fact	NOUN
ap-1874	44	12	is	be	AUX
ap-1874	44	13	seen	see	VERB
ap-1874	44	14	by	by	ADP
ap-1874	44	15	commuting	commute	VERB
ap-1874	44	16	ϑ	ϑ	PROPN
ap-1874	44	17	and	and	CCONJ
ap-1874	44	18	a	a	DET
ap-1874	44	19	=	=	X
ap-1874	44	20	c1	c1	NOUN
ap-1874	44	21	.	.	PUNCT
ap-1874	45	1	one	one	NUM
ap-1874	45	2	obtains	obtain	VERB
ap-1874	45	3	(	(	PUNCT
ap-1874	45	4	cϑ)†	cϑ)†	NOUN
ap-1874	45	5	=	=	SYM
ap-1874	45	6	cϑ†	cϑ†	PROPN
ap-1874	45	7	,	,	PUNCT
ap-1874	45	8	saying	say	VERB
ap-1874	45	9	:	:	PUNCT
ap-1874	45	10	ϑ→	ϑ→	ADP
ap-1874	45	11	ϑ†	ϑ†	X
ap-1874	45	12	is	be	AUX
ap-1874	45	13	a	a	DET
ap-1874	45	14	complex	complex	ADJ
ap-1874	45	15	linear	linear	ADJ
ap-1874	45	16	operation,(∑	operation,(∑	ADJ
ap-1874	45	17	cjϑj	cjϑj	NOUN
ap-1874	45	18	)	)	PUNCT
ap-1874	45	19	†	†	X
ap-1874	46	1	=	=	PUNCT
ap-1874	46	2	∑	∑	PUNCT
ap-1874	46	3	cjϑ	cjϑ	PROPN
ap-1874	46	4	†	†	PROPN
ap-1874	46	5	j	j	PROPN
ap-1874	46	6	.	.	PUNCT
ap-1874	47	1	(	(	PUNCT
ap-1874	47	2	3	3	X
ap-1874	47	3	)	)	PUNCT
ap-1874	47	4	this	this	PRON
ap-1874	47	5	is	be	AUX
ap-1874	47	6	an	an	DET
ap-1874	47	7	essential	essential	ADJ
ap-1874	47	8	difference	difference	NOUN
ap-1874	47	9	from	from	ADP
ap-1874	47	10	the	the	DET
ap-1874	47	11	linear	linear	ADJ
ap-1874	47	12	case	case	NOUN
ap-1874	47	13	:	:	PUNCT
ap-1874	47	14	taking	take	VERB
ap-1874	47	15	the	the	DET
ap-1874	47	16	hermitian	hermitian	ADJ
ap-1874	47	17	adjoint	adjoint	PROPN
ap-1874	47	18	is	be	AUX
ap-1874	47	19	a	a	DET
ap-1874	47	20	linear	linear	ADJ
ap-1874	47	21	operation	operation	NOUN
ap-1874	47	22	.	.	PUNCT
ap-1874	48	1	a	a	DET
ap-1874	48	2	similar	similar	ADJ
ap-1874	48	3	argument	argument	NOUN
ap-1874	48	4	shows	show	VERB
ap-1874	48	5	,	,	PUNCT
ap-1874	48	6	that	that	SCONJ
ap-1874	48	7	the	the	DET
ap-1874	48	8	eigenvalues	eigenvalue	NOUN
ap-1874	48	9	of	of	ADP
ap-1874	48	10	an	an	DET
ap-1874	48	11	anti	anti	ADJ
ap-1874	48	12	-	-	ADJ
ap-1874	48	13	linear	linear	ADJ
ap-1874	48	14	ϑ	ϑ	PRON
ap-1874	48	15	form	form	NOUN
ap-1874	48	16	circles	circle	NOUN
ap-1874	48	17	around	around	ADP
ap-1874	48	18	the	the	DET
ap-1874	48	19	null	null	ADJ
ap-1874	48	20	vector	vector	NOUN
ap-1874	48	21	.	.	PUNCT
ap-1874	49	1	if	if	SCONJ
ap-1874	49	2	there	there	PRON
ap-1874	49	3	is	be	VERB
ap-1874	49	4	at	at	ADV
ap-1874	49	5	least	least	ADJ
ap-1874	49	6	one	one	NUM
ap-1874	49	7	eigenvalue	eigenvalue	NOUN
ap-1874	49	8	and	and	CCONJ
ap-1874	49	9	d	d	NOUN
ap-1874	49	10	>	>	X
ap-1874	49	11	1	1	NUM
ap-1874	49	12	,	,	PUNCT
ap-1874	49	13	let	let	VERB
ap-1874	49	14	r	r	PRON
ap-1874	49	15	be	be	AUX
ap-1874	49	16	the	the	DET
ap-1874	49	17	radius	radius	NOUN
ap-1874	49	18	of	of	ADP
ap-1874	49	19	the	the	DET
ap-1874	49	20	largest	large	ADJ
ap-1874	49	21	such	such	ADJ
ap-1874	49	22	circle	circle	NOUN
ap-1874	49	23	.	.	PUNCT
ap-1874	50	1	the	the	DET
ap-1874	50	2	set	set	NOUN
ap-1874	50	3	of	of	ADP
ap-1874	50	4	all	all	DET
ap-1874	50	5	values	value	NOUN
ap-1874	50	6	〈	〈	PROPN
ap-1874	50	7	φ	φ	NOUN
ap-1874	50	8	,	,	PUNCT
ap-1874	50	9	ϑφ	ϑφ	PROPN
ap-1874	50	10	〉	〉	PROPN
ap-1874	50	11	,	,	PUNCT
ap-1874	50	12	φ	φ	NUM
ap-1874	50	13	running	run	VERB
ap-1874	50	14	through	through	ADP
ap-1874	50	15	all	all	DET
ap-1874	50	16	unit	unit	NOUN
ap-1874	50	17	vectors	vector	NOUN
ap-1874	50	18	,	,	PUNCT
ap-1874	50	19	is	be	AUX
ap-1874	50	20	the	the	DET
ap-1874	50	21	disk	disk	NOUN
ap-1874	50	22	with	with	ADP
ap-1874	50	23	radius	radius	PROPN
ap-1874	50	24	r.	r.	PROPN
ap-1874	50	25	see	see	VERB
ap-1874	51	1	[	[	X
ap-1874	51	2	6	6	NUM
ap-1874	51	3	]	]	PUNCT
ap-1874	51	4	for	for	ADP
ap-1874	51	5	the	the	DET
ap-1874	51	6	more	more	ADV
ap-1874	51	7	sophisticated	sophisticated	ADJ
ap-1874	51	8	real	real	ADJ
ap-1874	51	9	case	case	NOUN
ap-1874	51	10	.	.	PUNCT
ap-1874	52	1	we	we	PRON
ap-1874	52	2	need	need	VERB
ap-1874	52	3	some	some	DET
ap-1874	52	4	further	further	ADJ
ap-1874	52	5	definitions	definition	NOUN
ap-1874	52	6	.	.	PUNCT
ap-1874	53	1	definition	definition	NOUN
ap-1874	53	2	3	3	NUM
ap-1874	53	3	.	.	PUNCT
ap-1874	54	1	an	an	DET
ap-1874	54	2	anti	anti	ADJ
ap-1874	54	3	-	-	ADJ
ap-1874	54	4	linear	linear	ADJ
ap-1874	54	5	operator	operator	NOUN
ap-1874	54	6	ϑ	ϑ	NOUN
ap-1874	54	7	is	be	AUX
ap-1874	54	8	said	say	VERB
ap-1874	54	9	to	to	PART
ap-1874	54	10	be	be	AUX
ap-1874	54	11	hermitian	hermitian	ADJ
ap-1874	54	12	or	or	CCONJ
ap-1874	54	13	self	self	NOUN
ap-1874	54	14	-	-	PUNCT
ap-1874	54	15	adjoint	adjoint	NOUN
ap-1874	54	16	if	if	SCONJ
ap-1874	54	17	ϑ†	ϑ†	X
ap-1874	54	18	=	=	NOUN
ap-1874	54	19	ϑ.	ϑ.	NOUN
ap-1874	54	20	ϑ	ϑ	X
ap-1874	54	21	is	be	AUX
ap-1874	54	22	said	say	VERB
ap-1874	54	23	to	to	PART
ap-1874	54	24	be	be	AUX
ap-1874	54	25	skew	skew	ADJ
ap-1874	54	26	hermitian	hermitian	ADJ
ap-1874	54	27	or	or	CCONJ
ap-1874	54	28	skew	skew	ADJ
ap-1874	54	29	self	self	NOUN
ap-1874	54	30	-	-	PUNCT
ap-1874	54	31	adjoint	adjoint	NOUN
ap-1874	54	32	if	if	SCONJ
ap-1874	54	33	ϑ†	ϑ†	ADP
ap-1874	54	34	=	=	NOUN
ap-1874	54	35	−ϑ.	−ϑ.	DET
ap-1874	54	36	the	the	DET
ap-1874	54	37	linear	linear	ADJ
ap-1874	54	38	space	space	NOUN
ap-1874	54	39	of	of	ADP
ap-1874	54	40	all	all	DET
ap-1874	54	41	hermitian	hermitian	ADJ
ap-1874	54	42	(	(	PUNCT
ap-1874	54	43	skew	skew	ADJ
ap-1874	54	44	hermitian	hermitian	ADJ
ap-1874	54	45	)	)	PUNCT
ap-1874	54	46	anti	anti	ADJ
ap-1874	54	47	-	-	ADJ
ap-1874	54	48	linear	linear	ADJ
ap-1874	54	49	operators	operator	NOUN
ap-1874	54	50	are	be	AUX
ap-1874	54	51	denoted	denote	VERB
ap-1874	54	52	by	by	ADP
ap-1874	54	53	b(h)+	b(h)+	NOUN
ap-1874	54	54	anti	anti	X
ap-1874	54	55	respectively	respectively	ADV
ap-1874	54	56	b(h)−anti	b(h)−anti	PROPN
ap-1874	54	57	.	.	PUNCT
ap-1874	55	1	rank	rank	NOUN
ap-1874	55	2	-	-	PUNCT
ap-1874	55	3	one	one	NUM
ap-1874	55	4	linear	linear	NOUN
ap-1874	55	5	operators	operator	NOUN
ap-1874	55	6	are	be	AUX
ap-1874	55	7	as	as	ADV
ap-1874	55	8	usually	usually	ADV
ap-1874	55	9	written	write	VERB
ap-1874	55	10	(	(	PUNCT
ap-1874	55	11	|φ′〉〈φ′′|	|φ′〉〈φ′′|	X
ap-1874	55	12	)	)	PUNCT
ap-1874	56	1	φ	φ	NOUN
ap-1874	56	2	:	:	PUNCT
ap-1874	56	3	=	=	PUNCT
ap-1874	56	4	〈	〈	PROPN
ap-1874	56	5	φ′′	φ′′	PROPN
ap-1874	56	6	,	,	PUNCT
ap-1874	56	7	φ〉φ′	φ〉φ′	PROPN
ap-1874	56	8	,	,	PUNCT
ap-1874	56	9	and	and	CCONJ
ap-1874	56	10	we	we	PRON
ap-1874	56	11	define	define	VERB
ap-1874	56	12	similarly	similarly	ADV
ap-1874	56	13	(	(	PUNCT
ap-1874	56	14	|φ′〉〈φ′′|	|φ′〉〈φ′′|	ADV
ap-1874	56	15	)	)	PUNCT
ap-1874	56	16	anti	anti	NOUN
ap-1874	56	17	φ	φ	NOUN
ap-1874	56	18	:	:	PUNCT
ap-1874	56	19	=	=	PUNCT
ap-1874	56	20	〈	〈	PROPN
ap-1874	56	21	φ	φ	NUM
ap-1874	56	22	,	,	PUNCT
ap-1874	56	23	φ′′〉φ′	φ′′〉φ′	PROPN
ap-1874	56	24	,	,	PUNCT
ap-1874	56	25	(	(	PUNCT
ap-1874	56	26	4	4	X
ap-1874	56	27	)	)	PUNCT
ap-1874	56	28	projecting	project	VERB
ap-1874	56	29	any	any	DET
ap-1874	56	30	vector	vector	NOUN
ap-1874	56	31	φ	φ	X
ap-1874	56	32	onto	onto	ADP
ap-1874	56	33	a	a	DET
ap-1874	56	34	multiple	multiple	NOUN
ap-1874	56	35	of	of	ADP
ap-1874	56	36	φ′.	φ′.	ADJ
ap-1874	56	37	note	note	NOUN
ap-1874	56	38	that	that	SCONJ
ap-1874	56	39	we	we	PRON
ap-1874	56	40	do	do	AUX
ap-1874	56	41	not	not	PART
ap-1874	56	42	use	use	VERB
ap-1874	56	43	〈	〈	PROPN
ap-1874	56	44	φ′′|	φ′′|	PROPN
ap-1874	56	45	decoupled	decouple	VERB
ap-1874	56	46	from	from	ADP
ap-1874	56	47	its	its	PRON
ap-1874	56	48	other	other	ADJ
ap-1874	56	49	part	part	NOUN
ap-1874	56	50	.	.	PUNCT
ap-1874	57	1	we	we	PRON
ap-1874	57	2	do	do	AUX
ap-1874	57	3	not	not	PART
ap-1874	57	4	attach	attach	VERB
ap-1874	57	5	any	any	DET
ap-1874	57	6	meaning	meaning	NOUN
ap-1874	57	7	to	to	PART
ap-1874	57	8	〈	〈	VERB
ap-1874	57	9	φ′′|anti	φ′′|anti	PROPN
ap-1874	57	10	as	as	ADP
ap-1874	57	11	an	an	DET
ap-1874	57	12	expression	expression	NOUN
ap-1874	57	13	standing	stand	VERB
ap-1874	57	14	alone!1	alone!1	NOUN
ap-1874	57	15	an	an	DET
ap-1874	57	16	anti	anti	ADJ
ap-1874	57	17	-	-	ADJ
ap-1874	57	18	linear	linear	ADJ
ap-1874	57	19	operator	operator	NOUN
ap-1874	57	20	θ	θ	PROPN
ap-1874	57	21	is	be	AUX
ap-1874	57	22	called	call	VERB
ap-1874	57	23	a	a	DET
ap-1874	57	24	unitary	unitary	ADJ
ap-1874	57	25	operator	operator	NOUN
ap-1874	57	26	or	or	CCONJ
ap-1874	57	27	,	,	PUNCT
ap-1874	57	28	as	as	ADP
ap-1874	57	29	wigner	wigner	NOUN
ap-1874	57	30	used	use	VERB
ap-1874	57	31	to	to	PART
ap-1874	57	32	say	say	VERB
ap-1874	57	33	,	,	PUNCT
ap-1874	57	34	an	an	DET
ap-1874	57	35	anti	anti	ADJ
ap-1874	57	36	-	-	ADJ
ap-1874	57	37	unitary	unitary	ADJ
ap-1874	57	38	,	,	PUNCT
ap-1874	57	39	if	if	SCONJ
ap-1874	57	40	θ†	θ†	PROPN
ap-1874	57	41	=	=	SYM
ap-1874	57	42	θ−1	θ−1	PROPN
ap-1874	57	43	.	.	PUNCT
ap-1874	58	1	a	a	DET
ap-1874	58	2	conjugation	conjugation	NOUN
ap-1874	58	3	is	be	AUX
ap-1874	58	4	an	an	DET
ap-1874	58	5	anti	anti	ADJ
ap-1874	58	6	-	-	ADJ
ap-1874	58	7	unitary	unitary	ADJ
ap-1874	58	8	operator	operator	NOUN
ap-1874	58	9	which	which	PRON
ap-1874	58	10	is	be	AUX
ap-1874	58	11	hermitian	hermitian	ADJ
ap-1874	58	12	,	,	PUNCT
ap-1874	58	13	hence	hence	ADV
ap-1874	58	14	fulfilling	fulfil	VERB
ap-1874	58	15	θ2	θ2	PROPN
ap-1874	58	16	=	=	SYM
ap-1874	58	17	1	1	X
ap-1874	58	18	.	.	PUNCT
ap-1874	59	1	the	the	DET
ap-1874	59	2	anti	anti	ADJ
ap-1874	59	3	-	-	ADJ
ap-1874	59	4	unitary	unitary	ADJ
ap-1874	59	5	θ	θ	NOUN
ap-1874	59	6	will	will	AUX
ap-1874	59	7	be	be	AUX
ap-1874	59	8	called	call	VERB
ap-1874	59	9	a	a	DET
ap-1874	59	10	skew	skew	ADJ
ap-1874	59	11	conjugation	conjugation	NOUN
ap-1874	59	12	if	if	SCONJ
ap-1874	59	13	it	it	PRON
ap-1874	59	14	is	be	AUX
ap-1874	59	15	skew	skew	ADJ
ap-1874	59	16	hermitian	hermitian	ADJ
ap-1874	59	17	,	,	PUNCT
ap-1874	59	18	hence	hence	ADV
ap-1874	59	19	satisfying	satisfy	VERB
ap-1874	59	20	θ2	θ2	ADV
ap-1874	59	21	=	=	PUNCT
ap-1874	59	22	−1	−1	NOUN
ap-1874	59	23	.	.	PUNCT
ap-1874	60	1	3	3	X
ap-1874	60	2	.	.	X
ap-1874	60	3	the	the	DET
ap-1874	60	4	invariant	invariant	ADJ
ap-1874	60	5	hermitian	hermitian	ADJ
ap-1874	60	6	form	form	NOUN
ap-1874	60	7	while	while	SCONJ
ap-1874	60	8	the	the	DET
ap-1874	60	9	trace	trace	NOUN
ap-1874	60	10	of	of	ADP
ap-1874	60	11	an	an	DET
ap-1874	60	12	anti	anti	ADJ
ap-1874	60	13	-	-	ADJ
ap-1874	60	14	linear	linear	ADJ
ap-1874	60	15	operator	operator	NOUN
ap-1874	60	16	is	be	AUX
ap-1874	60	17	undefined	undefined	ADJ
ap-1874	60	18	,	,	PUNCT
ap-1874	60	19	the	the	DET
ap-1874	60	20	product	product	NOUN
ap-1874	60	21	of	of	ADP
ap-1874	60	22	two	two	NUM
ap-1874	60	23	anti	anti	ADJ
ap-1874	60	24	-	-	ADJ
ap-1874	60	25	linear	linear	ADJ
ap-1874	60	26	operators	operator	NOUN
ap-1874	60	27	is	be	AUX
ap-1874	60	28	linear	linear	ADJ
ap-1874	60	29	.	.	PUNCT
ap-1874	61	1	the	the	DET
ap-1874	61	2	trace	trace	NOUN
ap-1874	61	3	(	(	PUNCT
ap-1874	61	4	ϑ1	ϑ1	NOUN
ap-1874	61	5	,	,	PUNCT
ap-1874	61	6	ϑ2	ϑ2	PROPN
ap-1874	61	7	)	)	PUNCT
ap-1874	61	8	:	:	PUNCT
ap-1874	61	9	=	=	SYM
ap-1874	61	10	trϑ2ϑ1	trϑ2ϑ1	ADJ
ap-1874	61	11	(	(	PUNCT
ap-1874	61	12	5	5	X
ap-1874	61	13	)	)	PUNCT
ap-1874	61	14	will	will	AUX
ap-1874	61	15	be	be	AUX
ap-1874	61	16	called	call	VERB
ap-1874	61	17	the	the	DET
ap-1874	61	18	canonical	canonical	ADJ
ap-1874	61	19	hermitian	hermitian	ADJ
ap-1874	61	20	form	form	NOUN
ap-1874	61	21	,	,	PUNCT
ap-1874	61	22	or	or	CCONJ
ap-1874	61	23	just	just	ADV
ap-1874	61	24	the	the	DET
ap-1874	61	25	canonical	canonical	ADJ
ap-1874	61	26	form	form	NOUN
ap-1874	61	27	on	on	ADP
ap-1874	61	28	the	the	DET
ap-1874	61	29	the	the	DET
ap-1874	61	30	space	space	NOUN
ap-1874	61	31	of	of	ADP
ap-1874	61	32	anti	anti	ADJ
ap-1874	61	33	-	-	ADJ
ap-1874	61	34	linear	linear	ADJ
ap-1874	61	35	operators	operator	NOUN
ap-1874	61	36	.	.	PUNCT
ap-1874	62	1	an	an	DET
ap-1874	62	2	anti	anti	ADJ
ap-1874	62	3	-	-	ADJ
ap-1874	62	4	linear	linear	ADJ
ap-1874	62	5	ϑ	ϑ	NOUN
ap-1874	62	6	can	can	AUX
ap-1874	62	7	be	be	AUX
ap-1874	62	8	written	write	VERB
ap-1874	62	9	uniquely	uniquely	ADV
ap-1874	62	10	as	as	ADP
ap-1874	62	11	a	a	DET
ap-1874	62	12	sum	sum	NOUN
ap-1874	62	13	ϑ	ϑ	X
ap-1874	62	14	=	=	X
ap-1874	62	15	ϑ+	ϑ+	X
ap-1874	62	16	+	+	CCONJ
ap-1874	62	17	ϑ−	ϑ−	NOUN
ap-1874	62	18	of	of	ADP
ap-1874	62	19	an	an	DET
ap-1874	62	20	hermitian	hermitian	NOUN
ap-1874	62	21	and	and	CCONJ
ap-1874	62	22	a	a	DET
ap-1874	62	23	skew	skew	ADJ
ap-1874	62	24	hermitian	hermitian	ADJ
ap-1874	62	25	operator	operator	NOUN
ap-1874	62	26	with	with	ADP
ap-1874	62	27	ϑ→	ϑ→	NOUN
ap-1874	62	28	ϑ+	ϑ+	X
ap-1874	62	29	:	:	PUNCT
ap-1874	62	30	=	=	SYM
ap-1874	62	31	ϑ+	ϑ+	X
ap-1874	62	32	ϑ†	ϑ†	X
ap-1874	62	33	2	2	NUM
ap-1874	62	34	,	,	PUNCT
ap-1874	62	35	ϑ→	ϑ→	ADP
ap-1874	62	36	ϑ−	ϑ−	NOUN
ap-1874	62	37	:	:	PUNCT
ap-1874	62	38	=	=	SYM
ap-1874	62	39	ϑ−	ϑ−	NOUN
ap-1874	62	40	ϑ†	ϑ†	X
ap-1874	62	41	2	2	NUM
ap-1874	62	42	.	.	PUNCT
ap-1874	63	1	(	(	PUNCT
ap-1874	63	2	6	6	NUM
ap-1874	63	3	)	)	PUNCT
ap-1874	64	1	1though	1though	NUM
ap-1874	64	2	one	one	PRON
ap-1874	64	3	could	could	AUX
ap-1874	64	4	do	do	VERB
ap-1874	64	5	so	so	ADV
ap-1874	64	6	as	as	ADP
ap-1874	64	7	a	a	DET
ap-1874	64	8	conjugate	conjugate	ADJ
ap-1874	64	9	linear	linear	ADJ
ap-1874	64	10	form	form	NOUN
ap-1874	64	11	.	.	PUNCT
ap-1874	65	1	relying	rely	VERB
ap-1874	65	2	on	on	ADP
ap-1874	65	3	(	(	PUNCT
ap-1874	65	4	5	5	NUM
ap-1874	65	5	)	)	PUNCT
ap-1874	65	6	and	and	CCONJ
ap-1874	65	7	(	(	PUNCT
ap-1874	65	8	6	6	X
ap-1874	65	9	)	)	PUNCT
ap-1874	65	10	one	one	NUM
ap-1874	65	11	concludes	conclude	VERB
ap-1874	65	12	(	(	PUNCT
ap-1874	65	13	ϑ+	ϑ+	NOUN
ap-1874	65	14	,	,	PUNCT
ap-1874	65	15	ϑ+	ϑ+	NOUN
ap-1874	65	16	)	)	PUNCT
ap-1874	65	17	≥	≥	NOUN
ap-1874	65	18	0	0	NUM
ap-1874	65	19	,	,	PUNCT
ap-1874	65	20	(	(	PUNCT
ap-1874	65	21	ϑ−	ϑ−	PROPN
ap-1874	65	22	,	,	PUNCT
ap-1874	65	23	ϑ−	ϑ−	PROPN
ap-1874	65	24	)	)	PUNCT
ap-1874	65	25	≤	≤	NOUN
ap-1874	65	26	0	0	NUM
ap-1874	65	27	,	,	PUNCT
ap-1874	65	28	(	(	PUNCT
ap-1874	65	29	ϑ+	ϑ+	NOUN
ap-1874	65	30	,	,	PUNCT
ap-1874	65	31	ϑ−	ϑ−	NOUN
ap-1874	65	32	)	)	PUNCT
ap-1874	65	33	=	=	SYM
ap-1874	66	1	0	0	X
ap-1874	66	2	.	.	PUNCT
ap-1874	67	1	(	(	PUNCT
ap-1874	67	2	7	7	X
ap-1874	67	3	)	)	PUNCT
ap-1874	67	4	in	in	ADP
ap-1874	67	5	particular	particular	ADJ
ap-1874	67	6	,	,	PUNCT
ap-1874	67	7	equipped	equip	VERB
ap-1874	67	8	with	with	ADP
ap-1874	67	9	the	the	DET
ap-1874	67	10	canonical	canonical	ADJ
ap-1874	67	11	form	form	NOUN
ap-1874	67	12	,	,	PUNCT
ap-1874	67	13	b(h)+	b(h)+	X
ap-1874	67	14	anti	anti	X
ap-1874	67	15	becomes	become	VERB
ap-1874	67	16	an	an	DET
ap-1874	67	17	hilbert	hilbert	NOUN
ap-1874	67	18	space	space	NOUN
ap-1874	67	19	.	.	PUNCT
ap-1874	68	1	completely	completely	ADV
ap-1874	68	2	analogue	analogue	NOUN
ap-1874	68	3	,	,	PUNCT
ap-1874	68	4	−	−	PROPN
ap-1874	68	5	(	(	PUNCT
ap-1874	68	6	·	·	PUNCT
ap-1874	68	7	,	,	PUNCT
ap-1874	68	8	·	·	PUNCT
ap-1874	68	9	)	)	PUNCT
ap-1874	68	10	is	be	AUX
ap-1874	68	11	a	a	DET
ap-1874	68	12	positive	positive	ADJ
ap-1874	68	13	definite	definite	ADJ
ap-1874	68	14	scalar	scalar	ADJ
ap-1874	68	15	product	product	NOUN
ap-1874	68	16	on	on	ADP
ap-1874	68	17	b(h)−anti	b(h)−anti	NOUN
ap-1874	68	18	.	.	PUNCT
ap-1874	68	19	bases	basis	NOUN
ap-1874	68	20	of	of	ADP
ap-1874	68	21	these	these	DET
ap-1874	68	22	two	two	NUM
ap-1874	68	23	hilbert	hilbert	NOUN
ap-1874	68	24	spaces	space	NOUN
ap-1874	68	25	can	can	AUX
ap-1874	68	26	be	be	AUX
ap-1874	68	27	obtained	obtain	VERB
ap-1874	68	28	as	as	ADP
ap-1874	68	29	follows	follow	VERB
ap-1874	68	30	:	:	PUNCT
ap-1874	68	31	let	let	VERB
ap-1874	68	32	φ1	φ1	PROPN
ap-1874	68	33	,	,	PUNCT
ap-1874	68	34	φ2	φ2	PROPN
ap-1874	68	35	,	,	PUNCT
ap-1874	68	36	.	.	PUNCT
ap-1874	68	37	.	.	PUNCT
ap-1874	69	1	.	.	PUNCT
ap-1874	70	1	be	be	AUX
ap-1874	70	2	a	a	DET
ap-1874	70	3	basis	basis	NOUN
ap-1874	70	4	of	of	ADP
ap-1874	70	5	h.	h.	PROPN
ap-1874	70	6	then	then	ADV
ap-1874	70	7	(	(	PUNCT
ap-1874	70	8	|φj〉〈φj	|φj〉〈φj	ADJ
ap-1874	70	9	|	|	NOUN
ap-1874	70	10	)	)	PUNCT
ap-1874	70	11	anti	anti	ADJ
ap-1874	70	12	,	,	PUNCT
ap-1874	70	13	1√	1√	PROPN
ap-1874	70	14	2	2	NUM
ap-1874	70	15	(	(	PUNCT
ap-1874	70	16	(	(	PUNCT
ap-1874	70	17	|φj〉〈φk|	|φj〉〈φk|	X
ap-1874	70	18	)	)	PUNCT
ap-1874	71	1	anti	anti	X
ap-1874	71	2	+	+	CCONJ
ap-1874	71	3	(	(	PUNCT
ap-1874	71	4	|φk〉〈φj	|φk〉〈φj	NOUN
ap-1874	71	5	|	|	ADV
ap-1874	71	6	)	)	PUNCT
ap-1874	71	7	anti	anti	NOUN
ap-1874	71	8	)	)	PUNCT
ap-1874	71	9	,	,	PUNCT
ap-1874	71	10	(	(	PUNCT
ap-1874	71	11	8)	8)	NUM
ap-1874	71	12	where	where	SCONJ
ap-1874	71	13	j	j	PROPN
ap-1874	71	14	,	,	PUNCT
ap-1874	71	15	k	k	PROPN
ap-1874	71	16	=	=	SYM
ap-1874	71	17	1	1	NUM
ap-1874	71	18	,	,	PUNCT
ap-1874	71	19	.	.	PUNCT
ap-1874	71	20	.	.	PUNCT
ap-1874	71	21	.	.	PUNCT
ap-1874	72	1	,	,	PUNCT
ap-1874	72	2	d	d	NOUN
ap-1874	72	3	and	and	CCONJ
ap-1874	72	4	k	k	X
ap-1874	72	5	<	<	X
ap-1874	72	6	j	j	PROPN
ap-1874	72	7	,	,	PUNCT
ap-1874	72	8	is	be	AUX
ap-1874	72	9	a	a	DET
ap-1874	72	10	basis	basis	NOUN
ap-1874	72	11	of	of	ADP
ap-1874	72	12	b(h)+	b(h)+	PROPN
ap-1874	72	13	anti	anti	X
ap-1874	72	14	with	with	ADP
ap-1874	72	15	respect	respect	NOUN
ap-1874	72	16	to	to	ADP
ap-1874	72	17	the	the	DET
ap-1874	72	18	canonical	canonical	ADJ
ap-1874	72	19	form	form	NOUN
ap-1874	72	20	.	.	PUNCT
ap-1874	73	1	as	as	ADP
ap-1874	73	2	a	a	DET
ap-1874	73	3	basis	basis	NOUN
ap-1874	73	4	of	of	ADP
ap-1874	73	5	b(h)−anti	b(h)−anti	X
ap-1874	73	6	one	one	NOUN
ap-1874	73	7	can	can	AUX
ap-1874	73	8	use	use	VERB
ap-1874	73	9	the	the	DET
ap-1874	73	10	anti	anti	ADJ
ap-1874	73	11	-	-	ADJ
ap-1874	73	12	linear	linear	ADJ
ap-1874	73	13	operators	operator	NOUN
ap-1874	73	14	1√	1√	PROPN
ap-1874	73	15	2	2	NUM
ap-1874	73	16	(	(	PUNCT
ap-1874	73	17	(	(	PUNCT
ap-1874	73	18	|φj〉〈φk|	|φj〉〈φk|	X
ap-1874	73	19	)	)	PUNCT
ap-1874	73	20	anti	anti	ADJ
ap-1874	73	21	−	−	PROPN
ap-1874	73	22	(	(	PUNCT
ap-1874	73	23	|φk〉〈φj	|φk〉〈φj	NOUN
ap-1874	73	24	|	|	ADV
ap-1874	73	25	)	)	PUNCT
ap-1874	73	26	anti	anti	NOUN
ap-1874	73	27	)	)	PUNCT
ap-1874	73	28	.	.	PUNCT
ap-1874	74	1	(	(	PUNCT
ap-1874	74	2	9	9	NUM
ap-1874	74	3	)	)	PUNCT
ap-1874	74	4	by	by	ADP
ap-1874	74	5	counting	count	VERB
ap-1874	74	6	basis	basis	NOUN
ap-1874	74	7	lengths	length	NOUN
ap-1874	74	8	one	one	PRON
ap-1874	74	9	gets	get	VERB
ap-1874	74	10	dimb(h)±anti	dimb(h)±anti	ADJ
ap-1874	74	11	=	=	PUNCT
ap-1874	74	12	d(d±	d(d±	NOUN
ap-1874	74	13	1	1	NUM
ap-1874	74	14	)	)	PUNCT
ap-1874	74	15	2	2	NUM
ap-1874	74	16	.	.	PUNCT
ap-1874	75	1	(	(	PUNCT
ap-1874	75	2	10	10	NUM
ap-1874	75	3	)	)	PUNCT
ap-1874	75	4	it	it	PRON
ap-1874	75	5	follows	follow	VERB
ap-1874	75	6	:	:	PUNCT
ap-1874	75	7	the	the	DET
ap-1874	75	8	signature	signature	NOUN
ap-1874	75	9	of	of	ADP
ap-1874	75	10	the	the	DET
ap-1874	75	11	canonical	canonical	ADJ
ap-1874	75	12	hermitian	hermitian	ADJ
ap-1874	75	13	form	form	NOUN
ap-1874	75	14	is	be	AUX
ap-1874	75	15	equal	equal	ADJ
ap-1874	75	16	to	to	ADP
ap-1874	75	17	d	d	NOUN
ap-1874	75	18	=	=	SYM
ap-1874	75	19	dimh	dimh	PROPN
ap-1874	75	20	.	.	PUNCT
ap-1874	76	1	indeed	indeed	ADV
ap-1874	76	2	,	,	PUNCT
ap-1874	76	3	dimb(h)+	dimb(h)+	PUNCT
ap-1874	76	4	anti	anti	ADJ
ap-1874	76	5	−	−	PROPN
ap-1874	76	6	dimb(h)−anti	dimb(h)−anti	X
ap-1874	76	7	=	=	NOUN
ap-1874	76	8	dimh	dimh	PROPN
ap-1874	76	9	.	.	PUNCT
ap-1874	77	1	(	(	PUNCT
ap-1874	77	2	11	11	NUM
ap-1874	77	3	)	)	SYM
ap-1874	77	4	4	4	NUM
ap-1874	77	5	.	.	PUNCT
ap-1874	77	6	orthogonal	orthogonal	ADJ
ap-1874	77	7	(	(	PUNCT
ap-1874	77	8	skew	skew	NOUN
ap-1874	77	9	)	)	PUNCT
ap-1874	77	10	conjugations	conjugation	NOUN
ap-1874	77	11	the	the	DET
ap-1874	77	12	anti	anti	ADJ
ap-1874	77	13	-	-	ADJ
ap-1874	77	14	linear	linear	ADJ
ap-1874	77	15	(	(	PUNCT
ap-1874	77	16	skew	skew	NOUN
ap-1874	77	17	)	)	PUNCT
ap-1874	77	18	hermitian	hermitian	ADJ
ap-1874	77	19	operators	operator	NOUN
ap-1874	77	20	are	be	AUX
ap-1874	77	21	the	the	DET
ap-1874	77	22	elements	element	NOUN
ap-1874	77	23	of	of	ADP
ap-1874	77	24	hilbert	hilbert	PROPN
ap-1874	77	25	spaces	space	NOUN
ap-1874	77	26	.	.	PUNCT
ap-1874	78	1	their	their	PRON
ap-1874	78	2	scalar	scalar	ADJ
ap-1874	78	3	products	product	NOUN
ap-1874	78	4	are	be	AUX
ap-1874	78	5	restrictions	restriction	NOUN
ap-1874	78	6	of	of	ADP
ap-1874	78	7	the	the	DET
ap-1874	78	8	canonical	canonical	ADJ
ap-1874	78	9	form	form	NOUN
ap-1874	78	10	(	(	PUNCT
ap-1874	78	11	up	up	ADP
ap-1874	78	12	to	to	ADP
ap-1874	78	13	a	a	DET
ap-1874	78	14	sign	sign	NOUN
ap-1874	78	15	in	in	ADP
ap-1874	78	16	the	the	DET
ap-1874	78	17	skew	skew	ADJ
ap-1874	78	18	case	case	NOUN
ap-1874	78	19	)	)	PUNCT
ap-1874	78	20	.	.	PUNCT
ap-1874	79	1	it	it	PRON
ap-1874	79	2	is	be	AUX
ap-1874	79	3	therefore	therefore	ADV
ap-1874	79	4	a	a	DET
ap-1874	79	5	legitimate	legitimate	ADJ
ap-1874	79	6	question	question	NOUN
ap-1874	79	7	to	to	PART
ap-1874	79	8	ask	ask	VERB
ap-1874	79	9	for	for	ADP
ap-1874	79	10	the	the	DET
ap-1874	79	11	maximal	maximal	ADJ
ap-1874	79	12	number	number	NOUN
ap-1874	79	13	of	of	ADP
ap-1874	79	14	mutually	mutually	ADV
ap-1874	79	15	orthogonal	orthogonal	ADJ
ap-1874	79	16	conjugation	conjugation	NOUN
ap-1874	79	17	or	or	CCONJ
ap-1874	79	18	skew	skew	ADJ
ap-1874	79	19	conjugations	conjugation	NOUN
ap-1874	79	20	.	.	PUNCT
ap-1874	80	1	these	these	DET
ap-1874	80	2	two	two	NUM
ap-1874	80	3	numbers	number	NOUN
ap-1874	80	4	depend	depend	VERB
ap-1874	80	5	on	on	ADP
ap-1874	80	6	the	the	DET
ap-1874	80	7	dimension	dimension	NOUN
ap-1874	80	8	d	d	NOUN
ap-1874	80	9	=	=	PUNCT
ap-1874	80	10	dimh	dimh	NOUN
ap-1874	80	11	of	of	ADP
ap-1874	80	12	the	the	DET
ap-1874	80	13	hilbert	hilbert	NOUN
ap-1874	80	14	space	space	NOUN
ap-1874	80	15	only	only	ADV
ap-1874	80	16	.	.	PUNCT
ap-1874	81	1	let	let	VERB
ap-1874	81	2	us	we	PRON
ap-1874	81	3	denote	denote	VERB
ap-1874	81	4	by	by	ADP
ap-1874	81	5	n+(d	n+(d	NOUN
ap-1874	81	6	)	)	PUNCT
ap-1874	81	7	the	the	DET
ap-1874	81	8	maximal	maximal	ADJ
ap-1874	81	9	number	number	NOUN
ap-1874	81	10	of	of	ADP
ap-1874	81	11	orthogonal	orthogonal	ADJ
ap-1874	81	12	conjugations	conjugation	NOUN
ap-1874	81	13	and	and	CCONJ
ap-1874	81	14	by	by	ADP
ap-1874	81	15	n−(d	n−(d	PROPN
ap-1874	81	16	)	)	PUNCT
ap-1874	81	17	the	the	DET
ap-1874	81	18	maximal	maximal	ADJ
ap-1874	81	19	number	number	NOUN
ap-1874	81	20	of	of	ADP
ap-1874	81	21	skew	skew	ADJ
ap-1874	81	22	conjugations	conjugation	NOUN
ap-1874	81	23	.	.	PUNCT
ap-1874	82	1	by	by	ADP
ap-1874	82	2	(	(	PUNCT
ap-1874	82	3	10	10	NUM
ap-1874	82	4	)	)	PUNCT
ap-1874	82	5	it	it	PRON
ap-1874	82	6	is	be	AUX
ap-1874	82	7	n±(d	n±(d	PROPN
ap-1874	82	8	)	)	PUNCT
ap-1874	82	9	≤	≤	NUM
ap-1874	82	10	d(d±	d(d±	PROPN
ap-1874	82	11	1	1	NUM
ap-1874	82	12	)	)	PUNCT
ap-1874	82	13	2	2	NUM
ap-1874	82	14	.	.	PUNCT
ap-1874	83	1	(	(	PUNCT
ap-1874	83	2	12	12	NUM
ap-1874	83	3	)	)	PUNCT
ap-1874	83	4	to	to	PART
ap-1874	83	5	get	get	VERB
ap-1874	83	6	an	an	DET
ap-1874	83	7	estimation	estimation	NOUN
ap-1874	83	8	from	from	ADP
ap-1874	83	9	below	below	ADV
ap-1874	83	10	,	,	PUNCT
ap-1874	83	11	one	one	PRON
ap-1874	83	12	observes	observe	VERB
ap-1874	83	13	that	that	SCONJ
ap-1874	83	14	the	the	DET
ap-1874	83	15	tensor	tensor	NOUN
ap-1874	83	16	products	product	NOUN
ap-1874	83	17	of	of	ADP
ap-1874	83	18	two	two	NUM
ap-1874	83	19	conjugations	conjugation	NOUN
ap-1874	83	20	and	and	CCONJ
ap-1874	83	21	the	the	DET
ap-1874	83	22	tensor	tensor	NOUN
ap-1874	83	23	product	product	NOUN
ap-1874	83	24	of	of	ADP
ap-1874	83	25	two	two	NUM
ap-1874	83	26	skew	skew	ADJ
ap-1874	83	27	conjugations	conjugation	NOUN
ap-1874	83	28	are	be	AUX
ap-1874	83	29	conjugations	conjugation	NOUN
ap-1874	83	30	.	.	PUNCT
ap-1874	84	1	therefore	therefore	ADV
ap-1874	84	2	n+(d1d2	n+(d1d2	NOUN
ap-1874	84	3	)	)	PUNCT
ap-1874	84	4	≥	≥	NOUN
ap-1874	84	5	n+(d1)n+(d2	n+(d1)n+(d2	ADV
ap-1874	84	6	)	)	PUNCT
ap-1874	85	1	+	+	SYM
ap-1874	85	2	n−(d1)n−(d2	n−(d1)n−(d2	NOUN
ap-1874	85	3	)	)	PUNCT
ap-1874	85	4	(	(	PUNCT
ap-1874	85	5	13	13	NUM
ap-1874	85	6	)	)	PUNCT
ap-1874	85	7	and	and	CCONJ
ap-1874	85	8	,	,	PUNCT
ap-1874	85	9	similarly	similarly	ADV
ap-1874	85	10	,	,	PUNCT
ap-1874	85	11	n−(d1d2	n−(d1d2	PROPN
ap-1874	85	12	)	)	PUNCT
ap-1874	85	13	≥	≥	NOUN
ap-1874	85	14	n+(d1)n−(d2	n+(d1)n−(d2	ADV
ap-1874	85	15	)	)	PUNCT
ap-1874	86	1	+	+	SYM
ap-1874	86	2	n−(d1)n+(d2	n−(d1)n+(d2	ADV
ap-1874	86	3	)	)	PUNCT
ap-1874	86	4	(	(	PUNCT
ap-1874	86	5	14	14	NUM
ap-1874	86	6	)	)	PUNCT
ap-1874	86	7	because	because	SCONJ
ap-1874	86	8	the	the	DET
ap-1874	86	9	direct	direct	ADJ
ap-1874	86	10	product	product	NOUN
ap-1874	86	11	of	of	ADP
ap-1874	86	12	two	two	NUM
ap-1874	86	13	orthogonal	orthogonal	ADJ
ap-1874	86	14	(	(	PUNCT
ap-1874	86	15	skew	skew	NOUN
ap-1874	86	16	)	)	PUNCT
ap-1874	86	17	conjugations	conjugation	NOUN
ap-1874	86	18	is	be	AUX
ap-1874	86	19	orthogonal	orthogonal	ADJ
ap-1874	86	20	.	.	PUNCT
ap-1874	87	1	now	now	ADV
ap-1874	87	2	consider	consider	VERB
ap-1874	87	3	the	the	DET
ap-1874	87	4	case	case	NOUN
ap-1874	87	5	471	471	NUM
ap-1874	87	6	armin	armin	PROPN
ap-1874	87	7	uhlmann	uhlmann	PROPN
ap-1874	87	8	acta	acta	PROPN
ap-1874	87	9	polytechnica	polytechnica	PROPN
ap-1874	87	10	that	that	SCONJ
ap-1874	87	11	equality	equality	NOUN
ap-1874	87	12	holds	hold	VERB
ap-1874	87	13	in	in	ADP
ap-1874	87	14	(	(	PUNCT
ap-1874	87	15	12	12	NUM
ap-1874	87	16	)	)	PUNCT
ap-1874	87	17	for	for	ADP
ap-1874	87	18	d1	d1	PROPN
ap-1874	87	19	and	and	CCONJ
ap-1874	87	20	d2	d2	PROPN
ap-1874	87	21	.	.	PUNCT
ap-1874	88	1	then	then	ADV
ap-1874	88	2	one	one	PRON
ap-1874	88	3	gets	get	VERB
ap-1874	88	4	the	the	DET
ap-1874	88	5	inequality	inequality	NOUN
ap-1874	88	6	n+(d1d2	n+(d1d2	NOUN
ap-1874	88	7	)	)	PUNCT
ap-1874	88	8	≥	≥	NOUN
ap-1874	88	9	1	1	NUM
ap-1874	88	10	4	4	NUM
ap-1874	88	11	(	(	PUNCT
ap-1874	88	12	d1(d1	d1(d1	PROPN
ap-1874	88	13	+	+	PROPN
ap-1874	88	14	1)d2(d2	1)d2(d2	NUM
ap-1874	88	15	+	+	CCONJ
ap-1874	88	16	1	1	NUM
ap-1874	88	17	)	)	PUNCT
ap-1874	88	18	+	+	CCONJ
ap-1874	88	19	d1(d1	d1(d1	PRON
ap-1874	88	20	−	−	PROPN
ap-1874	88	21	1)d2(d2	1)d2(d2	NUM
ap-1874	88	22	−	−	PROPN
ap-1874	88	23	1	1	NUM
ap-1874	88	24	)	)	PUNCT
ap-1874	88	25	)	)	PUNCT
ap-1874	88	26	and	and	CCONJ
ap-1874	88	27	its	its	PRON
ap-1874	88	28	right	right	ADJ
ap-1874	88	29	hand	hand	NOUN
ap-1874	88	30	side	side	NOUN
ap-1874	88	31	yields	yield	VERB
ap-1874	88	32	d(d+1)/2	d(d+1)/2	NOUN
ap-1874	88	33	with	with	ADP
ap-1874	88	34	d	d	PROPN
ap-1874	88	35	=	=	SYM
ap-1874	88	36	d1d2	d1d2	NOUN
ap-1874	88	37	.	.	PUNCT
ap-1874	88	38	hence	hence	ADV
ap-1874	88	39	there	there	PRON
ap-1874	88	40	holds	hold	VERB
ap-1874	88	41	equality	equality	NOUN
ap-1874	88	42	in	in	ADP
ap-1874	88	43	(	(	PUNCT
ap-1874	88	44	13	13	NUM
ap-1874	88	45	)	)	PUNCT
ap-1874	88	46	.	.	PUNCT
ap-1874	89	1	a	a	DET
ap-1874	89	2	similar	similar	ADJ
ap-1874	89	3	reasoning	reasoning	NOUN
ap-1874	89	4	shows	show	VERB
ap-1874	89	5	equality	equality	NOUN
ap-1874	89	6	in	in	ADP
ap-1874	89	7	(	(	PUNCT
ap-1874	89	8	14	14	NUM
ap-1874	89	9	)	)	PUNCT
ap-1874	89	10	if	if	SCONJ
ap-1874	89	11	equality	equality	NOUN
ap-1874	89	12	holds	hold	VERB
ap-1874	89	13	in	in	ADP
ap-1874	89	14	(	(	PUNCT
ap-1874	89	15	12	12	NUM
ap-1874	89	16	)	)	PUNCT
ap-1874	89	17	.	.	PUNCT
ap-1874	90	1	hence	hence	ADV
ap-1874	90	2	:	:	PUNCT
ap-1874	90	3	the	the	DET
ap-1874	90	4	set	set	NOUN
ap-1874	90	5	of	of	ADP
ap-1874	90	6	dimensions	dimension	NOUN
ap-1874	90	7	for	for	ADP
ap-1874	90	8	which	which	PRON
ap-1874	90	9	equality	equality	NOUN
ap-1874	90	10	takes	take	VERB
ap-1874	90	11	place	place	NOUN
ap-1874	90	12	in	in	ADP
ap-1874	90	13	(	(	PUNCT
ap-1874	90	14	12	12	NUM
ap-1874	90	15	)	)	PUNCT
ap-1874	90	16	is	be	AUX
ap-1874	90	17	closed	close	VERB
ap-1874	90	18	under	under	ADP
ap-1874	90	19	multiplication	multiplication	NOUN
ap-1874	90	20	.	.	PUNCT
ap-1874	91	1	to	to	PART
ap-1874	91	2	rephrase	rephrase	VERB
ap-1874	91	3	this	this	DET
ap-1874	91	4	result	result	NOUN
ap-1874	91	5	we	we	PRON
ap-1874	91	6	call	call	VERB
ap-1874	91	7	nanti	nanti	INTJ
ap-1874	91	8	the	the	DET
ap-1874	91	9	set	set	NOUN
ap-1874	91	10	of	of	ADP
ap-1874	91	11	dimensions	dimension	NOUN
ap-1874	91	12	for	for	ADP
ap-1874	91	13	which	which	PRON
ap-1874	91	14	equality	equality	NOUN
ap-1874	91	15	holds	hold	VERB
ap-1874	91	16	in	in	ADP
ap-1874	91	17	(	(	PUNCT
ap-1874	91	18	12	12	NUM
ap-1874	91	19	):	):	PUNCT
ap-1874	91	20	if	if	SCONJ
ap-1874	91	21	d1	d1	PROPN
ap-1874	91	22	∈	∈	PROPN
ap-1874	91	23	nanti	nanti	X
ap-1874	91	24	and	and	CCONJ
ap-1874	91	25	d2	d2	PROPN
ap-1874	91	26	∈	∈	PROPN
ap-1874	91	27	nanti	nanti	PROPN
ap-1874	91	28	then	then	ADV
ap-1874	91	29	d1d2	d1d2	VERB
ap-1874	91	30	∈	∈	PROPN
ap-1874	91	31	nanti	nanti	PROPN
ap-1874	91	32	.	.	PUNCT
ap-1874	92	1	2	2	NUM
ap-1874	92	2	∈	∈	PROPN
ap-1874	92	3	nanti	nanti	X
ap-1874	92	4	will	will	AUX
ap-1874	92	5	be	be	AUX
ap-1874	92	6	shown	show	VERB
ap-1874	92	7	by	by	ADP
ap-1874	92	8	explicit	explicit	ADJ
ap-1874	92	9	calculations	calculation	NOUN
ap-1874	92	10	below	below	ADV
ap-1874	92	11	.	.	PUNCT
ap-1874	93	1	hence	hence	ADV
ap-1874	93	2	every	every	DET
ap-1874	93	3	power	power	NOUN
ap-1874	93	4	of	of	ADP
ap-1874	93	5	two	two	NUM
ap-1874	93	6	is	be	AUX
ap-1874	93	7	contained	contain	VERB
ap-1874	93	8	in	in	ADP
ap-1874	93	9	nanti	nanti	PROPN
ap-1874	93	10	.	.	PUNCT
ap-1874	94	1	let	let	VERB
ap-1874	94	2	us	we	PRON
ap-1874	94	3	briefly	briefly	ADV
ap-1874	94	4	look	look	VERB
ap-1874	94	5	at	at	ADP
ap-1874	94	6	dimh	dimh	NOUN
ap-1874	94	7	=	=	SYM
ap-1874	94	8	1	1	X
ap-1874	94	9	.	.	PUNCT
ap-1874	95	1	it	it	PRON
ap-1874	95	2	is	be	AUX
ap-1874	95	3	n+(1	n+(1	ADV
ap-1874	95	4	)	)	PUNCT
ap-1874	96	1	=	=	SYM
ap-1874	96	2	1	1	NUM
ap-1874	96	3	and	and	CCONJ
ap-1874	96	4	n−(1	n−(1	NUM
ap-1874	96	5	)	)	PUNCT
ap-1874	96	6	=	=	SYM
ap-1874	96	7	0	0	X
ap-1874	96	8	.	.	PUNCT
ap-1874	96	9	indeed	indeed	ADV
ap-1874	96	10	,	,	PUNCT
ap-1874	96	11	any	any	DET
ap-1874	96	12	anti	anti	ADJ
ap-1874	96	13	-	-	ADJ
ap-1874	96	14	linear	linear	ADJ
ap-1874	96	15	operator	operator	NOUN
ap-1874	96	16	in	in	ADP
ap-1874	96	17	c	c	PROPN
ap-1874	96	18	is	be	AUX
ap-1874	96	19	of	of	ADP
ap-1874	96	20	the	the	DET
ap-1874	96	21	form	form	NOUN
ap-1874	96	22	ϑaz	ϑaz	PROPN
ap-1874	96	23	=	=	SYM
ap-1874	96	24	az∗.	az∗.	PROPN
ap-1874	96	25	this	this	PRON
ap-1874	96	26	is	be	AUX
ap-1874	96	27	a	a	DET
ap-1874	96	28	conjugation	conjugation	NOUN
ap-1874	96	29	if	if	SCONJ
ap-1874	96	30	|a|	|a|	PROPN
ap-1874	96	31	=	=	SYM
ap-1874	96	32	1	1	X
ap-1874	96	33	.	.	PUNCT
ap-1874	97	1	there	there	PRON
ap-1874	97	2	are	be	VERB
ap-1874	97	3	no	no	DET
ap-1874	97	4	skew	skew	ADJ
ap-1874	97	5	conjugations	conjugation	NOUN
ap-1874	97	6	.	.	PUNCT
ap-1874	98	1	the	the	DET
ap-1874	98	2	canonical	canonical	ADJ
ap-1874	98	3	form	form	NOUN
ap-1874	98	4	reads	read	NOUN
ap-1874	98	5	(	(	PUNCT
ap-1874	98	6	ϑa	ϑa	PROPN
ap-1874	98	7	,	,	PUNCT
ap-1874	98	8	ϑb	ϑb	NOUN
ap-1874	98	9	)	)	PUNCT
ap-1874	98	10	=	=	PUNCT
ap-1874	98	11	a∗b	a∗b	PROPN
ap-1874	98	12	.	.	PUNCT
ap-1874	99	1	conjecture	conjecture	VERB
ap-1874	99	2	1	1	NUM
ap-1874	99	3	.	.	PUNCT
ap-1874	100	1	nanti	nanti	PROPN
ap-1874	100	2	consists	consist	VERB
ap-1874	100	3	of	of	ADP
ap-1874	100	4	the	the	DET
ap-1874	100	5	numbers	number	NOUN
ap-1874	100	6	2n	2n	NUM
ap-1874	100	7	,	,	PUNCT
ap-1874	100	8	n	n	PROPN
ap-1874	100	9	=	=	SYM
ap-1874	100	10	0	0	NUM
ap-1874	100	11	,	,	PUNCT
ap-1874	100	12	1	1	NUM
ap-1874	100	13	,	,	PUNCT
ap-1874	100	14	2	2	NUM
ap-1874	100	15	,	,	PUNCT
ap-1874	100	16	.	.	PUNCT
ap-1874	100	17	.	.	PUNCT
ap-1874	100	18	.	.	PUNCT
ap-1874	100	19	.	.	PUNCT
ap-1874	101	1	skew	skew	ADJ
ap-1874	101	2	hermitian	hermitian	PROPN
ap-1874	101	3	invertible	invertible	ADJ
ap-1874	101	4	operators	operator	NOUN
ap-1874	101	5	exist	exist	VERB
ap-1874	101	6	in	in	ADP
ap-1874	101	7	even	even	ADV
ap-1874	101	8	dimensional	dimensional	ADJ
ap-1874	101	9	hilbert	hilbert	NOUN
ap-1874	101	10	spaces	space	NOUN
ap-1874	101	11	only	only	ADV
ap-1874	101	12	.	.	PUNCT
ap-1874	102	1	therefore	therefore	ADV
ap-1874	102	2	,	,	PUNCT
ap-1874	102	3	no	no	DET
ap-1874	102	4	odd	odd	ADJ
ap-1874	102	5	number	number	NOUN
ap-1874	102	6	except	except	SCONJ
ap-1874	102	7	1	1	NUM
ap-1874	102	8	is	be	AUX
ap-1874	102	9	contained	contain	VERB
ap-1874	102	10	in	in	ADP
ap-1874	102	11	nanti	nanti	PROPN
ap-1874	102	12	.	.	PUNCT
ap-1874	103	1	this	this	PRON
ap-1874	103	2	,	,	PUNCT
ap-1874	103	3	however	however	ADV
ap-1874	103	4	,	,	PUNCT
ap-1874	103	5	is	be	AUX
ap-1874	103	6	a	a	DET
ap-1874	103	7	rather	rather	ADV
ap-1874	103	8	trivial	trivial	ADJ
ap-1874	103	9	case	case	NOUN
ap-1874	103	10	.	.	PUNCT
ap-1874	104	1	already	already	ADV
ap-1874	104	2	for	for	ADP
ap-1874	104	3	dimh	dimh	NOUN
ap-1874	104	4	=	=	SYM
ap-1874	104	5	3	3	NUM
ap-1874	104	6	the	the	DET
ap-1874	104	7	maximal	maximal	ADJ
ap-1874	104	8	number	number	NOUN
ap-1874	104	9	n+(3	n+(3	NOUN
ap-1874	104	10	)	)	PUNCT
ap-1874	104	11	of	of	ADP
ap-1874	104	12	orthogonal	orthogonal	ADJ
ap-1874	104	13	conjugations	conjugation	NOUN
ap-1874	104	14	seems	seem	VERB
ap-1874	104	15	not	not	PART
ap-1874	104	16	to	to	PART
ap-1874	104	17	be	be	AUX
ap-1874	104	18	known	know	VERB
ap-1874	104	19	.	.	PUNCT
ap-1874	105	1	4.1	4.1	NUM
ap-1874	105	2	.	.	PUNCT
ap-1874	106	1	the	the	DET
ap-1874	106	2	case	case	NOUN
ap-1874	106	3	dimh	dimh	NOUN
ap-1874	106	4	=	=	SYM
ap-1874	106	5	2	2	NUM
ap-1874	106	6	to	to	PART
ap-1874	106	7	show	show	VERB
ap-1874	106	8	that	that	SCONJ
ap-1874	106	9	2	2	NUM
ap-1874	106	10	∈	∈	PROPN
ap-1874	106	11	nanti	nanti	PROPN
ap-1874	106	12	one	one	NOUN
ap-1874	106	13	chooses	choose	VERB
ap-1874	106	14	a	a	DET
ap-1874	106	15	basis	basis	NOUN
ap-1874	106	16	φ1	φ1	NOUN
ap-1874	106	17	,	,	PUNCT
ap-1874	106	18	φ2	φ2	PROPN
ap-1874	106	19	of	of	ADP
ap-1874	106	20	the	the	DET
ap-1874	106	21	2	2	NUM
ap-1874	106	22	-	-	PUNCT
ap-1874	106	23	dimensional	dimensional	ADJ
ap-1874	106	24	hilbert	hilbert	NOUN
ap-1874	106	25	space	space	NOUN
ap-1874	106	26	h	h	NOUN
ap-1874	106	27	and	and	CCONJ
ap-1874	106	28	defines	define	VERB
ap-1874	106	29	τ0(c1φ1	τ0(c1φ1	PROPN
ap-1874	106	30	+	+	CCONJ
ap-1874	106	31	c2φ2	c2φ2	NOUN
ap-1874	106	32	)	)	PUNCT
ap-1874	107	1	=	=	SYM
ap-1874	107	2	c∗1φ2	c∗1φ2	PROPN
ap-1874	107	3	−	−	PROPN
ap-1874	107	4	c∗2φ1	c∗2φ1	PROPN
ap-1874	107	5	,	,	PUNCT
ap-1874	107	6	τ1(c1φ1	τ1(c1φ1	PROPN
ap-1874	107	7	+	+	CCONJ
ap-1874	107	8	c2φ2	c2φ2	NOUN
ap-1874	107	9	)	)	PUNCT
ap-1874	107	10	=	=	PUNCT
ap-1874	107	11	c∗1φ1	c∗1φ1	NOUN
ap-1874	107	12	−	−	ADP
ap-1874	108	1	c∗2φ2	c∗2φ2	NOUN
ap-1874	108	2	,	,	PUNCT
ap-1874	108	3	τ2(c1φ1	τ2(c1φ1	PROPN
ap-1874	108	4	+	+	CCONJ
ap-1874	108	5	c2φ2	c2φ2	NOUN
ap-1874	108	6	)	)	PUNCT
ap-1874	108	7	=	=	NOUN
ap-1874	108	8	ic∗1φ1	ic∗1φ1	NOUN
ap-1874	108	9	+	+	CCONJ
ap-1874	108	10	ic∗2φ2	ic∗2φ2	ADJ
ap-1874	108	11	,	,	PUNCT
ap-1874	108	12	τ3(c1φ1	τ3(c1φ1	PROPN
ap-1874	108	13	+	+	CCONJ
ap-1874	108	14	c2φ2	c2φ2	NOUN
ap-1874	108	15	)	)	PUNCT
ap-1874	108	16	=	=	SYM
ap-1874	108	17	c∗1φ2	c∗1φ2	PROPN
ap-1874	108	18	+	+	CCONJ
ap-1874	108	19	c∗2φ1	c∗2φ1	PROPN
ap-1874	108	20	.	.	PUNCT
ap-1874	109	1	(	(	PUNCT
ap-1874	109	2	15	15	NUM
ap-1874	109	3	)	)	PUNCT
ap-1874	109	4	for	for	ADP
ap-1874	109	5	j	j	PROPN
ap-1874	109	6	,	,	PUNCT
ap-1874	109	7	k	k	PROPN
ap-1874	109	8	∈	∈	PROPN
ap-1874	109	9	{	{	PUNCT
ap-1874	109	10	1	1	NUM
ap-1874	109	11	,	,	PUNCT
ap-1874	109	12	2	2	NUM
ap-1874	109	13	}	}	PUNCT
ap-1874	109	14	and	and	CCONJ
ap-1874	109	15	m	m	PROPN
ap-1874	109	16	∈	∈	NOUN
ap-1874	109	17	{	{	PUNCT
ap-1874	109	18	1	1	NUM
ap-1874	109	19	,	,	PUNCT
ap-1874	109	20	2	2	NUM
ap-1874	109	21	,	,	PUNCT
ap-1874	109	22	3	3	NUM
ap-1874	109	23	}	}	SYM
ap-1874	109	24	one	one	NOUN
ap-1874	109	25	gets	get	VERB
ap-1874	109	26	〈	〈	PROPN
ap-1874	109	27	φj	φj	NOUN
ap-1874	109	28	,	,	PUNCT
ap-1874	109	29	τmφk	τmφk	PROPN
ap-1874	110	1	〉	〉	PROPN
ap-1874	110	2	=	=	SYM
ap-1874	111	1	〈	〈	PROPN
ap-1874	111	2	φk	φk	ADP
ap-1874	111	3	,	,	PUNCT
ap-1874	111	4	τmφj	τmφj	ADJ
ap-1874	111	5	〉	〉	PROPN
ap-1874	111	6	saying	say	VERB
ap-1874	111	7	that	that	SCONJ
ap-1874	111	8	these	these	DET
ap-1874	111	9	anti	anti	ADJ
ap-1874	111	10	-	-	ADJ
ap-1874	111	11	linear	linear	ADJ
ap-1874	111	12	operators	operator	NOUN
ap-1874	111	13	are	be	AUX
ap-1874	111	14	hermitian	hermitian	ADJ
ap-1874	111	15	.	.	PUNCT
ap-1874	112	1	one	one	NOUN
ap-1874	112	2	also	also	ADV
ap-1874	112	3	has	have	VERB
ap-1874	112	4	τ2	τ2	NOUN
ap-1874	112	5	m	m	NOUN
ap-1874	112	6	=	=	NOUN
ap-1874	112	7	1	1	NUM
ap-1874	112	8	for	for	ADP
ap-1874	112	9	m	m	PROPN
ap-1874	112	10	∈	∈	NOUN
ap-1874	112	11	{	{	PUNCT
ap-1874	112	12	1	1	NUM
ap-1874	112	13	,	,	PUNCT
ap-1874	112	14	2	2	NUM
ap-1874	112	15	,	,	PUNCT
ap-1874	112	16	3	3	NUM
ap-1874	112	17	}	}	PUNCT
ap-1874	112	18	.	.	PUNCT
ap-1874	113	1	altogether	altogether	ADV
ap-1874	113	2	,	,	PUNCT
ap-1874	113	3	τ1	τ1	NOUN
ap-1874	113	4	,	,	PUNCT
ap-1874	113	5	τ2	τ2	PROPN
ap-1874	113	6	,	,	PUNCT
ap-1874	113	7	τ3	τ3	NOUN
ap-1874	113	8	are	be	AUX
ap-1874	113	9	conjugations	conjugation	NOUN
ap-1874	113	10	.	.	PUNCT
ap-1874	114	1	to	to	PART
ap-1874	114	2	see	see	VERB
ap-1874	114	3	that	that	SCONJ
ap-1874	114	4	they	they	PRON
ap-1874	114	5	are	be	AUX
ap-1874	114	6	orthogonal	orthogonal	ADJ
ap-1874	114	7	one	one	NUM
ap-1874	114	8	to	to	ADP
ap-1874	114	9	another	another	PRON
ap-1874	114	10	we	we	PRON
ap-1874	114	11	compute	compute	VERB
ap-1874	114	12	τ1τ2τ3	τ1τ2τ3	NOUN
ap-1874	114	13	=	=	SYM
ap-1874	114	14	iτ0	iτ0	NOUN
ap-1874	114	15	,	,	PUNCT
ap-1874	114	16	τ2τ1	τ2τ1	PUNCT
ap-1874	115	1	=	=	SYM
ap-1874	115	2	iσ3	iσ3	X
ap-1874	115	3	,	,	PUNCT
ap-1874	115	4	(	(	PUNCT
ap-1874	115	5	16	16	NUM
ap-1874	115	6	)	)	PUNCT
ap-1874	115	7	τ1τ3	τ1τ3	X
ap-1874	115	8	=	=	SYM
ap-1874	115	9	iσ2	iσ2	NOUN
ap-1874	115	10	,	,	PUNCT
ap-1874	115	11	τ2τ3	τ2τ3	NOUN
ap-1874	115	12	=	=	SYM
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ap-1874	115	14	,	,	PUNCT
ap-1874	115	15	(	(	PUNCT
ap-1874	115	16	17	17	NUM
ap-1874	115	17	)	)	PUNCT
ap-1874	115	18	and	and	CCONJ
ap-1874	115	19	τ2τ0	τ2τ0	X
ap-1874	115	20	=	=	X
ap-1874	115	21	σ2	σ2	PROPN
ap-1874	115	22	,	,	PUNCT
ap-1874	115	23	τ0τ1	τ0τ1	PUNCT
ap-1874	115	24	=	=	SYM
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ap-1874	115	26	,	,	PUNCT
ap-1874	115	27	τ3τ0	τ3τ0	PUNCT
ap-1874	115	28	=	=	SYM
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ap-1874	116	1	(	(	PUNCT
ap-1874	116	2	18	18	NUM
ap-1874	116	3	)	)	PUNCT
ap-1874	116	4	the	the	DET
ap-1874	116	5	trace	trace	NOUN
ap-1874	116	6	of	of	ADP
ap-1874	116	7	any	any	DET
ap-1874	116	8	σj	σj	NOUN
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ap-1874	116	10	zero	zero	NUM
ap-1874	116	11	.	.	PUNCT
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ap-1874	117	2	of	of	ADP
ap-1874	117	3	(	(	PUNCT
ap-1874	117	4	16	16	NUM
ap-1874	117	5	)	)	PUNCT
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ap-1874	117	7	(	(	PUNCT
ap-1874	117	8	18	18	NUM
ap-1874	117	9	)	)	PUNCT
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ap-1874	117	12	,	,	PUNCT
ap-1874	117	13	that	that	DET
ap-1874	117	14	τ1	τ1	NOUN
ap-1874	117	15	,	,	PUNCT
ap-1874	117	16	τ2	τ2	PROPN
ap-1874	117	17	,	,	PUNCT
ap-1874	117	18	τ3	τ3	NOUN
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ap-1874	117	20	an	an	DET
ap-1874	117	21	orthogonal	orthogonal	ADJ
ap-1874	117	22	set	set	NOUN
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ap-1874	119	4	n−(2	n−(2	NOUN
ap-1874	119	5	)	)	PUNCT
ap-1874	119	6	=	=	SYM
ap-1874	119	7	1	1	NUM
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ap-1874	119	9	was	be	AUX
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ap-1874	119	11	above	above	ADV
ap-1874	119	12	.	.	PUNCT
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ap-1874	120	2	i	i	PRON
ap-1874	120	3	would	would	AUX
ap-1874	120	4	like	like	VERB
ap-1874	120	5	to	to	PART
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ap-1874	120	7	b.	b.	PROPN
ap-1874	120	8	crell	crell	PROPN
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ap-1874	120	11	support	support	NOUN
ap-1874	120	12	.	.	PUNCT
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ap-1874	121	3	1	1	NUM
ap-1874	121	4	]	]	PUNCT
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ap-1874	121	10	,	,	PUNCT
ap-1874	121	11	c.	c.	PROPN
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ap-1874	121	22	.	.	PUNCT
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ap-1874	122	2	an	an	DET
ap-1874	122	3	unknown	unknown	ADJ
ap-1874	122	4	quantum	quantum	ADJ
ap-1874	122	5	state	state	NOUN
ap-1874	122	6	via	via	ADP
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ap-1874	122	11	-	-	PUNCT
ap-1874	122	12	podolskyrosen	podolskyrosen	NOUN
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ap-1874	122	14	,	,	PUNCT
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ap-1874	122	16	.	.	PUNCT
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ap-1874	123	5	,	,	PUNCT
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ap-1874	123	7	:	:	SYM
ap-1874	123	8	1895	1895	NUM
ap-1874	123	9	-	-	SYM
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ap-1874	123	11	,	,	PUNCT
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ap-1874	123	13	.	.	PUNCT
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ap-1874	124	2	2	2	NUM
ap-1874	124	3	]	]	X
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ap-1874	125	8	3	3	X
ap-1874	125	9	]	]	X
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ap-1874	130	1	j.	j.	PROPN
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ap-1874	132	2	:	:	SYM
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ap-1874	132	4	-	-	SYM
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ap-1874	132	6	,	,	PUNCT
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ap-1874	132	8	.	.	PUNCT
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ap-1874	133	2	5	5	X
ap-1874	133	3	]	]	PUNCT
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ap-1874	134	5	university	university	PROPN
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ap-1874	134	7	:	:	PUNCT
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ap-1874	136	9	r.	r.	PROPN
ap-1874	136	10	johnson	johnson	PROPN
ap-1874	136	11	.	.	PUNCT
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ap-1874	137	5	.	.	PUNCT
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ap-1874	139	2	7	7	X
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ap-1874	139	5	jost	jost	PROPN
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ap-1874	141	2	.	.	PUNCT
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ap-1874	142	2	.	.	PUNCT
ap-1874	143	1	[	[	X
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ap-1874	145	1	[	[	X
ap-1874	145	2	9	9	NUM
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ap-1874	147	7	-	-	SYM
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ap-1874	150	1	[	[	X
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ap-1874	150	6	[	[	X
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ap-1874	151	9	.	.	PUNCT
ap-1874	152	1	in	in	ADP
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ap-1874	153	5	,	,	PUNCT
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ap-1874	153	8	,	,	PUNCT
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ap-1874	153	11	,	,	PUNCT
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ap-1874	153	13	.	.	PUNCT
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ap-1874	159	1	klasse	klasse	PROPN
ap-1874	159	2	1932	1932	NUM
ap-1874	159	3	,	,	PUNCT
ap-1874	159	4	31	31	NUM
ap-1874	159	5	,	,	PUNCT
ap-1874	159	6	546–559	546–559	NUM
ap-1874	159	7	.	.	PUNCT
ap-1874	160	1	[	[	X
ap-1874	160	2	12	12	NUM
ap-1874	160	3	]	]	PUNCT
ap-1874	160	4	e.	e.	PROPN
ap-1874	160	5	p.	p.	PROPN
ap-1874	160	6	wigner	wigner	NOUN
ap-1874	160	7	:	:	PUNCT
ap-1874	160	8	normal	normal	ADJ
ap-1874	160	9	form	form	NOUN
ap-1874	160	10	of	of	ADP
ap-1874	160	11	anitunitary	anitunitary	ADJ
ap-1874	160	12	operators	operator	NOUN
ap-1874	160	13	.	.	PUNCT
ap-1874	161	1	j.	j.	PROPN
ap-1874	161	2	math	math	PROPN
ap-1874	161	3	.	.	PUNCT
ap-1874	162	1	phys	phy	NOUN
ap-1874	162	2	.	.	PUNCT
ap-1874	163	1	1960	1960	NUM
ap-1874	163	2	,	,	PUNCT
ap-1874	163	3	1	1	NUM
ap-1874	163	4	,	,	PUNCT
ap-1874	163	5	409–413	409–413	NUM
ap-1874	163	6	.	.	PUNCT
ap-1874	164	1	472	472	NUM
ap-1874	164	2	acta	acta	PROPN
ap-1874	164	3	polytechnica	polytechnica	PROPN
ap-1874	164	4	53(5):470–472	53(5):470–472	PROPN
ap-1874	164	5	,	,	PUNCT
ap-1874	164	6	2013	2013	NUM
ap-1874	164	7	1	1	NUM
ap-1874	164	8	introduction	introduction	NOUN
ap-1874	164	9	2	2	NUM
ap-1874	164	10	anti(or	anti(or	ADP
ap-1874	164	11	conjugate	conjugate	NOUN
ap-1874	164	12	)	)	PUNCT
ap-1874	164	13	linearity	linearity	NOUN
ap-1874	164	14	3	3	NUM
ap-1874	164	15	the	the	DET
ap-1874	164	16	invariant	invariant	ADJ
ap-1874	164	17	hermitian	hermitian	ADJ
ap-1874	164	18	form	form	NOUN
ap-1874	164	19	4	4	NUM
ap-1874	164	20	orthogonal	orthogonal	ADJ
ap-1874	164	21	(	(	PUNCT
ap-1874	164	22	skew	skew	NOUN
ap-1874	164	23	)	)	PUNCT
ap-1874	164	24	conjugations	conjugation	VERB
ap-1874	164	25	4.1	4.1	NUM
ap-1874	164	26	the	the	DET
ap-1874	164	27	case	case	NOUN
ap-1874	164	28	dim	dim	VERB
ap-1874	164	29	h=2	h=2	PRON
ap-1874	164	30	acknowledgements	acknowledgement	NOUN
ap-1874	164	31	references	reference	NOUN