id	sid	tid	token	lemma	pos
ap-2086	1	1	acta	acta	PROPN
ap-2086	1	2	polytechnica	polytechnica	PROPN
ap-2086	1	3	doi:10.14311	doi:10.14311	PROPN
ap-2086	1	4	/	/	SYM
ap-2086	1	5	ap.2014.54.0124	ap.2014.54.0124	PROPN
ap-2086	1	6	acta	acta	PROPN
ap-2086	1	7	polytechnica	polytechnica	PROPN
ap-2086	1	8	54(2):124–126	54(2):124–126	PROPN
ap-2086	1	9	,	,	PUNCT
ap-2086	1	10	2014	2014	NUM
ap-2086	1	11	©	©	PROPN
ap-2086	1	12	czech	czech	PROPN
ap-2086	1	13	technical	technical	PROPN
ap-2086	1	14	university	university	PROPN
ap-2086	1	15	in	in	ADP
ap-2086	1	16	prague	prague	PROPN
ap-2086	1	17	,	,	PUNCT
ap-2086	1	18	2014	2014	NUM
ap-2086	1	19	available	available	ADJ
ap-2086	1	20	online	online	ADV
ap-2086	1	21	at	at	ADP
ap-2086	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2086	1	23	on	on	ADP
ap-2086	1	24	two	two	NUM
ap-2086	1	25	ways	way	NOUN
ap-2086	1	26	to	to	PART
ap-2086	1	27	look	look	VERB
ap-2086	1	28	for	for	ADP
ap-2086	1	29	mutually	mutually	ADV
ap-2086	1	30	unbiased	unbiased	ADJ
ap-2086	1	31	bases	basis	NOUN
ap-2086	1	32	maurice	maurice	PROPN
ap-2086	1	33	r.	r.	PROPN
ap-2086	1	34	kibler	kibler	PROPN
ap-2086	1	35	université	université	PROPN
ap-2086	1	36	de	de	PROPN
ap-2086	1	37	lyon	lyon	PROPN
ap-2086	1	38	,	,	PUNCT
ap-2086	1	39	université	université	PROPN
ap-2086	1	40	claude	claude	PROPN
ap-2086	1	41	bernard	bernard	PROPN
ap-2086	1	42	lyon	lyon	PROPN
ap-2086	1	43	1	1	NUM
ap-2086	1	44	et	et	NOUN
ap-2086	1	45	cnrs	cnrs	NOUN
ap-2086	1	46	/	/	SYM
ap-2086	1	47	in2p3	in2p3	PROPN
ap-2086	1	48	,	,	PUNCT
ap-2086	1	49	institut	institut	PROPN
ap-2086	1	50	de	de	PROPN
ap-2086	1	51	physique	physique	PROPN
ap-2086	1	52	nucléaire	nucléaire	NOUN
ap-2086	1	53	,	,	PUNCT
ap-2086	1	54	4	4	NUM
ap-2086	1	55	rue	rue	X
ap-2086	1	56	enrico	enrico	PROPN
ap-2086	1	57	fermi	fermi	PROPN
ap-2086	1	58	,	,	PUNCT
ap-2086	1	59	69622	69622	NUM
ap-2086	1	60	villeurbanne	villeurbanne	PROPN
ap-2086	1	61	,	,	PUNCT
ap-2086	1	62	france	france	PROPN
ap-2086	1	63	correspondence	correspondence	NOUN
ap-2086	1	64	:	:	PUNCT
ap-2086	1	65	kibler@ipnl.in2p3.fr	kibler@ipnl.in2p3.fr	PROPN
ap-2086	1	66	abstract	abstract	NOUN
ap-2086	1	67	.	.	PUNCT
ap-2086	2	1	two	two	NUM
ap-2086	2	2	equivalent	equivalent	ADJ
ap-2086	2	3	ways	way	NOUN
ap-2086	2	4	of	of	ADP
ap-2086	2	5	looking	look	VERB
ap-2086	2	6	for	for	ADP
ap-2086	2	7	mutually	mutually	ADV
ap-2086	2	8	unbiased	unbiased	ADJ
ap-2086	2	9	bases	basis	NOUN
ap-2086	2	10	are	be	AUX
ap-2086	2	11	discussed	discuss	VERB
ap-2086	2	12	in	in	ADP
ap-2086	2	13	this	this	DET
ap-2086	2	14	note	note	NOUN
ap-2086	2	15	.	.	PUNCT
ap-2086	3	1	the	the	DET
ap-2086	3	2	passage	passage	NOUN
ap-2086	3	3	from	from	ADP
ap-2086	3	4	the	the	DET
ap-2086	3	5	search	search	NOUN
ap-2086	3	6	for	for	ADP
ap-2086	3	7	d+	d+	NOUN
ap-2086	3	8	1	1	NUM
ap-2086	3	9	mutually	mutually	ADV
ap-2086	3	10	unbiased	unbiased	ADJ
ap-2086	3	11	bases	basis	NOUN
ap-2086	3	12	in	in	ADP
ap-2086	3	13	cd	cd	PROPN
ap-2086	3	14	to	to	ADP
ap-2086	3	15	the	the	DET
ap-2086	3	16	search	search	NOUN
ap-2086	3	17	for	for	ADP
ap-2086	3	18	d(d+	d(d+	DET
ap-2086	3	19	1	1	X
ap-2086	3	20	)	)	PUNCT
ap-2086	3	21	vectors	vector	NOUN
ap-2086	3	22	in	in	ADP
ap-2086	3	23	cd2	cd2	PROPN
ap-2086	3	24	satisfying	satisfying	NOUN
ap-2086	3	25	constraint	constraint	NOUN
ap-2086	3	26	relations	relation	NOUN
ap-2086	3	27	is	be	AUX
ap-2086	3	28	clarified	clarify	VERB
ap-2086	3	29	.	.	PUNCT
ap-2086	4	1	symmetric	symmetric	ADJ
ap-2086	4	2	informationally	informationally	ADV
ap-2086	4	3	complete	complete	ADJ
ap-2086	4	4	positive	positive	ADJ
ap-2086	4	5	-	-	PUNCT
ap-2086	4	6	operator	operator	NOUN
ap-2086	4	7	-	-	PUNCT
ap-2086	4	8	valued	value	VERB
ap-2086	4	9	measures	measure	NOUN
ap-2086	4	10	are	be	AUX
ap-2086	4	11	briefly	briefly	ADV
ap-2086	4	12	discussed	discuss	VERB
ap-2086	4	13	in	in	ADP
ap-2086	4	14	a	a	DET
ap-2086	4	15	similar	similar	ADJ
ap-2086	4	16	vein	vein	NOUN
ap-2086	4	17	.	.	PUNCT
ap-2086	5	1	keywords	keyword	NOUN
ap-2086	5	2	:	:	PUNCT
ap-2086	5	3	finite	finite	ADJ
ap-2086	5	4	-	-	ADJ
ap-2086	5	5	dimensional	dimensional	ADJ
ap-2086	5	6	quantum	quantum	ADJ
ap-2086	5	7	mechanics	mechanic	NOUN
ap-2086	5	8	,	,	PUNCT
ap-2086	5	9	quantum	quantum	ADJ
ap-2086	5	10	information	information	NOUN
ap-2086	5	11	,	,	PUNCT
ap-2086	5	12	mubs	mub	NOUN
ap-2086	5	13	,	,	PUNCT
ap-2086	5	14	sic	sic	ADJ
ap-2086	5	15	povms	povms	NOUN
ap-2086	5	16	,	,	PUNCT
ap-2086	5	17	equiangular	equiangular	NOUN
ap-2086	5	18	lines	line	NOUN
ap-2086	5	19	,	,	PUNCT
ap-2086	5	20	equiangular	equiangular	NOUN
ap-2086	5	21	vectors	vector	NOUN
ap-2086	5	22	.	.	PUNCT
ap-2086	6	1	1	1	X
ap-2086	6	2	.	.	X
ap-2086	6	3	introduction	introduction	NOUN
ap-2086	6	4	the	the	DET
ap-2086	6	5	concept	concept	NOUN
ap-2086	6	6	of	of	ADP
ap-2086	6	7	mutually	mutually	ADV
ap-2086	6	8	unbiased	unbiased	ADJ
ap-2086	6	9	bases	basis	NOUN
ap-2086	6	10	(	(	PUNCT
ap-2086	6	11	mubs	mub	NOUN
ap-2086	6	12	)	)	PUNCT
ap-2086	6	13	plays	play	VERB
ap-2086	6	14	an	an	DET
ap-2086	6	15	important	important	ADJ
ap-2086	6	16	role	role	NOUN
ap-2086	6	17	in	in	ADP
ap-2086	6	18	finite	finite	ADJ
ap-2086	6	19	-	-	ADJ
ap-2086	6	20	dimensional	dimensional	ADJ
ap-2086	6	21	quantum	quantum	ADJ
ap-2086	6	22	mechanics	mechanic	NOUN
ap-2086	6	23	and	and	CCONJ
ap-2086	6	24	quantum	quantum	NOUN
ap-2086	6	25	information	information	NOUN
ap-2086	6	26	(	(	PUNCT
ap-2086	6	27	for	for	ADP
ap-2086	6	28	more	more	ADJ
ap-2086	6	29	details	detail	NOUN
ap-2086	6	30	,	,	PUNCT
ap-2086	6	31	see	see	VERB
ap-2086	6	32	[	[	X
ap-2086	6	33	1–4	1–4	NOUN
ap-2086	6	34	]	]	PUNCT
ap-2086	6	35	and	and	CCONJ
ap-2086	6	36	references	reference	NOUN
ap-2086	6	37	therein	therein	ADV
ap-2086	6	38	)	)	PUNCT
ap-2086	6	39	.	.	PUNCT
ap-2086	7	1	let	let	VERB
ap-2086	7	2	us	we	PRON
ap-2086	7	3	recall	recall	VERB
ap-2086	7	4	that	that	SCONJ
ap-2086	7	5	two	two	NUM
ap-2086	7	6	orthonormal	orthonormal	ADJ
ap-2086	7	7	bases	basis	NOUN
ap-2086	7	8	{	{	PUNCT
ap-2086	7	9	|aα	|aα	PROPN
ap-2086	7	10	〉	〉	PROPN
ap-2086	7	11	:	:	PUNCT
ap-2086	7	12	α	α	X
ap-2086	7	13	=	=	SYM
ap-2086	7	14	0	0	NUM
ap-2086	7	15	,	,	PUNCT
ap-2086	7	16	1	1	NUM
ap-2086	7	17	,	,	PUNCT
ap-2086	7	18	.	.	PUNCT
ap-2086	7	19	.	.	PUNCT
ap-2086	8	1	.	.	PUNCT
ap-2086	9	1	,	,	PUNCT
ap-2086	10	1	d	d	X
ap-2086	10	2	−	−	PROPN
ap-2086	10	3	1	1	NUM
ap-2086	10	4	}	}	PUNCT
ap-2086	10	5	and	and	CCONJ
ap-2086	10	6	{	{	PUNCT
ap-2086	10	7	|bβ	|bβ	NOUN
ap-2086	10	8	〉	〉	NOUN
ap-2086	10	9	:	:	PUNCT
ap-2086	10	10	β	β	X
ap-2086	10	11	=	=	SYM
ap-2086	10	12	0	0	NUM
ap-2086	10	13	,	,	PUNCT
ap-2086	10	14	1	1	NUM
ap-2086	10	15	,	,	PUNCT
ap-2086	10	16	.	.	PUNCT
ap-2086	10	17	.	.	PUNCT
ap-2086	11	1	.	.	PUNCT
ap-2086	12	1	,	,	PUNCT
ap-2086	12	2	d−	d−	PROPN
ap-2086	12	3	1	1	NUM
ap-2086	12	4	}	}	PUNCT
ap-2086	12	5	in	in	ADP
ap-2086	12	6	the	the	DET
ap-2086	12	7	d	d	ADJ
ap-2086	12	8	-	-	ADJ
ap-2086	12	9	dimensional	dimensional	ADJ
ap-2086	12	10	hilbert	hilbert	NOUN
ap-2086	12	11	space	space	NOUN
ap-2086	12	12	cd	cd	PROPN
ap-2086	12	13	(	(	PUNCT
ap-2086	12	14	endowed	endow	VERB
ap-2086	12	15	with	with	ADP
ap-2086	12	16	an	an	DET
ap-2086	12	17	inner	inner	ADJ
ap-2086	12	18	product	product	NOUN
ap-2086	12	19	denoted	denote	VERB
ap-2086	12	20	as	as	ADP
ap-2086	12	21	〈	〈	PROPN
ap-2086	12	22	|	|	PROPN
ap-2086	12	23	〉	〉	NOUN
ap-2086	12	24	)	)	PUNCT
ap-2086	12	25	are	be	AUX
ap-2086	12	26	said	say	VERB
ap-2086	12	27	to	to	PART
ap-2086	12	28	be	be	AUX
ap-2086	12	29	unbiased	unbiased	ADJ
ap-2086	12	30	if	if	SCONJ
ap-2086	12	31	the	the	DET
ap-2086	12	32	modulus	modulus	NOUN
ap-2086	12	33	of	of	ADP
ap-2086	12	34	the	the	DET
ap-2086	12	35	inner	inner	ADJ
ap-2086	12	36	product	product	NOUN
ap-2086	12	37	〈	〈	PROPN
ap-2086	12	38	aα|bβ	aα|bβ	NOUN
ap-2086	12	39	〉	〉	NOUN
ap-2086	12	40	of	of	ADP
ap-2086	12	41	any	any	DET
ap-2086	12	42	vector	vector	NOUN
ap-2086	12	43	|bβ	|bβ	NOUN
ap-2086	12	44	〉	〉	NOUN
ap-2086	12	45	with	with	ADP
ap-2086	12	46	any	any	DET
ap-2086	12	47	vector	vector	NOUN
ap-2086	12	48	|aα	|aα	PROPN
ap-2086	12	49	〉	〉	PROPN
ap-2086	12	50	is	be	AUX
ap-2086	12	51	equal	equal	ADJ
ap-2086	12	52	to	to	ADP
ap-2086	12	53	1/	1/	NUM
ap-2086	12	54	√	√	PROPN
ap-2086	13	1	d.	d.	PROPN
ap-2086	14	1	it	it	PRON
ap-2086	14	2	is	be	AUX
ap-2086	14	3	known	know	VERB
ap-2086	14	4	that	that	SCONJ
ap-2086	14	5	the	the	DET
ap-2086	14	6	maximum	maximum	ADJ
ap-2086	14	7	number	number	NOUN
ap-2086	14	8	of	of	ADP
ap-2086	14	9	mubs	mub	NOUN
ap-2086	14	10	in	in	ADP
ap-2086	14	11	cd	cd	PROPN
ap-2086	14	12	is	be	AUX
ap-2086	14	13	d+	d+	NOUN
ap-2086	14	14	1	1	NUM
ap-2086	14	15	and	and	CCONJ
ap-2086	14	16	that	that	SCONJ
ap-2086	14	17	this	this	DET
ap-2086	14	18	number	number	NOUN
ap-2086	14	19	is	be	AUX
ap-2086	14	20	reached	reach	VERB
ap-2086	14	21	when	when	SCONJ
ap-2086	14	22	d	d	NOUN
ap-2086	14	23	is	be	AUX
ap-2086	14	24	a	a	DET
ap-2086	14	25	power	power	NOUN
ap-2086	14	26	of	of	ADP
ap-2086	14	27	a	a	DET
ap-2086	14	28	prime	prime	ADJ
ap-2086	14	29	integer	integer	NOUN
ap-2086	14	30	.	.	PUNCT
ap-2086	15	1	in	in	ADP
ap-2086	15	2	the	the	DET
ap-2086	15	3	case	case	NOUN
ap-2086	15	4	where	where	SCONJ
ap-2086	15	5	d	d	NOUN
ap-2086	15	6	is	be	AUX
ap-2086	15	7	not	not	PART
ap-2086	15	8	a	a	DET
ap-2086	15	9	prime	prime	ADJ
ap-2086	15	10	integer	integer	NOUN
ap-2086	15	11	,	,	PUNCT
ap-2086	15	12	it	it	PRON
ap-2086	15	13	is	be	AUX
ap-2086	15	14	not	not	PART
ap-2086	15	15	known	know	VERB
ap-2086	15	16	if	if	SCONJ
ap-2086	15	17	one	one	PRON
ap-2086	15	18	can	can	AUX
ap-2086	15	19	construct	construct	VERB
ap-2086	15	20	d+	d+	PUNCT
ap-2086	15	21	1	1	NUM
ap-2086	15	22	mubs	mub	NOUN
ap-2086	15	23	(	(	PUNCT
ap-2086	15	24	see	see	VERB
ap-2086	15	25	[	[	X
ap-2086	15	26	4	4	X
ap-2086	15	27	]	]	PUNCT
ap-2086	15	28	for	for	ADP
ap-2086	15	29	a	a	DET
ap-2086	15	30	review	review	NOUN
ap-2086	15	31	)	)	PUNCT
ap-2086	15	32	.	.	PUNCT
ap-2086	16	1	in	in	ADP
ap-2086	16	2	a	a	DET
ap-2086	16	3	recent	recent	ADJ
ap-2086	16	4	paper	paper	NOUN
ap-2086	16	5	[	[	X
ap-2086	16	6	5	5	NUM
ap-2086	16	7	]	]	PUNCT
ap-2086	16	8	,	,	PUNCT
ap-2086	16	9	it	it	PRON
ap-2086	16	10	was	be	AUX
ap-2086	16	11	discussed	discuss	VERB
ap-2086	16	12	how	how	SCONJ
ap-2086	16	13	the	the	DET
ap-2086	16	14	search	search	NOUN
ap-2086	16	15	for	for	ADP
ap-2086	16	16	d	d	PROPN
ap-2086	16	17	+	+	NOUN
ap-2086	16	18	1	1	NUM
ap-2086	16	19	mutually	mutually	ADV
ap-2086	16	20	unbiased	unbiased	ADJ
ap-2086	16	21	bases	basis	NOUN
ap-2086	16	22	in	in	ADP
ap-2086	16	23	cd	cd	PROPN
ap-2086	16	24	can	can	AUX
ap-2086	16	25	be	be	AUX
ap-2086	16	26	approached	approach	VERB
ap-2086	16	27	via	via	ADP
ap-2086	16	28	the	the	DET
ap-2086	16	29	search	search	NOUN
ap-2086	16	30	for	for	ADP
ap-2086	16	31	d(d+	d(d+	DET
ap-2086	16	32	1	1	X
ap-2086	16	33	)	)	PUNCT
ap-2086	16	34	vectors	vector	NOUN
ap-2086	16	35	in	in	ADP
ap-2086	16	36	cd2	cd2	PROPN
ap-2086	16	37	satisfying	satisfy	VERB
ap-2086	16	38	constraint	constraint	NOUN
ap-2086	16	39	relations	relation	NOUN
ap-2086	16	40	.	.	PUNCT
ap-2086	17	1	the	the	DET
ap-2086	17	2	main	main	ADJ
ap-2086	17	3	aim	aim	NOUN
ap-2086	17	4	of	of	ADP
ap-2086	17	5	this	this	DET
ap-2086	17	6	note	note	NOUN
ap-2086	17	7	is	be	AUX
ap-2086	17	8	to	to	PART
ap-2086	17	9	make	make	VERB
ap-2086	17	10	the	the	DET
ap-2086	17	11	results	result	NOUN
ap-2086	17	12	in	in	ADP
ap-2086	17	13	[	[	X
ap-2086	17	14	5	5	NUM
ap-2086	17	15	]	]	X
ap-2086	17	16	more	more	ADV
ap-2086	17	17	precise	precise	ADJ
ap-2086	17	18	and	and	CCONJ
ap-2086	17	19	to	to	PART
ap-2086	17	20	show	show	VERB
ap-2086	17	21	that	that	SCONJ
ap-2086	17	22	the	the	DET
ap-2086	17	23	two	two	NUM
ap-2086	17	24	approaches	approach	NOUN
ap-2086	17	25	(	(	PUNCT
ap-2086	17	26	looking	look	VERB
ap-2086	17	27	for	for	ADP
ap-2086	17	28	d	d	PROPN
ap-2086	17	29	+	+	SYM
ap-2086	17	30	1	1	NUM
ap-2086	17	31	mubs	mub	NOUN
ap-2086	17	32	in	in	ADP
ap-2086	17	33	cd	cd	PROPN
ap-2086	17	34	or	or	CCONJ
ap-2086	17	35	for	for	ADP
ap-2086	17	36	d(d+1	d(d+1	NUM
ap-2086	17	37	)	)	PUNCT
ap-2086	17	38	vectors	vector	NOUN
ap-2086	17	39	in	in	ADP
ap-2086	17	40	cd2	cd2	PROPN
ap-2086	17	41	)	)	PUNCT
ap-2086	17	42	are	be	AUX
ap-2086	17	43	entirely	entirely	ADV
ap-2086	17	44	equivalent	equivalent	ADJ
ap-2086	17	45	.	.	PUNCT
ap-2086	18	1	the	the	DET
ap-2086	18	2	central	central	ADJ
ap-2086	18	3	results	result	NOUN
ap-2086	18	4	are	be	AUX
ap-2086	18	5	presented	present	VERB
ap-2086	18	6	in	in	ADP
ap-2086	18	7	sections	section	NOUN
ap-2086	18	8	2	2	NUM
ap-2086	18	9	and	and	CCONJ
ap-2086	18	10	3	3	NUM
ap-2086	18	11	.	.	PUNCT
ap-2086	19	1	in	in	ADP
ap-2086	19	2	section	section	NOUN
ap-2086	19	3	4	4	NUM
ap-2086	19	4	,	,	PUNCT
ap-2086	19	5	parallel	parallel	ADJ
ap-2086	19	6	developments	development	NOUN
ap-2086	19	7	for	for	ADP
ap-2086	19	8	the	the	DET
ap-2086	19	9	search	search	NOUN
ap-2086	19	10	for	for	ADP
ap-2086	19	11	a	a	DET
ap-2086	19	12	symmetric	symmetric	ADJ
ap-2086	19	13	informationally	informationally	ADV
ap-2086	19	14	complete	complete	ADJ
ap-2086	19	15	positive	positive	ADJ
ap-2086	19	16	-	-	PUNCT
ap-2086	19	17	operator	operator	NOUN
ap-2086	19	18	-	-	PUNCT
ap-2086	19	19	valued	value	VERB
ap-2086	19	20	measure	measure	NOUN
ap-2086	19	21	(	(	PUNCT
ap-2086	19	22	sic	sic	ADJ
ap-2086	19	23	povm	povm	NOUN
ap-2086	19	24	)	)	PUNCT
ap-2086	19	25	are	be	AUX
ap-2086	19	26	considered	consider	VERB
ap-2086	19	27	in	in	ADP
ap-2086	19	28	the	the	DET
ap-2086	19	29	framework	framework	NOUN
ap-2086	19	30	of	of	ADP
ap-2086	19	31	similar	similar	ADJ
ap-2086	19	32	approaches	approach	NOUN
ap-2086	19	33	.	.	PUNCT
ap-2086	20	1	some	some	DET
ap-2086	20	2	concluding	conclude	VERB
ap-2086	20	3	remarks	remark	NOUN
ap-2086	20	4	are	be	AUX
ap-2086	20	5	given	give	VERB
ap-2086	20	6	in	in	ADP
ap-2086	20	7	the	the	DET
ap-2086	20	8	last	last	ADJ
ap-2086	20	9	section	section	NOUN
ap-2086	20	10	.	.	PUNCT
ap-2086	21	1	2	2	X
ap-2086	21	2	.	.	X
ap-2086	21	3	the	the	DET
ap-2086	21	4	two	two	NUM
ap-2086	21	5	approaches	approach	NOUN
ap-2086	21	6	it	it	PRON
ap-2086	21	7	was	be	AUX
ap-2086	21	8	shown	show	VERB
ap-2086	21	9	in	in	ADP
ap-2086	21	10	[	[	X
ap-2086	21	11	5	5	NUM
ap-2086	21	12	]	]	PUNCT
ap-2086	21	13	how	how	SCONJ
ap-2086	21	14	the	the	DET
ap-2086	21	15	problem	problem	NOUN
ap-2086	21	16	of	of	ADP
ap-2086	21	17	finding	find	VERB
ap-2086	21	18	d+	d+	PUNCT
ap-2086	21	19	1	1	NUM
ap-2086	21	20	mubs	mub	NOUN
ap-2086	21	21	in	in	ADP
ap-2086	21	22	cd	cd	PROPN
ap-2086	21	23	,	,	PUNCT
ap-2086	21	24	i.e.	i.e.	X
ap-2086	21	25	,	,	PUNCT
ap-2086	21	26	d+	d+	X
ap-2086	21	27	1	1	NUM
ap-2086	21	28	bases	basis	NOUN
ap-2086	21	29	ba	ba	NOUN
ap-2086	21	30	=	=	PRON
ap-2086	21	31	{	{	PUNCT
ap-2086	21	32	|aα	|aα	PROPN
ap-2086	21	33	〉	〉	PROPN
ap-2086	21	34	:	:	PUNCT
ap-2086	21	35	α	α	X
ap-2086	21	36	=	=	SYM
ap-2086	21	37	0	0	NUM
ap-2086	21	38	,	,	PUNCT
ap-2086	21	39	1	1	NUM
ap-2086	21	40	,	,	PUNCT
ap-2086	21	41	.	.	PUNCT
ap-2086	21	42	.	.	PUNCT
ap-2086	22	1	.	.	PUNCT
ap-2086	23	1	,	,	PUNCT
ap-2086	23	2	d−	d−	PROPN
ap-2086	23	3	1	1	NUM
ap-2086	23	4	}	}	PUNCT
ap-2086	23	5	(	(	PUNCT
ap-2086	23	6	1	1	X
ap-2086	23	7	)	)	PUNCT
ap-2086	23	8	satisfying	satisfy	VERB
ap-2086	23	9	|〈aα|bβ〉|	|〈aα|bβ〉|	PROPN
ap-2086	23	10	=	=	SYM
ap-2086	23	11	δα	δα	NOUN
ap-2086	23	12	,	,	PUNCT
ap-2086	23	13	βδa	βδa	NOUN
ap-2086	23	14	,	,	PUNCT
ap-2086	23	15	b	b	PROPN
ap-2086	23	16	+	+	CCONJ
ap-2086	23	17	1√	1√	PROPN
ap-2086	23	18	d	d	PROPN
ap-2086	23	19	(	(	PUNCT
ap-2086	23	20	1−	1−	NUM
ap-2086	23	21	δa	δa	PROPN
ap-2086	23	22	,	,	PUNCT
ap-2086	23	23	b	b	NOUN
ap-2086	23	24	)	)	PUNCT
ap-2086	23	25	(	(	PUNCT
ap-2086	23	26	2	2	X
ap-2086	23	27	)	)	PUNCT
ap-2086	23	28	can	can	AUX
ap-2086	23	29	be	be	AUX
ap-2086	23	30	transformed	transform	VERB
ap-2086	23	31	into	into	ADP
ap-2086	23	32	the	the	DET
ap-2086	23	33	problem	problem	NOUN
ap-2086	23	34	of	of	ADP
ap-2086	23	35	finding	find	VERB
ap-2086	23	36	d(d+1	d(d+1	NOUN
ap-2086	23	37	)	)	PUNCT
ap-2086	23	38	vectors	vector	NOUN
ap-2086	23	39	w(aα	w(aα	NOUN
ap-2086	23	40	)	)	PUNCT
ap-2086	23	41	in	in	ADP
ap-2086	23	42	cd2	cd2	PROPN
ap-2086	23	43	,	,	PUNCT
ap-2086	23	44	of	of	ADP
ap-2086	23	45	components	component	NOUN
ap-2086	23	46	wpq(aα	wpq(aα	ADJ
ap-2086	23	47	)	)	PUNCT
ap-2086	23	48	,	,	PUNCT
ap-2086	23	49	satisfying	satisfy	VERB
ap-2086	23	50	wpq(aα	wpq(aα	NOUN
ap-2086	23	51	)	)	PUNCT
ap-2086	23	52	=	=	SYM
ap-2086	23	53	wqp(aα	wqp(aα	NOUN
ap-2086	23	54	)	)	PUNCT
ap-2086	23	55	,	,	PUNCT
ap-2086	23	56	p	p	X
ap-2086	23	57	,	,	PUNCT
ap-2086	23	58	q	q	PROPN
ap-2086	23	59	∈	∈	PROPN
ap-2086	23	60	z	z	X
ap-2086	23	61	/	/	SYM
ap-2086	23	62	dz	dz	X
ap-2086	23	63	(	(	PUNCT
ap-2086	23	64	3	3	NUM
ap-2086	23	65	)	)	PUNCT
ap-2086	23	66	d−1∑	d−1∑	PROPN
ap-2086	23	67	p=0	p=0	PROPN
ap-2086	23	68	wpp(aα	wpp(aα	VERB
ap-2086	23	69	)	)	PUNCT
ap-2086	23	70	=	=	SYM
ap-2086	23	71	1	1	NUM
ap-2086	23	72	(	(	PUNCT
ap-2086	23	73	4	4	NUM
ap-2086	23	74	)	)	PUNCT
ap-2086	23	75	and	and	CCONJ
ap-2086	23	76	d−1∑	d−1∑	ADJ
ap-2086	23	77	p=0	p=0	PROPN
ap-2086	23	78	d−1∑	d−1∑	PROPN
ap-2086	23	79	q=0	q=0	ADV
ap-2086	23	80	wpq(aα)wpq(bβ	wpq(aα)wpq(bβ	NUM
ap-2086	23	81	)	)	PUNCT
ap-2086	24	1	=	=	SYM
ap-2086	24	2	δα	δα	PROPN
ap-2086	24	3	,	,	PUNCT
ap-2086	24	4	βδa	βδa	NOUN
ap-2086	24	5	,	,	PUNCT
ap-2086	24	6	b	b	NOUN
ap-2086	24	7	+	+	CCONJ
ap-2086	24	8	1	1	NUM
ap-2086	24	9	d	d	NOUN
ap-2086	24	10	(	(	PUNCT
ap-2086	24	11	1−	1−	NUM
ap-2086	24	12	δa	δa	PROPN
ap-2086	24	13	,	,	PUNCT
ap-2086	24	14	b	b	NOUN
ap-2086	24	15	)	)	PUNCT
ap-2086	24	16	(	(	PUNCT
ap-2086	24	17	5	5	NUM
ap-2086	24	18	)	)	PUNCT
ap-2086	24	19	with	with	ADP
ap-2086	24	20	a	a	DET
ap-2086	24	21	,	,	PUNCT
ap-2086	24	22	b	b	NOUN
ap-2086	24	23	=	=	SYM
ap-2086	24	24	0	0	NUM
ap-2086	24	25	,	,	PUNCT
ap-2086	24	26	1	1	NUM
ap-2086	24	27	,	,	PUNCT
ap-2086	24	28	.	.	PUNCT
ap-2086	24	29	.	.	PUNCT
ap-2086	24	30	.	.	PUNCT
ap-2086	25	1	,	,	PUNCT
ap-2086	25	2	d	d	NOUN
ap-2086	25	3	and	and	CCONJ
ap-2086	25	4	α	α	NOUN
ap-2086	25	5	,	,	PUNCT
ap-2086	25	6	β	β	X
ap-2086	25	7	=	=	SYM
ap-2086	25	8	0	0	NUM
ap-2086	25	9	,	,	PUNCT
ap-2086	25	10	1	1	NUM
ap-2086	25	11	,	,	PUNCT
ap-2086	25	12	.	.	PUNCT
ap-2086	25	13	.	.	PUNCT
ap-2086	26	1	.	.	PUNCT
ap-2086	27	1	,	,	PUNCT
ap-2086	28	1	d	d	X
ap-2086	28	2	−	−	NOUN
ap-2086	28	3	1	1	NUM
ap-2086	28	4	in	in	ADP
ap-2086	28	5	(	(	PUNCT
ap-2086	28	6	1)–(5	1)–(5	NUM
ap-2086	28	7	)	)	PUNCT
ap-2086	28	8	.	.	PUNCT
ap-2086	29	1	(	(	PUNCT
ap-2086	29	2	in	in	ADP
ap-2086	29	3	this	this	DET
ap-2086	29	4	paper	paper	NOUN
ap-2086	29	5	,	,	PUNCT
ap-2086	29	6	the	the	DET
ap-2086	29	7	bar	bar	NOUN
ap-2086	29	8	denotes	denote	VERB
ap-2086	29	9	complex	complex	ADJ
ap-2086	29	10	conjugation	conjugation	NOUN
ap-2086	29	11	.	.	PUNCT
ap-2086	29	12	)	)	PUNCT
ap-2086	30	1	this	this	DET
ap-2086	30	2	result	result	NOUN
ap-2086	30	3	was	be	AUX
ap-2086	30	4	described	describe	VERB
ap-2086	30	5	by	by	ADP
ap-2086	30	6	proposition	proposition	NOUN
ap-2086	30	7	1	1	NUM
ap-2086	30	8	in	in	ADP
ap-2086	30	9	[	[	X
ap-2086	30	10	5	5	NUM
ap-2086	30	11	]	]	PUNCT
ap-2086	30	12	.	.	PUNCT
ap-2086	31	1	in	in	ADP
ap-2086	31	2	fact	fact	NOUN
ap-2086	31	3	,	,	PUNCT
ap-2086	31	4	the	the	DET
ap-2086	31	5	equivalence	equivalence	NOUN
ap-2086	31	6	of	of	ADP
ap-2086	31	7	the	the	DET
ap-2086	31	8	two	two	NUM
ap-2086	31	9	approaches	approach	NOUN
ap-2086	31	10	(	(	PUNCT
ap-2086	31	11	in	in	ADP
ap-2086	31	12	cd	cd	PROPN
ap-2086	31	13	and	and	CCONJ
ap-2086	31	14	cd2	cd2	PROPN
ap-2086	31	15	)	)	PUNCT
ap-2086	31	16	requires	require	VERB
ap-2086	31	17	that	that	SCONJ
ap-2086	31	18	each	each	DET
ap-2086	31	19	component	component	NOUN
ap-2086	31	20	wpq(aα	wpq(aα	NOUN
ap-2086	31	21	)	)	PUNCT
ap-2086	31	22	be	be	AUX
ap-2086	31	23	factorized	factorize	VERB
ap-2086	31	24	as	as	ADP
ap-2086	31	25	wpq(aα	wpq(aα	NOUN
ap-2086	31	26	)	)	PUNCT
ap-2086	31	27	=	=	SYM
ap-2086	31	28	ωp(aα)ωq(aα	ωp(aα)ωq(aα	X
ap-2086	31	29	)	)	PUNCT
ap-2086	31	30	(	(	PUNCT
ap-2086	31	31	6	6	NUM
ap-2086	31	32	)	)	PUNCT
ap-2086	31	33	for	for	ADP
ap-2086	31	34	a	a	DET
ap-2086	31	35	=	=	SYM
ap-2086	31	36	0	0	NUM
ap-2086	31	37	,	,	PUNCT
ap-2086	31	38	1	1	NUM
ap-2086	31	39	,	,	PUNCT
ap-2086	31	40	.	.	PUNCT
ap-2086	31	41	.	.	PUNCT
ap-2086	31	42	.	.	PUNCT
ap-2086	32	1	,	,	PUNCT
ap-2086	32	2	d	d	NOUN
ap-2086	32	3	and	and	CCONJ
ap-2086	32	4	α	α	NOUN
ap-2086	32	5	=	=	SYM
ap-2086	32	6	0	0	NUM
ap-2086	32	7	,	,	PUNCT
ap-2086	32	8	1	1	NUM
ap-2086	32	9	,	,	PUNCT
ap-2086	32	10	.	.	PUNCT
ap-2086	32	11	.	.	PUNCT
ap-2086	33	1	.	.	PUNCT
ap-2086	34	1	,	,	PUNCT
ap-2086	34	2	d−	d−	PROPN
ap-2086	34	3	1	1	NUM
ap-2086	34	4	,	,	PUNCT
ap-2086	34	5	a	a	DET
ap-2086	34	6	condition	condition	NOUN
ap-2086	34	7	satisfied	satisfy	VERB
ap-2086	34	8	by	by	ADP
ap-2086	34	9	the	the	DET
ap-2086	34	10	example	example	NOUN
ap-2086	34	11	given	give	VERB
ap-2086	34	12	in	in	ADP
ap-2086	34	13	[	[	X
ap-2086	34	14	5	5	NUM
ap-2086	34	15	]	]	PUNCT
ap-2086	34	16	.	.	PUNCT
ap-2086	35	1	the	the	DET
ap-2086	35	2	factorization	factorization	NOUN
ap-2086	35	3	of	of	ADP
ap-2086	35	4	wpq(aα	wpq(aα	NOUN
ap-2086	35	5	)	)	PUNCT
ap-2086	35	6	follows	follow	VERB
ap-2086	35	7	from	from	ADP
ap-2086	35	8	the	the	DET
ap-2086	35	9	fact	fact	NOUN
ap-2086	35	10	that	that	SCONJ
ap-2086	35	11	the	the	DET
ap-2086	35	12	operator	operator	NOUN
ap-2086	35	13	πaα	πaα	PRON
ap-2086	35	14	defined	define	VERB
ap-2086	35	15	in	in	ADP
ap-2086	35	16	[	[	X
ap-2086	35	17	5	5	NUM
ap-2086	35	18	]	]	PUNCT
ap-2086	35	19	is	be	AUX
ap-2086	35	20	a	a	DET
ap-2086	35	21	projection	projection	NOUN
ap-2086	35	22	operator	operator	NOUN
ap-2086	35	23	.	.	PUNCT
ap-2086	36	1	the	the	DET
ap-2086	36	2	introduction	introduction	NOUN
ap-2086	36	3	of	of	ADP
ap-2086	36	4	(	(	PUNCT
ap-2086	36	5	6	6	NUM
ap-2086	36	6	)	)	PUNCT
ap-2086	36	7	in	in	ADP
ap-2086	36	8	(	(	PUNCT
ap-2086	36	9	3	3	NUM
ap-2086	36	10	)	)	PUNCT
ap-2086	36	11	,	,	PUNCT
ap-2086	36	12	(	(	PUNCT
ap-2086	36	13	4	4	NUM
ap-2086	36	14	)	)	PUNCT
ap-2086	36	15	and	and	CCONJ
ap-2086	36	16	(	(	PUNCT
ap-2086	36	17	5	5	X
ap-2086	36	18	)	)	PUNCT
ap-2086	36	19	leads	lead	VERB
ap-2086	36	20	to	to	ADP
ap-2086	36	21	some	some	DET
ap-2086	36	22	simplifications	simplification	NOUN
ap-2086	36	23	.	.	PUNCT
ap-2086	37	1	first	first	ADV
ap-2086	37	2	,	,	PUNCT
ap-2086	37	3	(	(	PUNCT
ap-2086	37	4	6	6	NUM
ap-2086	37	5	)	)	PUNCT
ap-2086	37	6	implies	imply	VERB
ap-2086	37	7	the	the	DET
ap-2086	37	8	hermiticity	hermiticity	NOUN
ap-2086	37	9	condition	condition	NOUN
ap-2086	37	10	(	(	PUNCT
ap-2086	37	11	3	3	NUM
ap-2086	37	12	)	)	PUNCT
ap-2086	37	13	.	.	PUNCT
ap-2086	38	1	second	second	ADJ
ap-2086	38	2	,	,	PUNCT
ap-2086	38	3	by	by	ADP
ap-2086	38	4	introducing	introduce	VERB
ap-2086	38	5	(	(	PUNCT
ap-2086	38	6	6	6	NUM
ap-2086	38	7	)	)	PUNCT
ap-2086	38	8	into	into	ADP
ap-2086	38	9	(	(	PUNCT
ap-2086	38	10	4	4	NUM
ap-2086	38	11	)	)	PUNCT
ap-2086	38	12	and	and	CCONJ
ap-2086	38	13	(	(	PUNCT
ap-2086	38	14	5	5	NUM
ap-2086	38	15	)	)	PUNCT
ap-2086	38	16	,	,	PUNCT
ap-2086	38	17	we	we	PRON
ap-2086	38	18	obtain	obtain	VERB
ap-2086	38	19	d−1∑	d−1∑	ADJ
ap-2086	38	20	p=0	p=0	PROPN
ap-2086	38	21	|ωp(aα)|2	|ωp(aα)|2	NOUN
ap-2086	39	1	=	=	SYM
ap-2086	39	2	1	1	NUM
ap-2086	39	3	(	(	PUNCT
ap-2086	39	4	7	7	NUM
ap-2086	39	5	)	)	PUNCT
ap-2086	39	6	and∣∣∣∣∣	and∣∣∣∣∣	NOUN
ap-2086	39	7	d−1∑	d−1∑	PROPN
ap-2086	39	8	p=0	p=0	PROPN
ap-2086	39	9	ωp(aα)ωp(bβ	ωp(aα)ωp(bβ	NOUN
ap-2086	39	10	)	)	PUNCT
ap-2086	39	11	∣∣∣∣∣	∣∣∣∣∣	ADP
ap-2086	39	12	2	2	NUM
ap-2086	39	13	=	=	SYM
ap-2086	39	14	δα	δα	NOUN
ap-2086	39	15	,	,	PUNCT
ap-2086	39	16	βδa	βδa	NOUN
ap-2086	39	17	,	,	PUNCT
ap-2086	39	18	b	b	NOUN
ap-2086	39	19	+	+	CCONJ
ap-2086	39	20	1	1	NUM
ap-2086	39	21	d	d	NOUN
ap-2086	39	22	(	(	PUNCT
ap-2086	39	23	1−	1−	NUM
ap-2086	39	24	δa	δa	PROPN
ap-2086	39	25	,	,	PUNCT
ap-2086	39	26	b	b	NOUN
ap-2086	39	27	)	)	PUNCT
ap-2086	39	28	(	(	PUNCT
ap-2086	39	29	8)	8)	NUM
ap-2086	39	30	respectively	respectively	ADV
ap-2086	39	31	.	.	PUNCT
ap-2086	40	1	it	it	PRON
ap-2086	40	2	is	be	AUX
ap-2086	40	3	clear	clear	ADJ
ap-2086	40	4	that	that	SCONJ
ap-2086	40	5	(	(	PUNCT
ap-2086	40	6	7	7	X
ap-2086	40	7	)	)	PUNCT
ap-2086	40	8	follows	follow	VERB
ap-2086	40	9	from	from	ADP
ap-2086	40	10	(	(	PUNCT
ap-2086	40	11	8)	8)	NUM
ap-2086	40	12	with	with	ADP
ap-2086	40	13	a	a	DET
ap-2086	40	14	=	=	SYM
ap-2086	40	15	b	b	PROPN
ap-2086	40	16	and	and	CCONJ
ap-2086	40	17	α	α	NOUN
ap-2086	40	18	=	=	SYM
ap-2086	40	19	β	β	X
ap-2086	40	20	.	.	PUNCT
ap-2086	41	1	therefore	therefore	ADV
ap-2086	41	2	,	,	PUNCT
ap-2086	41	3	(	(	PUNCT
ap-2086	41	4	3	3	X
ap-2086	41	5	)	)	PUNCT
ap-2086	41	6	and	and	CCONJ
ap-2086	41	7	(	(	PUNCT
ap-2086	41	8	7	7	X
ap-2086	41	9	)	)	PUNCT
ap-2086	41	10	are	be	AUX
ap-2086	41	11	redundant	redundant	ADJ
ap-2086	42	1	124	124	NUM
ap-2086	42	2	http://dx.doi.org/10.14311/ap.2014.54.0124	http://dx.doi.org/10.14311/ap.2014.54.0124	NOUN
ap-2086	42	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-2086	42	4	vol	vol	NOUN
ap-2086	42	5	.	.	PUNCT
ap-2086	43	1	54	54	NUM
ap-2086	43	2	no	no	NOUN
ap-2086	43	3	.	.	PUNCT
ap-2086	44	1	2/2014	2/2014	NOUN
ap-2086	44	2	on	on	ADP
ap-2086	44	3	two	two	NUM
ap-2086	44	4	ways	way	NOUN
ap-2086	44	5	to	to	PART
ap-2086	44	6	look	look	VERB
ap-2086	44	7	for	for	ADP
ap-2086	44	8	mutually	mutually	ADV
ap-2086	44	9	unbiased	unbiased	ADJ
ap-2086	44	10	bases	basis	NOUN
ap-2086	44	11	in	in	ADP
ap-2086	44	12	view	view	NOUN
ap-2086	44	13	of	of	ADP
ap-2086	44	14	(	(	PUNCT
ap-2086	44	15	5	5	NUM
ap-2086	44	16	)	)	PUNCT
ap-2086	44	17	and	and	CCONJ
ap-2086	44	18	(	(	PUNCT
ap-2086	44	19	6	6	NUM
ap-2086	44	20	)	)	PUNCT
ap-2086	44	21	.	.	PUNCT
ap-2086	45	1	as	as	ADP
ap-2086	45	2	a	a	DET
ap-2086	45	3	consequence	consequence	NOUN
ap-2086	45	4	,	,	PUNCT
ap-2086	45	5	proposition	proposition	NOUN
ap-2086	45	6	1	1	NUM
ap-2086	45	7	in	in	ADP
ap-2086	45	8	[	[	X
ap-2086	45	9	5	5	NUM
ap-2086	45	10	]	]	PUNCT
ap-2086	45	11	can	can	AUX
ap-2086	45	12	be	be	AUX
ap-2086	45	13	precised	precis	VERB
ap-2086	45	14	and	and	CCONJ
ap-2086	45	15	reformulated	reformulate	VERB
ap-2086	45	16	in	in	ADP
ap-2086	45	17	the	the	DET
ap-2086	45	18	following	following	ADJ
ap-2086	45	19	way	way	NOUN
ap-2086	45	20	.	.	PUNCT
ap-2086	46	1	proposition	proposition	NOUN
ap-2086	46	2	1	1	NUM
ap-2086	46	3	.	.	PUNCT
ap-2086	47	1	for	for	ADP
ap-2086	47	2	d	d	PROPN
ap-2086	47	3	≥	≥	NUM
ap-2086	47	4	2	2	NUM
ap-2086	47	5	,	,	PUNCT
ap-2086	47	6	finding	find	VERB
ap-2086	47	7	d	d	PROPN
ap-2086	47	8	+	+	NOUN
ap-2086	47	9	1	1	NUM
ap-2086	47	10	mubs	mub	NOUN
ap-2086	47	11	in	in	ADP
ap-2086	47	12	cd	cd	PROPN
ap-2086	47	13	(	(	PUNCT
ap-2086	47	14	if	if	SCONJ
ap-2086	47	15	they	they	PRON
ap-2086	47	16	exist	exist	VERB
ap-2086	47	17	)	)	PUNCT
ap-2086	47	18	is	be	AUX
ap-2086	47	19	equivalent	equivalent	ADJ
ap-2086	47	20	to	to	ADP
ap-2086	47	21	finding	find	VERB
ap-2086	47	22	d(d+	d(d+	ADP
ap-2086	47	23	1	1	NUM
ap-2086	47	24	)	)	PUNCT
ap-2086	47	25	vectors	vector	NOUN
ap-2086	47	26	w(aα	w(aα	NOUN
ap-2086	47	27	)	)	PUNCT
ap-2086	47	28	in	in	ADP
ap-2086	47	29	cd2	cd2	PROPN
ap-2086	47	30	,	,	PUNCT
ap-2086	47	31	of	of	ADP
ap-2086	47	32	components	component	NOUN
ap-2086	47	33	wpq(aα	wpq(aα	ADJ
ap-2086	47	34	)	)	PUNCT
ap-2086	47	35	such	such	ADJ
ap-2086	47	36	that	that	SCONJ
ap-2086	47	37	d−1∑	d−1∑	PROPN
ap-2086	47	38	p=0	p=0	PROPN
ap-2086	47	39	d−1∑	d−1∑	PROPN
ap-2086	47	40	q=0	q=0	ADV
ap-2086	47	41	wpq(aα)wpq(bβ	wpq(aα)wpq(bβ	NUM
ap-2086	47	42	)	)	PUNCT
ap-2086	48	1	=	=	SYM
ap-2086	48	2	δα	δα	PROPN
ap-2086	48	3	,	,	PUNCT
ap-2086	48	4	βδa	βδa	NOUN
ap-2086	48	5	,	,	PUNCT
ap-2086	48	6	b	b	NOUN
ap-2086	48	7	+	+	CCONJ
ap-2086	48	8	1	1	NUM
ap-2086	48	9	d	d	NOUN
ap-2086	48	10	(	(	PUNCT
ap-2086	48	11	1−	1−	NUM
ap-2086	48	12	δa	δa	PROPN
ap-2086	48	13	,	,	PUNCT
ap-2086	48	14	b	b	NOUN
ap-2086	48	15	)	)	PUNCT
ap-2086	48	16	(	(	PUNCT
ap-2086	48	17	9	9	NUM
ap-2086	48	18	)	)	PUNCT
ap-2086	48	19	and	and	CCONJ
ap-2086	48	20	wpq(aα	wpq(aα	X
ap-2086	48	21	)	)	PUNCT
ap-2086	48	22	=	=	SYM
ap-2086	48	23	ωp(aα)ωq(aα	ωp(aα)ωq(aα	X
ap-2086	48	24	)	)	PUNCT
ap-2086	48	25	,	,	PUNCT
ap-2086	48	26	p	p	X
ap-2086	48	27	,	,	PUNCT
ap-2086	48	28	q	q	PROPN
ap-2086	48	29	∈	∈	PROPN
ap-2086	48	30	z	z	X
ap-2086	48	31	/	/	SYM
ap-2086	48	32	dz	dz	X
ap-2086	48	33	(	(	PUNCT
ap-2086	48	34	10	10	NUM
ap-2086	48	35	)	)	PUNCT
ap-2086	48	36	where	where	SCONJ
ap-2086	48	37	a	a	PRON
ap-2086	48	38	,	,	PUNCT
ap-2086	48	39	b	b	NOUN
ap-2086	48	40	=	=	SYM
ap-2086	48	41	0	0	NUM
ap-2086	48	42	,	,	PUNCT
ap-2086	48	43	1	1	NUM
ap-2086	48	44	,	,	PUNCT
ap-2086	48	45	.	.	PUNCT
ap-2086	48	46	.	.	PUNCT
ap-2086	48	47	.	.	PUNCT
ap-2086	49	1	,	,	PUNCT
ap-2086	49	2	d	d	NOUN
ap-2086	49	3	and	and	CCONJ
ap-2086	49	4	α	α	NOUN
ap-2086	49	5	,	,	PUNCT
ap-2086	49	6	β	β	X
ap-2086	49	7	=	=	SYM
ap-2086	49	8	0	0	NUM
ap-2086	49	9	,	,	PUNCT
ap-2086	49	10	1	1	NUM
ap-2086	49	11	,	,	PUNCT
ap-2086	49	12	.	.	PUNCT
ap-2086	49	13	.	.	PUNCT
ap-2086	50	1	.	.	PUNCT
ap-2086	51	1	,	,	PUNCT
ap-2086	51	2	d−	d−	PROPN
ap-2086	51	3	1	1	NUM
ap-2086	51	4	.	.	PUNCT
ap-2086	52	1	this	this	DET
ap-2086	52	2	result	result	NOUN
ap-2086	52	3	can	can	AUX
ap-2086	52	4	be	be	AUX
ap-2086	52	5	transcribed	transcribe	VERB
ap-2086	52	6	in	in	ADP
ap-2086	52	7	matrix	matrix	NOUN
ap-2086	52	8	form	form	NOUN
ap-2086	52	9	.	.	PUNCT
ap-2086	53	1	therefore	therefore	ADV
ap-2086	53	2	,	,	PUNCT
ap-2086	53	3	we	we	PRON
ap-2086	53	4	have	have	VERB
ap-2086	53	5	the	the	DET
ap-2086	53	6	following	follow	VERB
ap-2086	53	7	proposition	proposition	NOUN
ap-2086	53	8	.	.	PUNCT
ap-2086	54	1	proposition	proposition	NOUN
ap-2086	54	2	2	2	NUM
ap-2086	54	3	.	.	PUNCT
ap-2086	55	1	for	for	ADP
ap-2086	55	2	d	d	PROPN
ap-2086	55	3	≥	≥	NUM
ap-2086	55	4	2	2	NUM
ap-2086	55	5	,	,	PUNCT
ap-2086	55	6	finding	find	VERB
ap-2086	55	7	d	d	PROPN
ap-2086	55	8	+	+	NOUN
ap-2086	55	9	1	1	NUM
ap-2086	55	10	mubs	mub	NOUN
ap-2086	55	11	in	in	ADP
ap-2086	55	12	cd	cd	PROPN
ap-2086	55	13	(	(	PUNCT
ap-2086	55	14	if	if	SCONJ
ap-2086	55	15	they	they	PRON
ap-2086	55	16	exist	exist	VERB
ap-2086	55	17	)	)	PUNCT
ap-2086	55	18	is	be	AUX
ap-2086	55	19	equivalent	equivalent	ADJ
ap-2086	55	20	to	to	ADP
ap-2086	55	21	finding	find	VERB
ap-2086	55	22	d(d+	d(d+	ADP
ap-2086	55	23	1	1	NUM
ap-2086	55	24	)	)	PUNCT
ap-2086	55	25	matrices	matrix	NOUN
ap-2086	55	26	maα	maα	NOUN
ap-2086	55	27	of	of	ADP
ap-2086	55	28	dimension	dimension	NOUN
ap-2086	56	1	d	d	PROPN
ap-2086	56	2	,	,	PUNCT
ap-2086	56	3	with	with	ADP
ap-2086	56	4	elements	element	NOUN
ap-2086	56	5	(	(	PUNCT
ap-2086	56	6	maα)pq	maα)pq	NOUN
ap-2086	56	7	=	=	SYM
ap-2086	56	8	ωp(aα)ωq(aα	ωp(aα)ωq(aα	X
ap-2086	56	9	)	)	PUNCT
ap-2086	56	10	,	,	PUNCT
ap-2086	56	11	p	p	X
ap-2086	56	12	,	,	PUNCT
ap-2086	56	13	q	q	PROPN
ap-2086	56	14	∈	∈	PROPN
ap-2086	56	15	z	z	X
ap-2086	56	16	/	/	SYM
ap-2086	56	17	dz	dz	X
ap-2086	56	18	(	(	PUNCT
ap-2086	56	19	11	11	NUM
ap-2086	56	20	)	)	PUNCT
ap-2086	56	21	and	and	CCONJ
ap-2086	56	22	satisfying	satisfy	VERB
ap-2086	56	23	the	the	DET
ap-2086	56	24	trace	trace	NOUN
ap-2086	56	25	relations	relation	NOUN
ap-2086	56	26	tr	tr	NOUN
ap-2086	56	27	(	(	PUNCT
ap-2086	56	28	maαmbβ	maαmbβ	PROPN
ap-2086	56	29	)	)	PUNCT
ap-2086	56	30	=	=	SYM
ap-2086	56	31	δα	δα	PROPN
ap-2086	56	32	,	,	PUNCT
ap-2086	56	33	βδa	βδa	NOUN
ap-2086	56	34	,	,	PUNCT
ap-2086	56	35	b	b	NOUN
ap-2086	56	36	+	+	CCONJ
ap-2086	56	37	1	1	NUM
ap-2086	56	38	d	d	NOUN
ap-2086	56	39	(	(	PUNCT
ap-2086	56	40	1−	1−	NUM
ap-2086	56	41	δa	δa	PROPN
ap-2086	56	42	,	,	PUNCT
ap-2086	56	43	b	b	NOUN
ap-2086	56	44	)	)	PUNCT
ap-2086	56	45	(	(	PUNCT
ap-2086	56	46	12	12	NUM
ap-2086	56	47	)	)	PUNCT
ap-2086	56	48	where	where	SCONJ
ap-2086	56	49	a	a	PRON
ap-2086	56	50	,	,	PUNCT
ap-2086	56	51	b	b	NOUN
ap-2086	56	52	=	=	SYM
ap-2086	56	53	0	0	NUM
ap-2086	56	54	,	,	PUNCT
ap-2086	56	55	1	1	NUM
ap-2086	56	56	,	,	PUNCT
ap-2086	56	57	.	.	PUNCT
ap-2086	56	58	.	.	PUNCT
ap-2086	56	59	.	.	PUNCT
ap-2086	57	1	,	,	PUNCT
ap-2086	57	2	d	d	NOUN
ap-2086	57	3	and	and	CCONJ
ap-2086	57	4	α	α	NOUN
ap-2086	57	5	,	,	PUNCT
ap-2086	57	6	β	β	X
ap-2086	57	7	=	=	SYM
ap-2086	57	8	0	0	NUM
ap-2086	57	9	,	,	PUNCT
ap-2086	57	10	1	1	NUM
ap-2086	57	11	,	,	PUNCT
ap-2086	57	12	.	.	PUNCT
ap-2086	57	13	.	.	PUNCT
ap-2086	58	1	.	.	PUNCT
ap-2086	59	1	,	,	PUNCT
ap-2086	59	2	d−	d−	PROPN
ap-2086	59	3	1	1	NUM
ap-2086	59	4	.	.	NOUN
ap-2086	59	5	3	3	X
ap-2086	59	6	.	.	X
ap-2086	59	7	equivalence	equivalence	NOUN
ap-2086	59	8	suppose	suppose	VERB
ap-2086	59	9	that	that	SCONJ
ap-2086	59	10	we	we	PRON
ap-2086	59	11	have	have	VERB
ap-2086	59	12	a	a	DET
ap-2086	59	13	complete	complete	ADJ
ap-2086	59	14	set	set	NOUN
ap-2086	59	15	{	{	PUNCT
ap-2086	59	16	ba	ba	NOUN
ap-2086	59	17	:	:	PUNCT
ap-2086	59	18	a	a	PRON
ap-2086	59	19	=	=	SYM
ap-2086	59	20	0	0	NUM
ap-2086	59	21	,	,	PUNCT
ap-2086	59	22	1	1	NUM
ap-2086	59	23	,	,	PUNCT
ap-2086	59	24	.	.	PUNCT
ap-2086	59	25	.	.	PUNCT
ap-2086	60	1	.	.	PUNCT
ap-2086	61	1	,	,	PUNCT
ap-2086	61	2	d	d	X
ap-2086	61	3	}	}	PUNCT
ap-2086	61	4	of	of	ADP
ap-2086	61	5	d+	d+	NOUN
ap-2086	61	6	1	1	NUM
ap-2086	61	7	mubs	mub	NOUN
ap-2086	61	8	in	in	ADP
ap-2086	61	9	cd	cd	PROPN
ap-2086	61	10	,	,	PUNCT
ap-2086	61	11	i.e.	i.e.	X
ap-2086	61	12	,	,	PUNCT
ap-2086	61	13	d(d+	d(d+	PRON
ap-2086	61	14	1	1	NUM
ap-2086	61	15	)	)	PUNCT
ap-2086	61	16	vectors	vector	NOUN
ap-2086	61	17	|aα	|aα	NOUN
ap-2086	61	18	〉	〉	PROPN
ap-2086	61	19	satisfying	satisfying	NOUN
ap-2086	61	20	(	(	PUNCT
ap-2086	61	21	2	2	NUM
ap-2086	61	22	)	)	PUNCT
ap-2086	61	23	,	,	PUNCT
ap-2086	61	24	then	then	ADV
ap-2086	61	25	we	we	PRON
ap-2086	61	26	can	can	AUX
ap-2086	61	27	find	find	VERB
ap-2086	61	28	d(d+	d(d+	DET
ap-2086	61	29	1	1	NUM
ap-2086	61	30	)	)	PUNCT
ap-2086	61	31	vectors	vector	NOUN
ap-2086	61	32	w(aα	w(aα	NOUN
ap-2086	61	33	)	)	PUNCT
ap-2086	61	34	in	in	ADP
ap-2086	61	35	cd2	cd2	PROPN
ap-2086	61	36	,	,	PUNCT
ap-2086	61	37	of	of	ADP
ap-2086	61	38	components	component	NOUN
ap-2086	61	39	wpq(aα	wpq(aα	ADJ
ap-2086	61	40	)	)	PUNCT
ap-2086	61	41	,	,	PUNCT
ap-2086	61	42	satisfying	satisfy	VERB
ap-2086	61	43	(	(	PUNCT
ap-2086	61	44	9	9	NUM
ap-2086	61	45	)	)	PUNCT
ap-2086	61	46	and	and	CCONJ
ap-2086	61	47	(	(	PUNCT
ap-2086	61	48	10	10	NUM
ap-2086	61	49	)	)	PUNCT
ap-2086	61	50	.	.	PUNCT
ap-2086	62	1	this	this	PRON
ap-2086	62	2	can	can	AUX
ap-2086	62	3	be	be	AUX
ap-2086	62	4	achieved	achieve	VERB
ap-2086	62	5	by	by	ADP
ap-2086	62	6	introducing	introduce	VERB
ap-2086	62	7	the	the	DET
ap-2086	62	8	projection	projection	NOUN
ap-2086	62	9	operators	operator	NOUN
ap-2086	62	10	πaα	πaα	ADV
ap-2086	62	11	=	=	SYM
ap-2086	62	12	|aα〉〈aα|	|aα〉〈aα|	X
ap-2086	62	13	(	(	PUNCT
ap-2086	62	14	13	13	NUM
ap-2086	62	15	)	)	PUNCT
ap-2086	62	16	where	where	SCONJ
ap-2086	62	17	a	a	DET
ap-2086	62	18	=	=	SYM
ap-2086	62	19	0	0	NUM
ap-2086	62	20	,	,	PUNCT
ap-2086	62	21	1	1	NUM
ap-2086	62	22	,	,	PUNCT
ap-2086	62	23	.	.	PUNCT
ap-2086	62	24	.	.	PUNCT
ap-2086	62	25	.	.	PUNCT
ap-2086	63	1	,	,	PUNCT
ap-2086	63	2	d	d	NOUN
ap-2086	63	3	and	and	CCONJ
ap-2086	63	4	α	α	NOUN
ap-2086	63	5	=	=	SYM
ap-2086	63	6	0	0	NUM
ap-2086	63	7	,	,	PUNCT
ap-2086	63	8	1	1	NUM
ap-2086	63	9	,	,	PUNCT
ap-2086	63	10	.	.	PUNCT
ap-2086	63	11	.	.	PUNCT
ap-2086	64	1	.	.	PUNCT
ap-2086	65	1	,	,	PUNCT
ap-2086	66	1	d	d	X
ap-2086	66	2	−	−	NOUN
ap-2086	67	1	1	1	X
ap-2086	67	2	.	.	PUNCT
ap-2086	68	1	in	in	ADP
ap-2086	68	2	fact	fact	NOUN
ap-2086	68	3	,	,	PUNCT
ap-2086	68	4	it	it	PRON
ap-2086	68	5	is	be	AUX
ap-2086	68	6	sufficient	sufficient	ADJ
ap-2086	68	7	to	to	PART
ap-2086	68	8	develop	develop	VERB
ap-2086	68	9	πaα	πaα	PROPN
ap-2086	68	10	in	in	ADP
ap-2086	68	11	terms	term	NOUN
ap-2086	68	12	of	of	ADP
ap-2086	68	13	the	the	DET
ap-2086	68	14	epq	epq	NOUN
ap-2086	68	15	generators	generator	NOUN
ap-2086	68	16	of	of	ADP
ap-2086	68	17	the	the	DET
ap-2086	68	18	gl(d	gl(d	ADJ
ap-2086	68	19	,	,	PUNCT
ap-2086	68	20	c	c	NOUN
ap-2086	68	21	)	)	PUNCT
ap-2086	68	22	complex	complex	ADJ
ap-2086	68	23	lie	lie	NOUN
ap-2086	68	24	group	group	NOUN
ap-2086	68	25	;	;	PUNCT
ap-2086	68	26	the	the	DET
ap-2086	68	27	coefficients	coefficient	NOUN
ap-2086	68	28	of	of	ADP
ap-2086	68	29	the	the	DET
ap-2086	68	30	development	development	NOUN
ap-2086	68	31	are	be	AUX
ap-2086	68	32	nothing	nothing	PRON
ap-2086	68	33	but	but	SCONJ
ap-2086	68	34	the	the	DET
ap-2086	68	35	wpq(aα	wpq(aα	ADJ
ap-2086	68	36	)	)	PUNCT
ap-2086	68	37	complex	complex	ADJ
ap-2086	68	38	numbers	number	NOUN
ap-2086	68	39	satisfying	satisfy	VERB
ap-2086	68	40	(	(	PUNCT
ap-2086	68	41	9	9	NUM
ap-2086	68	42	)	)	PUNCT
ap-2086	68	43	and	and	CCONJ
ap-2086	68	44	(	(	PUNCT
ap-2086	68	45	10	10	NUM
ap-2086	68	46	)	)	PUNCT
ap-2086	68	47	,	,	PUNCT
ap-2086	68	48	see	see	VERB
ap-2086	68	49	[	[	X
ap-2086	68	50	5	5	X
ap-2086	68	51	]	]	PUNCT
ap-2086	68	52	for	for	ADP
ap-2086	68	53	more	more	ADJ
ap-2086	68	54	details	detail	NOUN
ap-2086	68	55	.	.	PUNCT
ap-2086	69	1	reciprocally	reciprocally	ADV
ap-2086	69	2	,	,	PUNCT
ap-2086	69	3	should	should	AUX
ap-2086	69	4	we	we	PRON
ap-2086	69	5	find	find	VERB
ap-2086	69	6	d(d+	d(d+	DET
ap-2086	69	7	1	1	X
ap-2086	69	8	)	)	PUNCT
ap-2086	69	9	vectors	vector	NOUN
ap-2086	69	10	w(aα	w(aα	NOUN
ap-2086	69	11	)	)	PUNCT
ap-2086	69	12	in	in	ADP
ap-2086	69	13	cd2	cd2	PROPN
ap-2086	69	14	,	,	PUNCT
ap-2086	69	15	of	of	ADP
ap-2086	69	16	components	component	NOUN
ap-2086	69	17	wpq(aα	wpq(aα	ADJ
ap-2086	69	18	)	)	PUNCT
ap-2086	69	19	,	,	PUNCT
ap-2086	69	20	satisfying	satisfy	VERB
ap-2086	69	21	(	(	PUNCT
ap-2086	69	22	9	9	NUM
ap-2086	69	23	)	)	PUNCT
ap-2086	69	24	and	and	CCONJ
ap-2086	69	25	(	(	PUNCT
ap-2086	69	26	10	10	NUM
ap-2086	69	27	)	)	PUNCT
ap-2086	69	28	,	,	PUNCT
ap-2086	69	29	then	then	ADV
ap-2086	69	30	we	we	PRON
ap-2086	69	31	could	could	AUX
ap-2086	69	32	construct	construct	VERB
ap-2086	69	33	d(d+1	d(d+1	NUM
ap-2086	69	34	)	)	PUNCT
ap-2086	69	35	vectors	vector	NOUN
ap-2086	69	36	|aα	|aα	NOUN
ap-2086	69	37	〉	〉	PROPN
ap-2086	69	38	satisfying	satisfying	NOUN
ap-2086	69	39	(	(	PUNCT
ap-2086	69	40	2	2	NUM
ap-2086	69	41	)	)	PUNCT
ap-2086	69	42	.	.	PUNCT
ap-2086	70	1	this	this	PRON
ap-2086	70	2	can	can	AUX
ap-2086	70	3	be	be	AUX
ap-2086	70	4	done	do	VERB
ap-2086	70	5	by	by	ADP
ap-2086	70	6	means	mean	NOUN
ap-2086	70	7	of	of	ADP
ap-2086	70	8	a	a	DET
ap-2086	70	9	diagonalization	diagonalization	NOUN
ap-2086	70	10	procedure	procedure	NOUN
ap-2086	70	11	of	of	ADP
ap-2086	70	12	the	the	DET
ap-2086	70	13	matrices	matrix	NOUN
ap-2086	70	14	maα	maα	NOUN
ap-2086	71	1	=	=	SYM
ap-2086	71	2	d−1∑	d−1∑	NOUN
ap-2086	71	3	p=0	p=0	PROPN
ap-2086	71	4	d−1∑	d−1∑	PROPN
ap-2086	72	1	q=0	q=0	ADV
ap-2086	72	2	wpq(aα)epq	wpq(aα)epq	PROPN
ap-2086	72	3	(	(	PUNCT
ap-2086	72	4	14	14	NUM
ap-2086	72	5	)	)	PUNCT
ap-2086	72	6	where	where	SCONJ
ap-2086	72	7	a	a	DET
ap-2086	72	8	=	=	SYM
ap-2086	72	9	0	0	NUM
ap-2086	72	10	,	,	PUNCT
ap-2086	72	11	1	1	NUM
ap-2086	72	12	,	,	PUNCT
ap-2086	72	13	.	.	PUNCT
ap-2086	72	14	.	.	PUNCT
ap-2086	72	15	.	.	PUNCT
ap-2086	73	1	,	,	PUNCT
ap-2086	73	2	d	d	NOUN
ap-2086	73	3	and	and	CCONJ
ap-2086	73	4	α	α	NOUN
ap-2086	73	5	=	=	SYM
ap-2086	73	6	0	0	NUM
ap-2086	73	7	,	,	PUNCT
ap-2086	73	8	1	1	NUM
ap-2086	73	9	,	,	PUNCT
ap-2086	73	10	.	.	PUNCT
ap-2086	73	11	.	.	PUNCT
ap-2086	74	1	.	.	PUNCT
ap-2086	75	1	,	,	PUNCT
ap-2086	76	1	d	d	X
ap-2086	76	2	−	−	NOUN
ap-2086	77	1	1	1	NUM
ap-2086	77	2	.	.	PUNCT
ap-2086	78	1	an	an	DET
ap-2086	78	2	alternative	alternative	ADJ
ap-2086	78	3	and	and	CCONJ
ap-2086	78	4	more	more	ADV
ap-2086	78	5	simple	simple	ADJ
ap-2086	78	6	way	way	NOUN
ap-2086	78	7	to	to	PART
ap-2086	78	8	obtain	obtain	VERB
ap-2086	78	9	the	the	DET
ap-2086	78	10	|aα	|aα	PROPN
ap-2086	78	11	〉	〉	PROPN
ap-2086	78	12	vectors	vector	NOUN
ap-2086	78	13	from	from	ADP
ap-2086	78	14	the	the	DET
ap-2086	78	15	w(aα	w(aα	PROPN
ap-2086	78	16	)	)	PUNCT
ap-2086	78	17	vectors	vector	NOUN
ap-2086	78	18	is	be	AUX
ap-2086	78	19	as	as	SCONJ
ap-2086	78	20	follows	follow	VERB
ap-2086	78	21	.	.	PUNCT
ap-2086	79	1	equation	equation	NOUN
ap-2086	79	2	(	(	PUNCT
ap-2086	79	3	8)	8)	NUM
ap-2086	79	4	leads	lead	VERB
ap-2086	79	5	to∣∣∣∣∣	to∣∣∣∣∣	ADJ
ap-2086	79	6	d−1∑	d−1∑	PROPN
ap-2086	79	7	p=0	p=0	PROPN
ap-2086	79	8	ωp(aα)ωp(bβ	ωp(aα)ωp(bβ	NOUN
ap-2086	79	9	)	)	PUNCT
ap-2086	79	10	∣∣∣∣∣	∣∣∣∣∣	ADP
ap-2086	80	1	=	=	SYM
ap-2086	80	2	δα	δα	PROPN
ap-2086	80	3	,	,	PUNCT
ap-2086	80	4	βδa	βδa	NOUN
ap-2086	80	5	,	,	PUNCT
ap-2086	80	6	b	b	PROPN
ap-2086	80	7	+	+	CCONJ
ap-2086	80	8	1√	1√	PROPN
ap-2086	80	9	d	d	PROPN
ap-2086	80	10	(	(	PUNCT
ap-2086	80	11	1−	1−	NUM
ap-2086	80	12	δa	δa	PROPN
ap-2086	80	13	,	,	PUNCT
ap-2086	80	14	b	b	NOUN
ap-2086	80	15	)	)	PUNCT
ap-2086	80	16	(	(	PUNCT
ap-2086	80	17	15	15	NUM
ap-2086	80	18	)	)	PUNCT
ap-2086	80	19	to	to	PART
ap-2086	80	20	be	be	AUX
ap-2086	80	21	compared	compare	VERB
ap-2086	80	22	with	with	ADP
ap-2086	80	23	(	(	PUNCT
ap-2086	80	24	2	2	NUM
ap-2086	80	25	)	)	PUNCT
ap-2086	80	26	.	.	PUNCT
ap-2086	81	1	then	then	ADV
ap-2086	81	2	,	,	PUNCT
ap-2086	81	3	the	the	DET
ap-2086	81	4	|aα	|aα	PROPN
ap-2086	81	5	〉	〉	PROPN
ap-2086	81	6	vectors	vector	NOUN
ap-2086	81	7	can	can	AUX
ap-2086	81	8	be	be	AUX
ap-2086	81	9	constructed	construct	VERB
ap-2086	81	10	once	once	ADV
ap-2086	81	11	the	the	DET
ap-2086	81	12	w(aα	w(aα	NOUN
ap-2086	81	13	)	)	PUNCT
ap-2086	81	14	vectors	vector	NOUN
ap-2086	81	15	are	be	AUX
ap-2086	81	16	known	know	VERB
ap-2086	81	17	.	.	PUNCT
ap-2086	82	1	the	the	DET
ap-2086	82	2	solution	solution	NOUN
ap-2086	82	3	,	,	PUNCT
ap-2086	82	4	in	in	ADP
ap-2086	82	5	matrix	matrix	NOUN
ap-2086	82	6	form	form	NOUN
ap-2086	82	7	,	,	PUNCT
ap-2086	82	8	is	be	AUX
ap-2086	82	9	|aα	|aα	PROPN
ap-2086	82	10	〉	〉	NOUN
ap-2086	82	11	=	=	PUNCT
ap-2086	82	12			X
ap-2086	82	13	ω0(aα	ω0(aα	X
ap-2086	82	14	)	)	PUNCT
ap-2086	82	15	ω1(aα	ω1(aα	NUM
ap-2086	82	16	)	)	PUNCT
ap-2086	82	17	...	...	PUNCT
ap-2086	83	1	ωd−1(aα	ωd−1(aα	X
ap-2086	83	2	)	)	PUNCT
ap-2086	83	3			PROPN
ap-2086	83	4	(	(	PUNCT
ap-2086	83	5	16	16	NUM
ap-2086	83	6	)	)	PUNCT
ap-2086	83	7	a	a	DET
ap-2086	83	8	=	=	SYM
ap-2086	83	9	0	0	NUM
ap-2086	83	10	,	,	PUNCT
ap-2086	83	11	1	1	NUM
ap-2086	83	12	,	,	PUNCT
ap-2086	83	13	.	.	PUNCT
ap-2086	83	14	.	.	PUNCT
ap-2086	83	15	.	.	PUNCT
ap-2086	84	1	,	,	PUNCT
ap-2086	84	2	d	d	X
ap-2086	84	3	α	α	NOUN
ap-2086	84	4	=	=	SYM
ap-2086	84	5	0	0	NUM
ap-2086	84	6	,	,	PUNCT
ap-2086	84	7	1	1	NUM
ap-2086	84	8	,	,	PUNCT
ap-2086	84	9	.	.	PUNCT
ap-2086	84	10	.	.	PUNCT
ap-2086	84	11	.	.	PUNCT
ap-2086	85	1	,	,	PUNCT
ap-2086	85	2	d−	d−	PROPN
ap-2086	85	3	1	1	NUM
ap-2086	85	4	(	(	PUNCT
ap-2086	85	5	17	17	NUM
ap-2086	85	6	)	)	PUNCT
ap-2086	85	7	therefore	therefore	ADV
ap-2086	85	8	,	,	PUNCT
ap-2086	85	9	we	we	PRON
ap-2086	85	10	can	can	AUX
ap-2086	85	11	construct	construct	VERB
ap-2086	85	12	a	a	DET
ap-2086	85	13	complete	complete	ADJ
ap-2086	85	14	set	set	NOUN
ap-2086	85	15	{	{	PUNCT
ap-2086	85	16	ba	ba	NOUN
ap-2086	85	17	:	:	PUNCT
ap-2086	85	18	a	a	PRON
ap-2086	85	19	=	=	SYM
ap-2086	85	20	0	0	NUM
ap-2086	85	21	,	,	PUNCT
ap-2086	85	22	1	1	NUM
ap-2086	85	23	,	,	PUNCT
ap-2086	85	24	.	.	PUNCT
ap-2086	85	25	.	.	PUNCT
ap-2086	86	1	.	.	PUNCT
ap-2086	87	1	,	,	PUNCT
ap-2086	87	2	d	d	X
ap-2086	87	3	}	}	PUNCT
ap-2086	87	4	of	of	ADP
ap-2086	87	5	d	d	PROPN
ap-2086	87	6	+	+	CCONJ
ap-2086	87	7	1	1	NUM
ap-2086	87	8	mubs	mub	NOUN
ap-2086	87	9	from	from	ADP
ap-2086	87	10	the	the	DET
ap-2086	87	11	knowledge	knowledge	NOUN
ap-2086	87	12	of	of	ADP
ap-2086	87	13	d(d+	d(d+	PRON
ap-2086	87	14	1	1	NUM
ap-2086	87	15	)	)	PUNCT
ap-2086	87	16	vectors	vector	NOUN
ap-2086	87	17	w(aα	w(aα	NOUN
ap-2086	87	18	)	)	PUNCT
ap-2086	87	19	.	.	PUNCT
ap-2086	88	1	note	note	VERB
ap-2086	88	2	that	that	SCONJ
ap-2086	88	3	,	,	PUNCT
ap-2086	88	4	for	for	ADP
ap-2086	88	5	fixed	fix	VERB
ap-2086	88	6	a	a	PRON
ap-2086	88	7	and	and	CCONJ
ap-2086	88	8	α	α	NOUN
ap-2086	88	9	,	,	PUNCT
ap-2086	88	10	the	the	DET
ap-2086	88	11	|aα	|aα	PROPN
ap-2086	88	12	〉	〉	PROPN
ap-2086	88	13	vector	vector	NOUN
ap-2086	88	14	is	be	AUX
ap-2086	88	15	an	an	DET
ap-2086	88	16	eigenvector	eigenvector	NOUN
ap-2086	88	17	of	of	ADP
ap-2086	88	18	the	the	DET
ap-2086	88	19	maα	maα	NOUN
ap-2086	88	20	matrix	matrix	NOUN
ap-2086	88	21	with	with	ADP
ap-2086	88	22	eigenvalue	eigenvalue	PROPN
ap-2086	88	23	1	1	NUM
ap-2086	88	24	.	.	PUNCT
ap-2086	89	1	this	this	PRON
ap-2086	89	2	establishes	establish	VERB
ap-2086	89	3	a	a	DET
ap-2086	89	4	link	link	NOUN
ap-2086	89	5	with	with	ADP
ap-2086	89	6	the	the	DET
ap-2086	89	7	above	above	ADV
ap-2086	89	8	-	-	PUNCT
ap-2086	89	9	mentioned	mention	VERB
ap-2086	89	10	diagonalization	diagonalization	NOUN
ap-2086	89	11	procedure	procedure	NOUN
ap-2086	89	12	.	.	PUNCT
ap-2086	90	1	4	4	X
ap-2086	90	2	.	.	X
ap-2086	90	3	a	a	DET
ap-2086	90	4	parallel	parallel	ADJ
ap-2086	90	5	problem	problem	NOUN
ap-2086	90	6	the	the	DET
ap-2086	90	7	present	present	ADJ
ap-2086	90	8	work	work	NOUN
ap-2086	90	9	takes	take	VERB
ap-2086	90	10	its	its	PRON
ap-2086	90	11	origin	origin	NOUN
ap-2086	90	12	in	in	ADP
ap-2086	90	13	[	[	X
ap-2086	90	14	6	6	NUM
ap-2086	90	15	]	]	PUNCT
ap-2086	90	16	,	,	PUNCT
ap-2086	90	17	where	where	SCONJ
ap-2086	90	18	some	some	DET
ap-2086	90	19	similar	similar	ADJ
ap-2086	90	20	developments	development	NOUN
ap-2086	90	21	were	be	AUX
ap-2086	90	22	achieved	achieve	VERB
ap-2086	90	23	in	in	ADP
ap-2086	90	24	the	the	DET
ap-2086	90	25	search	search	NOUN
ap-2086	90	26	of	of	ADP
ap-2086	90	27	a	a	DET
ap-2086	90	28	sic	sic	ADJ
ap-2086	90	29	povm	povm	NOUN
ap-2086	90	30	.	.	PUNCT
ap-2086	91	1	symmetric	symmetric	ADJ
ap-2086	91	2	informationally	informationally	ADV
ap-2086	91	3	complete	complete	ADJ
ap-2086	91	4	positive	positive	ADJ
ap-2086	91	5	-	-	PUNCT
ap-2086	91	6	operator	operator	NOUN
ap-2086	91	7	-	-	PUNCT
ap-2086	91	8	valued	value	VERB
ap-2086	91	9	measures	measure	NOUN
ap-2086	91	10	play	play	VERB
ap-2086	91	11	an	an	DET
ap-2086	91	12	important	important	ADJ
ap-2086	91	13	role	role	NOUN
ap-2086	91	14	in	in	ADP
ap-2086	91	15	quantum	quantum	ADJ
ap-2086	91	16	information	information	NOUN
ap-2086	91	17	.	.	PUNCT
ap-2086	92	1	their	their	PRON
ap-2086	92	2	existence	existence	NOUN
ap-2086	92	3	in	in	ADP
ap-2086	92	4	arbitrary	arbitrary	ADJ
ap-2086	92	5	dimension	dimension	NOUN
ap-2086	92	6	is	be	AUX
ap-2086	92	7	still	still	ADV
ap-2086	92	8	the	the	DET
ap-2086	92	9	object	object	NOUN
ap-2086	92	10	of	of	ADP
ap-2086	92	11	numerous	numerous	ADJ
ap-2086	92	12	studies	study	NOUN
ap-2086	92	13	(	(	PUNCT
ap-2086	92	14	see	see	VERB
ap-2086	92	15	for	for	ADP
ap-2086	92	16	instance	instance	NOUN
ap-2086	92	17	[	[	X
ap-2086	92	18	7	7	NUM
ap-2086	92	19	]	]	NUM
ap-2086	92	20	)	)	PUNCT
ap-2086	92	21	.	.	PUNCT
ap-2086	93	1	a	a	DET
ap-2086	93	2	sic	sic	ADJ
ap-2086	93	3	povm	povm	NOUN
ap-2086	93	4	in	in	ADP
ap-2086	93	5	dimension	dimension	NOUN
ap-2086	93	6	d	d	NOUN
ap-2086	93	7	can	can	AUX
ap-2086	93	8	be	be	AUX
ap-2086	93	9	defined	define	VERB
ap-2086	93	10	as	as	ADP
ap-2086	93	11	a	a	DET
ap-2086	93	12	set	set	NOUN
ap-2086	93	13	of	of	ADP
ap-2086	93	14	d2	d2	PROPN
ap-2086	93	15	nonnegative	nonnegative	ADJ
ap-2086	93	16	operators	operator	NOUN
ap-2086	93	17	px	px	X
ap-2086	93	18	=	=	PUNCT
ap-2086	93	19	|φx〉〈φx|	|φx〉〈φx|	PUNCT
ap-2086	93	20	acting	act	VERB
ap-2086	93	21	on	on	ADP
ap-2086	93	22	cd	cd	PROPN
ap-2086	93	23	and	and	CCONJ
ap-2086	93	24	satisfying	satisfy	VERB
ap-2086	93	25	1	1	NUM
ap-2086	93	26	d	d	NOUN
ap-2086	93	27	d2∑	d2∑	PROPN
ap-2086	93	28	x=1	x=1	PUNCT
ap-2086	94	1	px	px	PROPN
ap-2086	94	2	=	=	PUNCT
ap-2086	94	3	i	i	PROPN
ap-2086	94	4	(	(	PUNCT
ap-2086	94	5	18	18	NUM
ap-2086	94	6	)	)	PUNCT
ap-2086	94	7	and	and	CCONJ
ap-2086	94	8	tr	tr	VERB
ap-2086	94	9	(	(	PUNCT
ap-2086	94	10	pxpy	pxpy	ADJ
ap-2086	94	11	)	)	PUNCT
ap-2086	94	12	=	=	SYM
ap-2086	94	13	dδx	dδx	VERB
ap-2086	94	14	,	,	PUNCT
ap-2086	94	15	y	y	PROPN
ap-2086	94	16	+	+	NOUN
ap-2086	94	17	1	1	NUM
ap-2086	94	18	d+	d+	SYM
ap-2086	94	19	1	1	NUM
ap-2086	94	20	(	(	PUNCT
ap-2086	94	21	19	19	NUM
ap-2086	94	22	)	)	PUNCT
ap-2086	94	23	where	where	SCONJ
ap-2086	94	24	i	i	PRON
ap-2086	94	25	is	be	AUX
ap-2086	94	26	the	the	DET
ap-2086	94	27	identity	identity	NOUN
ap-2086	94	28	operator	operator	NOUN
ap-2086	94	29	.	.	PUNCT
ap-2086	95	1	the	the	DET
ap-2086	95	2	search	search	NOUN
ap-2086	95	3	for	for	ADP
ap-2086	95	4	such	such	DET
ap-2086	95	5	a	a	DET
ap-2086	95	6	sic	sic	ADJ
ap-2086	95	7	povm	povm	NOUN
ap-2086	95	8	amounts	amount	NOUN
ap-2086	95	9	to	to	PART
ap-2086	95	10	find	find	VERB
ap-2086	95	11	d2	d2	PROPN
ap-2086	95	12	vectors	vector	NOUN
ap-2086	95	13	|φx	|φx	NOUN
ap-2086	95	14	〉	〉	NOUN
ap-2086	95	15	in	in	ADP
ap-2086	95	16	cd	cd	PROPN
ap-2086	95	17	satisfying	satisfy	VERB
ap-2086	95	18	1	1	NUM
ap-2086	95	19	d	d	NOUN
ap-2086	95	20	d2∑	d2∑	PROPN
ap-2086	95	21	x=1	x=1	PUNCT
ap-2086	96	1	|φx〉〈φx|	|φx〉〈φx|	NUM
ap-2086	96	2	=	=	SYM
ap-2086	96	3	i	i	PROPN
ap-2086	96	4	(	(	PUNCT
ap-2086	96	5	20	20	NUM
ap-2086	96	6	)	)	PUNCT
ap-2086	96	7	and	and	CCONJ
ap-2086	96	8	|〈φx|φy〉|	|〈φx|φy〉|	NOUN
ap-2086	96	9	=	=	SYM
ap-2086	96	10	√	√	NOUN
ap-2086	96	11	dδx	dδx	VERB
ap-2086	96	12	,	,	PUNCT
ap-2086	96	13	y	y	PROPN
ap-2086	96	14	+	+	NOUN
ap-2086	96	15	1	1	NUM
ap-2086	96	16	d+	d+	SYM
ap-2086	96	17	1	1	NUM
ap-2086	96	18	(	(	PUNCT
ap-2086	96	19	21	21	NUM
ap-2086	96	20	)	)	PUNCT
ap-2086	96	21	with	with	ADP
ap-2086	96	22	x	x	PROPN
ap-2086	96	23	,	,	PUNCT
ap-2086	96	24	y	y	PROPN
ap-2086	96	25	=	=	SYM
ap-2086	96	26	1	1	NUM
ap-2086	96	27	,	,	PUNCT
ap-2086	96	28	2	2	NUM
ap-2086	96	29	,	,	PUNCT
ap-2086	96	30	.	.	PUNCT
ap-2086	96	31	.	.	PUNCT
ap-2086	96	32	.	.	PUNCT
ap-2086	97	1	,	,	PUNCT
ap-2086	97	2	d2	d2	PROPN
ap-2086	97	3	.	.	PUNCT
ap-2086	98	1	the	the	DET
ap-2086	98	2	px	px	PROPN
ap-2086	98	3	operator	operator	NOUN
ap-2086	98	4	can	can	AUX
ap-2086	98	5	be	be	AUX
ap-2086	98	6	developed	develop	VERB
ap-2086	98	7	as	as	ADP
ap-2086	98	8	px	px	PROPN
ap-2086	98	9	=	=	PUNCT
ap-2086	98	10	d−1∑	d−1∑	PRON
ap-2086	98	11	p=0	p=0	PROPN
ap-2086	98	12	d−1∑	d−1∑	PROPN
ap-2086	98	13	q=0	q=0	ADP
ap-2086	98	14	vpq(x)epq	vpq(x)epq	PROPN
ap-2086	98	15	(	(	PUNCT
ap-2086	98	16	22	22	NUM
ap-2086	98	17	)	)	PUNCT
ap-2086	98	18	so	so	SCONJ
ap-2086	98	19	that	that	SCONJ
ap-2086	98	20	the	the	DET
ap-2086	98	21	determination	determination	NOUN
ap-2086	98	22	of	of	ADP
ap-2086	98	23	d2	d2	PROPN
ap-2086	98	24	operators	operator	NOUN
ap-2086	98	25	px	px	X
ap-2086	98	26	(	(	PUNCT
ap-2086	98	27	or	or	CCONJ
ap-2086	98	28	d2	d2	PROPN
ap-2086	98	29	vectors	vector	NOUN
ap-2086	98	30	|φx	|φx	NOUN
ap-2086	98	31	〉	〉	NOUN
ap-2086	98	32	)	)	PUNCT
ap-2086	98	33	is	be	AUX
ap-2086	98	34	equivalent	equivalent	ADJ
ap-2086	98	35	to	to	ADP
ap-2086	98	36	the	the	DET
ap-2086	98	37	determination	determination	NOUN
ap-2086	98	38	of	of	ADP
ap-2086	98	39	d2	d2	PROPN
ap-2086	98	40	vectors	vector	NOUN
ap-2086	98	41	v(x	v(x	PROPN
ap-2086	98	42	)	)	PUNCT
ap-2086	98	43	,	,	PUNCT
ap-2086	98	44	of	of	ADP
ap-2086	98	45	components	component	NOUN
ap-2086	98	46	vpq(x	vpq(x	PROPN
ap-2086	98	47	)	)	PUNCT
ap-2086	98	48	,	,	PUNCT
ap-2086	98	49	in	in	ADP
ap-2086	98	50	cd	cd	PROPN
ap-2086	98	51	2	2	NUM
ap-2086	98	52	.	.	PUNCT
ap-2086	99	1	in	in	ADP
ap-2086	99	2	the	the	DET
ap-2086	99	3	spirit	spirit	NOUN
ap-2086	99	4	of	of	ADP
ap-2086	99	5	the	the	DET
ap-2086	99	6	preceding	precede	VERB
ap-2086	99	7	sections	section	NOUN
ap-2086	99	8	,	,	PUNCT
ap-2086	99	9	we	we	PRON
ap-2086	99	10	have	have	VERB
ap-2086	99	11	the	the	DET
ap-2086	99	12	following	follow	VERB
ap-2086	99	13	result	result	NOUN
ap-2086	99	14	.	.	PUNCT
ap-2086	100	1	125	125	NUM
ap-2086	100	2	maurice	maurice	PROPN
ap-2086	100	3	r.	r.	PROPN
ap-2086	100	4	kibler	kibler	PROPN
ap-2086	100	5	acta	acta	PROPN
ap-2086	100	6	polytechnica	polytechnica	PROPN
ap-2086	100	7	proposition	proposition	NOUN
ap-2086	100	8	3	3	X
ap-2086	100	9	.	.	PUNCT
ap-2086	100	10	for	for	ADP
ap-2086	100	11	d	d	PROPN
ap-2086	100	12	≥	≥	NUM
ap-2086	100	13	2	2	NUM
ap-2086	100	14	,	,	PUNCT
ap-2086	100	15	finding	find	VERB
ap-2086	100	16	a	a	DET
ap-2086	100	17	sic	sic	ADJ
ap-2086	100	18	povm	povm	NOUN
ap-2086	100	19	in	in	ADP
ap-2086	100	20	cd	cd	PROPN
ap-2086	100	21	(	(	PUNCT
ap-2086	100	22	if	if	SCONJ
ap-2086	100	23	it	it	PRON
ap-2086	100	24	exists	exist	VERB
ap-2086	100	25	)	)	PUNCT
ap-2086	100	26	is	be	AUX
ap-2086	100	27	equivalent	equivalent	ADJ
ap-2086	100	28	to	to	ADP
ap-2086	100	29	finding	find	VERB
ap-2086	100	30	d2	d2	NOUN
ap-2086	100	31	vectors	vector	NOUN
ap-2086	100	32	v(x	v(x	NOUN
ap-2086	100	33	)	)	PUNCT
ap-2086	100	34	in	in	ADP
ap-2086	100	35	cd2	cd2	PROPN
ap-2086	100	36	,	,	PUNCT
ap-2086	100	37	of	of	ADP
ap-2086	100	38	components	component	NOUN
ap-2086	100	39	vpq(x	vpq(x	PROPN
ap-2086	100	40	)	)	PUNCT
ap-2086	100	41	such	such	ADJ
ap-2086	100	42	that	that	SCONJ
ap-2086	100	43	1	1	NUM
ap-2086	100	44	d	d	NOUN
ap-2086	100	45	d2∑	d2∑	PROPN
ap-2086	100	46	x=1	x=1	PUNCT
ap-2086	101	1	vpq(x	vpq(x	PROPN
ap-2086	101	2	)	)	PUNCT
ap-2086	101	3	=	=	SYM
ap-2086	101	4	δp	δp	PROPN
ap-2086	101	5	,	,	PUNCT
ap-2086	101	6	q	q	X
ap-2086	101	7	,	,	PUNCT
ap-2086	101	8	p	p	X
ap-2086	101	9	,	,	PUNCT
ap-2086	101	10	q	q	PROPN
ap-2086	101	11	∈	∈	PROPN
ap-2086	101	12	z	z	X
ap-2086	101	13	/	/	SYM
ap-2086	101	14	dz	dz	X
ap-2086	101	15	(	(	PUNCT
ap-2086	101	16	23	23	NUM
ap-2086	101	17	)	)	PUNCT
ap-2086	101	18	d−1∑	d−1∑	PROPN
ap-2086	101	19	p=0	p=0	PROPN
ap-2086	101	20	d−1∑	d−1∑	PROPN
ap-2086	101	21	q=0	q=0	PROPN
ap-2086	101	22	vpq(x)vpq(y	vpq(x)vpq(y	PROPN
ap-2086	101	23	)	)	PUNCT
ap-2086	102	1	=	=	SYM
ap-2086	102	2	dδx	dδx	VERB
ap-2086	102	3	,	,	PUNCT
ap-2086	102	4	y	y	PROPN
ap-2086	103	1	+	+	NOUN
ap-2086	103	2	1	1	NUM
ap-2086	103	3	d+	d+	SYM
ap-2086	103	4	1	1	NUM
ap-2086	103	5	(	(	PUNCT
ap-2086	103	6	24	24	NUM
ap-2086	103	7	)	)	PUNCT
ap-2086	103	8	and	and	CCONJ
ap-2086	103	9	vpq(x	vpq(x	PROPN
ap-2086	103	10	)	)	PUNCT
ap-2086	103	11	=	=	SYM
ap-2086	103	12	νp(x)νq(x	νp(x)νq(x	PROPN
ap-2086	103	13	)	)	PUNCT
ap-2086	103	14	,	,	PUNCT
ap-2086	103	15	p	p	X
ap-2086	103	16	,	,	PUNCT
ap-2086	103	17	q	q	PROPN
ap-2086	103	18	∈	∈	PROPN
ap-2086	103	19	z	z	X
ap-2086	103	20	/	/	SYM
ap-2086	103	21	dz	dz	PROPN
ap-2086	103	22	(	(	PUNCT
ap-2086	103	23	25	25	NUM
ap-2086	103	24	)	)	PUNCT
ap-2086	103	25	where	where	SCONJ
ap-2086	103	26	x	x	X
ap-2086	103	27	,	,	PUNCT
ap-2086	103	28	y	y	PROPN
ap-2086	103	29	=	=	SYM
ap-2086	103	30	1	1	NUM
ap-2086	103	31	,	,	PUNCT
ap-2086	103	32	2	2	NUM
ap-2086	103	33	,	,	PUNCT
ap-2086	103	34	.	.	PUNCT
ap-2086	103	35	.	.	PUNCT
ap-2086	103	36	.	.	PUNCT
ap-2086	104	1	,	,	PUNCT
ap-2086	104	2	d2	d2	PROPN
ap-2086	104	3	.	.	PROPN
ap-2086	105	1	5	5	NUM
ap-2086	105	2	.	.	X
ap-2086	105	3	concluding	conclude	VERB
ap-2086	105	4	remarks	remark	VERB
ap-2086	105	5	the	the	DET
ap-2086	105	6	equivalence	equivalence	NOUN
ap-2086	105	7	discussed	discuss	VERB
ap-2086	105	8	in	in	ADP
ap-2086	105	9	this	this	DET
ap-2086	105	10	work	work	NOUN
ap-2086	105	11	of	of	ADP
ap-2086	105	12	the	the	DET
ap-2086	105	13	two	two	NUM
ap-2086	105	14	ways	way	NOUN
ap-2086	105	15	of	of	ADP
ap-2086	105	16	looking	look	VERB
ap-2086	105	17	at	at	ADP
ap-2086	105	18	mubs	mub	NOUN
ap-2086	105	19	amounts	amount	VERB
ap-2086	105	20	in	in	ADP
ap-2086	105	21	some	some	DET
ap-2086	105	22	sense	sense	NOUN
ap-2086	105	23	to	to	ADP
ap-2086	105	24	the	the	DET
ap-2086	105	25	equivalence	equivalence	NOUN
ap-2086	105	26	between	between	ADP
ap-2086	105	27	the	the	DET
ap-2086	105	28	search	search	NOUN
ap-2086	105	29	for	for	ADP
ap-2086	105	30	equiangular	equiangular	NOUN
ap-2086	105	31	lines	line	NOUN
ap-2086	105	32	in	in	ADP
ap-2086	105	33	cd	cd	PROPN
ap-2086	105	34	and	and	CCONJ
ap-2086	105	35	for	for	ADP
ap-2086	105	36	equiangular	equiangular	NOUN
ap-2086	105	37	vectors	vector	NOUN
ap-2086	105	38	in	in	ADP
ap-2086	105	39	cd2	cd2	PROPN
ap-2086	105	40	(	(	PUNCT
ap-2086	105	41	cf	cf	NOUN
ap-2086	105	42	.	.	PUNCT
ap-2086	106	1	[	[	X
ap-2086	106	2	8	8	NUM
ap-2086	106	3	]	]	NUM
ap-2086	106	4	)	)	PUNCT
ap-2086	106	5	.	.	PUNCT
ap-2086	107	1	equiangular	equiangular	NOUN
ap-2086	107	2	lines	line	NOUN
ap-2086	107	3	in	in	ADP
ap-2086	107	4	cd	cd	PROPN
ap-2086	107	5	correspond	correspond	VERB
ap-2086	107	6	to	to	ADP
ap-2086	107	7	|〈aα|bβ〉|	|〈aα|bβ〉|	PROPN
ap-2086	107	8	=	=	SYM
ap-2086	107	9	1√	1√	PROPN
ap-2086	107	10	d	d	PROPN
ap-2086	107	11	for	for	ADP
ap-2086	107	12	a	a	DET
ap-2086	107	13	6=	6=	PROPN
ap-2086	107	14	b	b	PROPN
ap-2086	107	15	(	(	PUNCT
ap-2086	107	16	26	26	NUM
ap-2086	107	17	)	)	PUNCT
ap-2086	107	18	while	while	SCONJ
ap-2086	107	19	equiangular	equiangular	NOUN
ap-2086	107	20	vectors	vector	NOUN
ap-2086	107	21	in	in	ADP
ap-2086	107	22	cd2	cd2	PROPN
ap-2086	107	23	correspond	correspond	PROPN
ap-2086	107	24	to	to	ADP
ap-2086	107	25	w(aα	w(aα	PROPN
ap-2086	107	26	)	)	PUNCT
ap-2086	107	27	·	·	PUNCT
ap-2086	107	28	w(bβ	w(bβ	X
ap-2086	107	29	)	)	PUNCT
ap-2086	107	30	=	=	SYM
ap-2086	107	31	1	1	NUM
ap-2086	107	32	d	d	NOUN
ap-2086	107	33	for	for	ADP
ap-2086	107	34	a	a	DET
ap-2086	107	35	6=	6=	PROPN
ap-2086	107	36	b	b	PROPN
ap-2086	107	37	(	(	PUNCT
ap-2086	107	38	27	27	NUM
ap-2086	107	39	)	)	PUNCT
ap-2086	107	40	where	where	SCONJ
ap-2086	107	41	the	the	DET
ap-2086	107	42	w(aα)·w(bβ	w(aα)·w(bβ	NOUN
ap-2086	107	43	)	)	PUNCT
ap-2086	107	44	inner	inner	ADJ
ap-2086	107	45	product	product	NOUN
ap-2086	107	46	in	in	ADP
ap-2086	107	47	cd2	cd2	PROPN
ap-2086	107	48	is	be	AUX
ap-2086	107	49	defined	define	VERB
ap-2086	107	50	as	as	ADP
ap-2086	107	51	w(aα	w(aα	NOUN
ap-2086	107	52	)	)	PUNCT
ap-2086	107	53	·	·	PUNCT
ap-2086	107	54	w(bβ	w(bβ	X
ap-2086	107	55	)	)	PUNCT
ap-2086	107	56	=	=	PUNCT
ap-2086	108	1	d−1∑	d−1∑	NUM
ap-2086	108	2	p=0	p=0	PROPN
ap-2086	108	3	d−1∑	d−1∑	PROPN
ap-2086	108	4	q=0	q=0	ADV
ap-2086	108	5	wpq(aα)wpq(bβ	wpq(aα)wpq(bβ	NUM
ap-2086	108	6	)	)	PUNCT
ap-2086	108	7	(	(	PUNCT
ap-2086	108	8	28	28	X
ap-2086	108	9	)	)	PUNCT
ap-2086	108	10	observe	observe	VERB
ap-2086	108	11	that	that	SCONJ
ap-2086	108	12	the	the	DET
ap-2086	108	13	modulus	modulus	NOUN
ap-2086	108	14	disappears	disappear	VERB
ap-2086	108	15	and	and	CCONJ
ap-2086	108	16	the	the	DET
ap-2086	108	17	1/	1/	NUM
ap-2086	108	18	√	√	PROPN
ap-2086	108	19	d	d	NOUN
ap-2086	108	20	factor	factor	NOUN
ap-2086	108	21	is	be	AUX
ap-2086	108	22	replaced	replace	VERB
ap-2086	108	23	by	by	ADP
ap-2086	108	24	1	1	NUM
ap-2086	108	25	/	/	SYM
ap-2086	108	26	d	d	NOUN
ap-2086	108	27	when	when	SCONJ
ap-2086	108	28	passing	pass	VERB
ap-2086	108	29	from	from	ADP
ap-2086	108	30	(	(	PUNCT
ap-2086	108	31	26	26	NUM
ap-2086	108	32	)	)	PUNCT
ap-2086	108	33	to	to	ADP
ap-2086	108	34	(	(	PUNCT
ap-2086	108	35	27	27	NUM
ap-2086	108	36	)	)	PUNCT
ap-2086	108	37	.	.	PUNCT
ap-2086	109	1	it	it	PRON
ap-2086	109	2	was	be	AUX
ap-2086	109	3	questioned	question	VERB
ap-2086	109	4	in	in	ADP
ap-2086	109	5	[	[	X
ap-2086	109	6	5	5	NUM
ap-2086	109	7	]	]	PUNCT
ap-2086	109	8	if	if	SCONJ
ap-2086	109	9	the	the	DET
ap-2086	109	10	equiangular	equiangular	NOUN
ap-2086	109	11	vectors	vector	NOUN
ap-2086	109	12	approach	approach	NOUN
ap-2086	109	13	can	can	AUX
ap-2086	109	14	shed	shed	VERB
ap-2086	109	15	light	light	NOUN
ap-2086	109	16	on	on	ADP
ap-2086	109	17	the	the	DET
ap-2086	109	18	still	still	ADV
ap-2086	109	19	unsolved	unsolved	ADJ
ap-2086	109	20	question	question	NOUN
ap-2086	109	21	whether	whether	SCONJ
ap-2086	109	22	one	one	PRON
ap-2086	109	23	can	can	AUX
ap-2086	109	24	find	find	VERB
ap-2086	109	25	d	d	NOUN
ap-2086	109	26	+	+	NOUN
ap-2086	109	27	1	1	NUM
ap-2086	109	28	mubs	mub	NOUN
ap-2086	109	29	when	when	SCONJ
ap-2086	109	30	d	d	NOUN
ap-2086	109	31	is	be	AUX
ap-2086	109	32	not	not	PART
ap-2086	109	33	a	a	DET
ap-2086	109	34	(	(	PUNCT
ap-2086	109	35	strictly	strictly	ADV
ap-2086	109	36	positive	positive	ADJ
ap-2086	109	37	)	)	PUNCT
ap-2086	109	38	power	power	NOUN
ap-2086	109	39	of	of	ADP
ap-2086	109	40	a	a	DET
ap-2086	109	41	prime	prime	ADJ
ap-2086	109	42	integer	integer	NOUN
ap-2086	109	43	.	.	PUNCT
ap-2086	110	1	in	in	ADP
ap-2086	110	2	the	the	DET
ap-2086	110	3	case	case	NOUN
ap-2086	110	4	where	where	SCONJ
ap-2086	110	5	d	d	NOUN
ap-2086	110	6	is	be	AUX
ap-2086	110	7	not	not	PART
ap-2086	110	8	a	a	DET
ap-2086	110	9	power	power	NOUN
ap-2086	110	10	of	of	ADP
ap-2086	110	11	a	a	DET
ap-2086	110	12	prime	prime	NOUN
ap-2086	110	13	,	,	PUNCT
ap-2086	110	14	the	the	DET
ap-2086	110	15	impossibility	impossibility	NOUN
ap-2086	110	16	of	of	ADP
ap-2086	110	17	finding	find	VERB
ap-2086	110	18	d(d+1	d(d+1	NOUN
ap-2086	110	19	)	)	PUNCT
ap-2086	110	20	vectors	vector	NOUN
ap-2086	110	21	w(aα	w(aα	NOUN
ap-2086	110	22	)	)	PUNCT
ap-2086	110	23	or	or	CCONJ
ap-2086	110	24	d(d+1	d(d+1	NUM
ap-2086	110	25	)	)	PUNCT
ap-2086	110	26	matricesmaα	matricesmaα	ADP
ap-2086	110	27	satisfying	satisfy	VERB
ap-2086	110	28	the	the	DET
ap-2086	110	29	conditions	condition	NOUN
ap-2086	110	30	in	in	ADP
ap-2086	110	31	propositions	proposition	NOUN
ap-2086	110	32	1	1	NUM
ap-2086	110	33	and	and	CCONJ
ap-2086	110	34	2	2	NUM
ap-2086	110	35	would	would	AUX
ap-2086	110	36	mean	mean	VERB
ap-2086	110	37	that	that	SCONJ
ap-2086	110	38	d+	d+	NOUN
ap-2086	110	39	1	1	NUM
ap-2086	110	40	mubs	mub	NOUN
ap-2086	110	41	do	do	AUX
ap-2086	110	42	not	not	PART
ap-2086	110	43	exist	exist	VERB
ap-2086	110	44	in	in	ADP
ap-2086	110	45	cd	cd	PROPN
ap-2086	110	46	.	.	PUNCT
ap-2086	111	1	however	however	ADV
ap-2086	111	2	,	,	PUNCT
ap-2086	111	3	it	it	PRON
ap-2086	111	4	is	be	AUX
ap-2086	111	5	hard	hard	ADJ
ap-2086	111	6	to	to	PART
ap-2086	111	7	know	know	VERB
ap-2086	111	8	if	if	SCONJ
ap-2086	111	9	one	one	NUM
ap-2086	111	10	approach	approach	NOUN
ap-2086	111	11	is	be	AUX
ap-2086	111	12	better	well	ADJ
ap-2086	111	13	than	than	ADP
ap-2086	111	14	the	the	DET
ap-2086	111	15	other	other	ADJ
ap-2086	111	16	.	.	PUNCT
ap-2086	112	1	it	it	PRON
ap-2086	112	2	is	be	AUX
ap-2086	112	3	the	the	DET
ap-2086	112	4	hope	hope	NOUN
ap-2086	112	5	of	of	ADP
ap-2086	112	6	the	the	DET
ap-2086	112	7	author	author	NOUN
ap-2086	112	8	that	that	SCONJ
ap-2086	112	9	the	the	DET
ap-2086	112	10	equiangular	equiangular	NOUN
ap-2086	112	11	vectors	vector	NOUN
ap-2086	112	12	approach	approach	NOUN
ap-2086	112	13	can	can	AUX
ap-2086	112	14	be	be	AUX
ap-2086	112	15	tested	test	VERB
ap-2086	112	16	in	in	ADP
ap-2086	112	17	the	the	DET
ap-2086	112	18	d	d	PROPN
ap-2086	112	19	=	=	SYM
ap-2086	112	20	6	6	NUM
ap-2086	112	21	case	case	NOUN
ap-2086	112	22	for	for	ADP
ap-2086	112	23	which	which	PRON
ap-2086	112	24	one	one	PRON
ap-2086	112	25	knows	know	VERB
ap-2086	112	26	only	only	ADV
ap-2086	112	27	three	three	NUM
ap-2086	112	28	mubs	mub	NOUN
ap-2086	112	29	instead	instead	ADV
ap-2086	112	30	of	of	ADP
ap-2086	112	31	d+1	d+1	NOUN
ap-2086	112	32	=	=	PROPN
ap-2086	112	33	7	7	NUM
ap-2086	112	34	in	in	ADP
ap-2086	112	35	spite	spite	NOUN
ap-2086	112	36	of	of	ADP
ap-2086	112	37	numerous	numerous	ADJ
ap-2086	112	38	numerical	numerical	ADJ
ap-2086	112	39	studies	study	NOUN
ap-2086	112	40	(	(	PUNCT
ap-2086	112	41	see	see	VERB
ap-2086	112	42	[	[	X
ap-2086	112	43	9–11	9–11	X
ap-2086	112	44	]	]	PUNCT
ap-2086	112	45	and	and	CCONJ
ap-2086	112	46	references	reference	NOUN
ap-2086	112	47	therein	therein	ADV
ap-2086	112	48	for	for	ADP
ap-2086	112	49	an	an	DET
ap-2086	112	50	extensive	extensive	ADJ
ap-2086	112	51	list	list	NOUN
ap-2086	112	52	of	of	ADP
ap-2086	112	53	related	relate	VERB
ap-2086	112	54	works	work	NOUN
ap-2086	112	55	)	)	PUNCT
ap-2086	112	56	.	.	PUNCT
ap-2086	113	1	similar	similar	ADJ
ap-2086	113	2	remarks	remark	NOUN
ap-2086	113	3	apply	apply	VERB
ap-2086	113	4	to	to	ADP
ap-2086	113	5	sic	sic	ADJ
ap-2086	113	6	povms	povms	NOUN
ap-2086	113	7	.	.	PUNCT
ap-2086	114	1	the	the	DET
ap-2086	114	2	existence	existence	NOUN
ap-2086	114	3	problem	problem	NOUN
ap-2086	114	4	of	of	ADP
ap-2086	114	5	sic	sic	ADJ
ap-2086	114	6	povms	povms	NOUN
ap-2086	114	7	in	in	ADP
ap-2086	114	8	arbitrary	arbitrary	ADJ
ap-2086	114	9	dimension	dimension	NOUN
ap-2086	114	10	is	be	AUX
ap-2086	114	11	still	still	ADV
ap-2086	114	12	unsolved	unsolved	ADJ
ap-2086	114	13	although	although	SCONJ
ap-2086	114	14	sic	sic	ADJ
ap-2086	114	15	povms	povms	NOUN
ap-2086	114	16	have	have	AUX
ap-2086	114	17	been	be	AUX
ap-2086	114	18	constructed	construct	VERB
ap-2086	114	19	in	in	ADP
ap-2086	114	20	every	every	DET
ap-2086	114	21	dimension	dimension	NOUN
ap-2086	114	22	d	d	X
ap-2086	114	23	≤	≤	NUM
ap-2086	114	24	67	67	NUM
ap-2086	114	25	(	(	PUNCT
ap-2086	114	26	see	see	VERB
ap-2086	114	27	[	[	X
ap-2086	114	28	7	7	X
ap-2086	114	29	]	]	PUNCT
ap-2086	114	30	and	and	CCONJ
ap-2086	114	31	references	reference	NOUN
ap-2086	114	32	therein	therein	ADV
ap-2086	114	33	)	)	PUNCT
ap-2086	114	34	.	.	PUNCT
ap-2086	115	1	for	for	ADP
ap-2086	115	2	sic	sic	ADJ
ap-2086	115	3	povms	povms	NOUN
ap-2086	115	4	,	,	PUNCT
ap-2086	115	5	the	the	DET
ap-2086	115	6	equiangular	equiangular	NOUN
ap-2086	115	7	lines	line	NOUN
ap-2086	115	8	in	in	ADP
ap-2086	115	9	cd	cd	PROPN
ap-2086	115	10	correspond	correspond	NOUN
ap-2086	115	11	to	to	ADP
ap-2086	115	12	|〈φx|φy〉|	|〈φx|φy〉|	NOUN
ap-2086	115	13	=	=	SYM
ap-2086	115	14	1√	1√	ADJ
ap-2086	115	15	d+	d+	NOUN
ap-2086	115	16	1	1	NUM
ap-2086	115	17	for	for	ADP
ap-2086	115	18	x	x	SYM
ap-2086	115	19	6=	6=	PROPN
ap-2086	115	20	y	y	PROPN
ap-2086	115	21	(	(	PUNCT
ap-2086	115	22	29	29	NUM
ap-2086	115	23	)	)	PUNCT
ap-2086	115	24	and	and	CCONJ
ap-2086	115	25	the	the	DET
ap-2086	115	26	equiangular	equiangular	NOUN
ap-2086	115	27	vectors	vector	NOUN
ap-2086	115	28	in	in	ADP
ap-2086	115	29	cd2	cd2	PROPN
ap-2086	115	30	to	to	ADP
ap-2086	115	31	v(x	v(x	PROPN
ap-2086	115	32	)	)	PUNCT
ap-2086	115	33	·	·	PUNCT
ap-2086	116	1	v(y	v(y	X
ap-2086	116	2	)	)	PUNCT
ap-2086	116	3	=	=	SYM
ap-2086	116	4	1	1	NUM
ap-2086	116	5	d+	d+	NOUN
ap-2086	116	6	1	1	NUM
ap-2086	116	7	for	for	ADP
ap-2086	116	8	x	x	SYM
ap-2086	116	9	6=	6=	PROPN
ap-2086	116	10	y	y	PROPN
ap-2086	116	11	(	(	PUNCT
ap-2086	116	12	30	30	NUM
ap-2086	116	13	)	)	PUNCT
ap-2086	116	14	where	where	SCONJ
ap-2086	116	15	the	the	DET
ap-2086	116	16	v(x	v(x	PROPN
ap-2086	116	17	)	)	PUNCT
ap-2086	116	18	·	·	PUNCT
ap-2086	116	19	v(y	v(y	NUM
ap-2086	116	20	)	)	PUNCT
ap-2086	116	21	inner	inner	ADJ
ap-2086	116	22	product	product	NOUN
ap-2086	116	23	in	in	ADP
ap-2086	116	24	cd2	cd2	PROPN
ap-2086	116	25	is	be	AUX
ap-2086	116	26	defined	define	VERB
ap-2086	116	27	as	as	ADP
ap-2086	116	28	v(x	v(x	PROPN
ap-2086	116	29	)	)	PUNCT
ap-2086	116	30	·	·	PUNCT
ap-2086	116	31	v(y	v(y	X
ap-2086	116	32	)	)	PUNCT
ap-2086	116	33	=	=	PUNCT
ap-2086	117	1	d−1∑	d−1∑	NUM
ap-2086	117	2	p=0	p=0	PROPN
ap-2086	117	3	d−1∑	d−1∑	PROPN
ap-2086	117	4	q=0	q=0	PROPN
ap-2086	117	5	vpq(x)vpq(y	vpq(x)vpq(y	PROPN
ap-2086	117	6	)	)	PUNCT
ap-2086	117	7	(	(	PUNCT
ap-2086	117	8	31	31	NUM
ap-2086	117	9	)	)	PUNCT
ap-2086	117	10	the	the	DET
ap-2086	117	11	parallel	parallel	NOUN
ap-2086	117	12	between	between	ADP
ap-2086	117	13	mubs	mub	NOUN
ap-2086	117	14	and	and	CCONJ
ap-2086	117	15	sic	sic	ADJ
ap-2086	117	16	povm	povm	NOUN
ap-2086	117	17	characterized	characterize	VERB
ap-2086	117	18	by	by	ADP
ap-2086	117	19	the	the	DET
ap-2086	117	20	couples	couple	NOUN
ap-2086	117	21	of	of	ADP
ap-2086	117	22	equations	equation	NOUN
ap-2086	117	23	(	(	PUNCT
ap-2086	117	24	26)-(29	26)-(29	NUM
ap-2086	117	25	)	)	PUNCT
ap-2086	117	26	,	,	PUNCT
ap-2086	117	27	(	(	PUNCT
ap-2086	117	28	27)-(30	27)-(30	NUM
ap-2086	117	29	)	)	PUNCT
ap-2086	117	30	and	and	CCONJ
ap-2086	117	31	(	(	PUNCT
ap-2086	117	32	28)-(31	28)-(31	NUM
ap-2086	117	33	)	)	PUNCT
ap-2086	117	34	should	should	AUX
ap-2086	117	35	be	be	AUX
ap-2086	117	36	noted	note	VERB
ap-2086	117	37	.	.	PUNCT
ap-2086	118	1	these	these	DET
ap-2086	118	2	matters	matter	NOUN
ap-2086	118	3	will	will	AUX
ap-2086	118	4	be	be	AUX
ap-2086	118	5	the	the	DET
ap-2086	118	6	subject	subject	NOUN
ap-2086	118	7	of	of	ADP
ap-2086	118	8	future	future	ADJ
ap-2086	118	9	work	work	NOUN
ap-2086	118	10	.	.	PUNCT
ap-2086	119	1	acknowledgements	acknowledgement	NOUN
ap-2086	119	2	the	the	DET
ap-2086	119	3	material	material	NOUN
ap-2086	119	4	contained	contain	VERB
ap-2086	119	5	in	in	ADP
ap-2086	119	6	the	the	DET
ap-2086	119	7	present	present	ADJ
ap-2086	119	8	note	note	NOUN
ap-2086	119	9	was	be	AUX
ap-2086	119	10	planned	plan	VERB
ap-2086	119	11	to	to	PART
ap-2086	119	12	be	be	AUX
ap-2086	119	13	presented	present	VERB
ap-2086	119	14	at	at	ADP
ap-2086	119	15	the	the	DET
ap-2086	119	16	eleventh	eleventh	ADJ
ap-2086	119	17	edition	edition	NOUN
ap-2086	119	18	of	of	ADP
ap-2086	119	19	the	the	DET
ap-2086	119	20	workshop	workshop	NOUN
ap-2086	119	21	analytic	analytic	ADJ
ap-2086	119	22	and	and	CCONJ
ap-2086	119	23	algebraic	algebraic	ADJ
ap-2086	119	24	methods	method	NOUN
ap-2086	119	25	in	in	ADP
ap-2086	119	26	physics	physics	PROPN
ap-2086	119	27	(	(	PUNCT
ap-2086	119	28	aamp	aamp	PROPN
ap-2086	119	29	xi	xi	PROPN
ap-2086	119	30	)	)	PUNCT
ap-2086	119	31	.	.	PUNCT
ap-2086	120	1	unfortunately	unfortunately	ADV
ap-2086	120	2	,	,	PUNCT
ap-2086	120	3	the	the	DET
ap-2086	120	4	author	author	NOUN
ap-2086	120	5	was	be	AUX
ap-2086	120	6	unable	unable	ADJ
ap-2086	120	7	to	to	PART
ap-2086	120	8	participate	participate	VERB
ap-2086	120	9	in	in	ADP
ap-2086	120	10	aamp	aamp	PROPN
ap-2086	120	11	xi	xi	PROPN
ap-2086	120	12	.	.	PUNCT
ap-2086	121	1	he	he	PRON
ap-2086	121	2	is	be	AUX
ap-2086	121	3	greatly	greatly	ADV
ap-2086	121	4	indebted	indebted	ADJ
ap-2086	121	5	to	to	PART
ap-2086	121	6	miloslav	miloslav	VERB
ap-2086	121	7	znojil	znojil	NOUN
ap-2086	121	8	for	for	ADP
ap-2086	121	9	suggesting	suggest	VERB
ap-2086	121	10	that	that	SCONJ
ap-2086	121	11	he	he	PRON
ap-2086	121	12	submits	submit	VERB
ap-2086	121	13	this	this	DET
ap-2086	121	14	work	work	NOUN
ap-2086	121	15	to	to	PART
ap-2086	121	16	acta	acta	PROPN
ap-2086	121	17	polytechnica	polytechnica	PROPN
ap-2086	121	18	.	.	PUNCT
ap-2086	122	1	references	reference	NOUN
ap-2086	122	2	[	[	X
ap-2086	122	3	1	1	NUM
ap-2086	122	4	]	]	PUNCT
ap-2086	122	5	a.	a.	NOUN
ap-2086	122	6	vourdas	vourda	VERB
ap-2086	122	7	.	.	PUNCT
ap-2086	123	1	quantum	quantum	NOUN
ap-2086	123	2	systems	system	NOUN
ap-2086	123	3	with	with	ADP
ap-2086	123	4	finite	finite	ADJ
ap-2086	123	5	hilbert	hilbert	PROPN
ap-2086	123	6	space	space	NOUN
ap-2086	123	7	.	.	PUNCT
ap-2086	124	1	rep	rep	PROPN
ap-2086	124	2	prog	prog	PROPN
ap-2086	124	3	phys	phys	PROPN
ap-2086	124	4	67(3):267–320	67(3):267–320	PROPN
ap-2086	124	5	,	,	PUNCT
ap-2086	124	6	2004	2004	NUM
ap-2086	124	7	.	.	PUNCT
ap-2086	125	1	doi	doi	NOUN
ap-2086	125	2	:	:	PUNCT
ap-2086	125	3	10.1088/0034	10.1088/0034	NUM
ap-2086	125	4	-	-	PUNCT
ap-2086	125	5	4885/67/3	4885/67/3	NUM
ap-2086	125	6	/	/	SYM
ap-2086	125	7	r03	r03	NOUN
ap-2086	125	8	[	[	X
ap-2086	125	9	2	2	X
ap-2086	125	10	]	]	PUNCT
ap-2086	125	11	j.	j.	PROPN
ap-2086	125	12	tolar	tolar	PROPN
ap-2086	125	13	,	,	PUNCT
ap-2086	125	14	g.	g.	PROPN
ap-2086	125	15	chadzitaskos	chadzitaskos	PROPN
ap-2086	125	16	.	.	PUNCT
ap-2086	126	1	feynman	feynman	PROPN
ap-2086	126	2	’s	’s	PART
ap-2086	126	3	path	path	PROPN
ap-2086	126	4	integral	integral	ADJ
ap-2086	126	5	and	and	CCONJ
ap-2086	126	6	mutually	mutually	ADV
ap-2086	126	7	unbiased	unbiased	ADJ
ap-2086	126	8	bases	basis	NOUN
ap-2086	126	9	.	.	PUNCT
ap-2086	127	1	j	j	PROPN
ap-2086	127	2	phys	phy	NOUN
ap-2086	127	3	a	a	DET
ap-2086	127	4	:	:	PUNCT
ap-2086	127	5	math	math	PROPN
ap-2086	127	6	theor	theor	PROPN
ap-2086	127	7	42(24):1–11	42(24):1–11	NUM
ap-2086	127	8	,	,	PUNCT
ap-2086	127	9	2009	2009	NUM
ap-2086	127	10	.	.	PUNCT
ap-2086	128	1	doi	doi	NOUN
ap-2086	128	2	:	:	PUNCT
ap-2086	128	3	10.1088/1751	10.1088/1751	NUM
ap-2086	128	4	-	-	PUNCT
ap-2086	128	5	8113/42/24/245306	8113/42/24/245306	PROPN
ap-2086	128	6	[	[	X
ap-2086	128	7	3	3	NUM
ap-2086	128	8	]	]	PUNCT
ap-2086	128	9	m.	m.	PROPN
ap-2086	128	10	r.	r.	PROPN
ap-2086	128	11	kibler	kibler	PROPN
ap-2086	128	12	.	.	PUNCT
ap-2086	129	1	an	an	DET
ap-2086	129	2	angular	angular	ADJ
ap-2086	129	3	momentum	momentum	NOUN
ap-2086	129	4	approach	approach	NOUN
ap-2086	129	5	to	to	ADP
ap-2086	129	6	quadratic	quadratic	ADJ
ap-2086	129	7	fourier	fourier	NOUN
ap-2086	129	8	transform	transform	NOUN
ap-2086	129	9	,	,	PUNCT
ap-2086	129	10	hadamard	hadamard	ADJ
ap-2086	129	11	matrices	matrix	NOUN
ap-2086	129	12	,	,	PUNCT
ap-2086	129	13	gauss	gauss	NOUN
ap-2086	129	14	sums	sum	NOUN
ap-2086	129	15	,	,	PUNCT
ap-2086	129	16	mutually	mutually	ADV
ap-2086	129	17	unbiased	unbiased	ADJ
ap-2086	129	18	bases	basis	NOUN
ap-2086	129	19	,	,	PUNCT
ap-2086	129	20	unitary	unitary	ADJ
ap-2086	129	21	group	group	NOUN
ap-2086	129	22	and	and	CCONJ
ap-2086	129	23	pauli	pauli	PROPN
ap-2086	129	24	group	group	PROPN
ap-2086	129	25	.	.	PUNCT
ap-2086	130	1	j	j	PROPN
ap-2086	130	2	phys	phy	NOUN
ap-2086	130	3	a	a	PRON
ap-2086	130	4	:	:	PUNCT
ap-2086	130	5	math	math	PROPN
ap-2086	130	6	theor	theor	PROPN
ap-2086	130	7	42(35):1–28	42(35):1–28	PROPN
ap-2086	130	8	,	,	PUNCT
ap-2086	130	9	2009	2009	NUM
ap-2086	130	10	.	.	PUNCT
ap-2086	131	1	doi	doi	NOUN
ap-2086	131	2	:	:	PUNCT
ap-2086	131	3	10.1088/1751	10.1088/1751	NUM
ap-2086	131	4	-	-	PUNCT
ap-2086	131	5	8113/42/35/353001	8113/42/35/353001	PROPN
ap-2086	131	6	[	[	X
ap-2086	131	7	4	4	X
ap-2086	131	8	]	]	PUNCT
ap-2086	131	9	t.	t.	PROPN
ap-2086	131	10	durt	durt	PROPN
ap-2086	131	11	,	,	PUNCT
ap-2086	131	12	b.-g	b.-g	PROPN
ap-2086	131	13	.	.	PUNCT
ap-2086	132	1	englert	englert	PROPN
ap-2086	132	2	,	,	PUNCT
ap-2086	132	3	i.	i.	PROPN
ap-2086	132	4	bengtsson	bengtsson	PROPN
ap-2086	132	5	,	,	PUNCT
ap-2086	132	6	k.	k.	PROPN
ap-2086	132	7	życzkowski	życzkowski	PROPN
ap-2086	132	8	.	.	PUNCT
ap-2086	133	1	on	on	ADP
ap-2086	133	2	mutually	mutually	ADV
ap-2086	133	3	unbiased	unbiased	ADJ
ap-2086	133	4	bases	basis	NOUN
ap-2086	133	5	.	.	PUNCT
ap-2086	134	1	int	int	NOUN
ap-2086	134	2	j	j	PROPN
ap-2086	134	3	quantum	quantum	PROPN
ap-2086	134	4	inf	inf	NOUN
ap-2086	134	5	8(4):535–640	8(4):535–640	NUM
ap-2086	134	6	,	,	PUNCT
ap-2086	134	7	2010	2010	NUM
ap-2086	134	8	.	.	PUNCT
ap-2086	135	1	doi	doi	NOUN
ap-2086	135	2	:	:	PUNCT
ap-2086	135	3	10.1142	10.1142	NUM
ap-2086	135	4	/	/	SYM
ap-2086	135	5	s0219749910006502	s0219749910006502	VERB
ap-2086	136	1	[	[	X
ap-2086	136	2	5	5	NUM
ap-2086	136	3	]	]	PUNCT
ap-2086	136	4	m.	m.	PROPN
ap-2086	136	5	r.	r.	PROPN
ap-2086	136	6	kibler	kibler	PROPN
ap-2086	136	7	.	.	PUNCT
ap-2086	137	1	equiangular	equiangular	NOUN
ap-2086	137	2	vectors	vector	NOUN
ap-2086	137	3	approach	approach	VERB
ap-2086	137	4	to	to	ADP
ap-2086	137	5	mutually	mutually	ADV
ap-2086	137	6	unbiased	unbiased	ADJ
ap-2086	137	7	bases	basis	NOUN
ap-2086	137	8	.	.	PUNCT
ap-2086	138	1	entropy	entropy	PROPN
ap-2086	138	2	15(5):1726–1737	15(5):1726–1737	NUM
ap-2086	138	3	,	,	PUNCT
ap-2086	138	4	2013	2013	NUM
ap-2086	138	5	.	.	PUNCT
ap-2086	139	1	doi	doi	NOUN
ap-2086	139	2	:	:	PUNCT
ap-2086	139	3	10.3390	10.3390	NUM
ap-2086	139	4	/	/	SYM
ap-2086	139	5	e15051726	e15051726	NOUN
ap-2086	139	6	[	[	NOUN
ap-2086	139	7	6	6	NUM
ap-2086	139	8	]	]	PUNCT
ap-2086	139	9	o.	o.	NOUN
ap-2086	139	10	albouy	albouy	PROPN
ap-2086	139	11	,	,	PUNCT
ap-2086	139	12	m.	m.	PROPN
ap-2086	139	13	r.	r.	PROPN
ap-2086	139	14	kibler	kibler	PROPN
ap-2086	139	15	.	.	PUNCT
ap-2086	140	1	a	a	DET
ap-2086	140	2	unified	unified	ADJ
ap-2086	140	3	approach	approach	NOUN
ap-2086	140	4	to	to	ADP
ap-2086	140	5	sic	sic	ADJ
ap-2086	140	6	-	-	PUNCT
ap-2086	140	7	povms	povms	NOUN
ap-2086	140	8	and	and	CCONJ
ap-2086	140	9	mubs	mub	NOUN
ap-2086	140	10	.	.	PUNCT
ap-2086	141	1	j	j	PROPN
ap-2086	141	2	russian	russian	PROPN
ap-2086	141	3	laser	laser	NOUN
ap-2086	141	4	res	re	VERB
ap-2086	141	5	28(5):429–438	28(5):429–438	NUM
ap-2086	141	6	,	,	PUNCT
ap-2086	141	7	2007	2007	NUM
ap-2086	141	8	.	.	PUNCT
ap-2086	142	1	doi	doi	NOUN
ap-2086	142	2	:	:	PUNCT
ap-2086	142	3	10.1007	10.1007	NUM
ap-2086	142	4	/	/	SYM
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ap-2086	142	6	-	-	PUNCT
ap-2086	142	7	007	007	NUM
ap-2086	142	8	-	-	PUNCT
ap-2086	142	9	0032	0032	NUM
ap-2086	142	10	-	-	SYM
ap-2086	142	11	5	5	NUM
ap-2086	142	12	[	[	X
ap-2086	142	13	7	7	NUM
ap-2086	142	14	]	]	X
ap-2086	142	15	d.	d.	PROPN
ap-2086	142	16	m.	m.	PROPN
ap-2086	142	17	appleby	appleby	PROPN
ap-2086	142	18	,	,	PUNCT
ap-2086	142	19	c.	c.	PROPN
ap-2086	142	20	a.	a.	PROPN
ap-2086	142	21	fuchs	fuchs	PROPN
ap-2086	142	22	,	,	PUNCT
ap-2086	142	23	h.	h.	PROPN
ap-2086	142	24	zhu	zhu	PROPN
ap-2086	142	25	.	.	PUNCT
ap-2086	143	1	group	group	PROPN
ap-2086	143	2	theoretic	theoretic	PROPN
ap-2086	143	3	,	,	PUNCT
ap-2086	143	4	lie	lie	VERB
ap-2086	143	5	algebraic	algebraic	ADJ
ap-2086	143	6	and	and	CCONJ
ap-2086	143	7	jordan	jordan	PROPN
ap-2086	143	8	algebraic	algebraic	PROPN
ap-2086	143	9	formulations	formulation	NOUN
ap-2086	143	10	of	of	ADP
ap-2086	143	11	the	the	DET
ap-2086	143	12	sic	sic	ADJ
ap-2086	143	13	existence	existence	NOUN
ap-2086	143	14	problem	problem	NOUN
ap-2086	143	15	.	.	PUNCT
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ap-2086	145	3	]	]	X
ap-2086	145	4	c.	c.	NOUN
ap-2086	145	5	godsil	godsil	PROPN
ap-2086	145	6	,	,	PUNCT
ap-2086	145	7	a.	a.	PROPN
ap-2086	145	8	roy	roy	PROPN
ap-2086	145	9	.	.	PROPN
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ap-2086	145	12	,	,	PUNCT
ap-2086	145	13	mutually	mutually	ADV
ap-2086	145	14	unbiased	unbiased	ADJ
ap-2086	145	15	bases	basis	NOUN
ap-2086	145	16	,	,	PUNCT
ap-2086	145	17	and	and	CCONJ
ap-2086	145	18	spin	spin	NOUN
ap-2086	145	19	models	model	NOUN
ap-2086	145	20	.	.	PUNCT
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ap-2086	146	7	.	.	PUNCT
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ap-2086	147	4	/	/	SYM
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ap-2086	148	3	]	]	PUNCT
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ap-2086	148	9	.	.	PUNCT
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ap-2086	149	2	evidence	evidence	NOUN
ap-2086	149	3	for	for	ADP
ap-2086	149	4	the	the	DET
ap-2086	149	5	maximum	maximum	ADJ
ap-2086	149	6	number	number	NOUN
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ap-2086	149	11	in	in	ADP
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ap-2086	150	4	369(1	369(1	NUM
ap-2086	150	5	-	-	SYM
ap-2086	150	6	2):5–8	2):5–8	NUM
ap-2086	150	7	,	,	PUNCT
ap-2086	150	8	2007	2007	NUM
ap-2086	150	9	.	.	PUNCT
ap-2086	151	1	doi	doi	NOUN
ap-2086	151	2	:	:	PUNCT
ap-2086	151	3	10.1016	10.1016	NUM
ap-2086	151	4	/	/	SYM
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ap-2086	152	6	,	,	PUNCT
ap-2086	152	7	s.	s.	PROPN
ap-2086	152	8	weigert	weigert	PROPN
ap-2086	152	9	.	.	PUNCT
ap-2086	153	1	constructing	construct	VERB
ap-2086	153	2	mutually	mutually	ADV
ap-2086	153	3	unbiased	unbiased	ADJ
ap-2086	153	4	bases	basis	NOUN
ap-2086	153	5	in	in	ADP
ap-2086	153	6	dimension	dimension	NOUN
ap-2086	153	7	six	six	NUM
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ap-2086	154	2	rev	rev	VERB
ap-2086	154	3	a	a	DET
ap-2086	154	4	79(5):1–13	79(5):1–13	NUM
ap-2086	154	5	,	,	PUNCT
ap-2086	154	6	2009	2009	NUM
ap-2086	154	7	.	.	PUNCT
ap-2086	155	1	doi	doi	NOUN
ap-2086	155	2	:	:	PUNCT
ap-2086	155	3	10.1103	10.1103	NUM
ap-2086	155	4	/	/	SYM
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ap-2086	156	3	]	]	X
ap-2086	156	4	d.	d.	PROPN
ap-2086	156	5	mcnulty	mcnulty	PROPN
ap-2086	156	6	,	,	PUNCT
ap-2086	156	7	s.	s.	PROPN
ap-2086	156	8	weigert	weigert	PROPN
ap-2086	156	9	.	.	PUNCT
ap-2086	157	1	on	on	ADP
ap-2086	157	2	the	the	DET
ap-2086	157	3	impossibility	impossibility	NOUN
ap-2086	157	4	to	to	PART
ap-2086	157	5	extend	extend	VERB
ap-2086	157	6	triples	triple	NOUN
ap-2086	157	7	of	of	ADP
ap-2086	157	8	mutually	mutually	ADV
ap-2086	157	9	unbiased	unbiased	ADJ
ap-2086	157	10	product	product	NOUN
ap-2086	157	11	bases	basis	NOUN
ap-2086	157	12	in	in	ADP
ap-2086	157	13	dimension	dimension	NOUN
ap-2086	157	14	six	six	NUM
ap-2086	157	15	.	.	PUNCT
ap-2086	158	1	int	int	PROPN
ap-2086	158	2	j	j	PROPN
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ap-2086	158	5	10(5):1–11	10(5):1–11	NUM
ap-2086	158	6	,	,	PUNCT
ap-2086	158	7	2012	2012	NUM
ap-2086	158	8	.	.	PUNCT
ap-2086	159	1	doi	doi	NOUN
ap-2086	159	2	:	:	PUNCT
ap-2086	159	3	10.1142	10.1142	NUM
ap-2086	159	4	/	/	SYM
ap-2086	159	5	s0219749912500566	s0219749912500566	PROPN
ap-2086	159	6	126	126	NUM
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ap-2086	159	9	http://dx.doi.org/10.1088/1751-8113/42/35/353001	http://dx.doi.org/10.1088/1751-8113/42/35/353001	NUM
ap-2086	160	1	http://dx.doi.org/10.1142/s0219749910006502	http://dx.doi.org/10.1142/s0219749910006502	INTJ
ap-2086	161	1	http://dx.doi.org/10.3390/e15051726	http://dx.doi.org/10.3390/e15051726	NOUN
ap-2086	161	2	http://dx.doi.org/10.1007/s10946-007-0032-5	http://dx.doi.org/10.1007/s10946-007-0032-5	NUM
ap-2086	161	3	http://arxiv.org/abs/1312.0555v1	http://arxiv.org/abs/1312.0555v1	PROPN
ap-2086	161	4	http://dx.doi.org/10.1016/j.ejc.2008.01.002	http://dx.doi.org/10.1016/j.ejc.2008.01.002	NOUN
ap-2086	161	5	http://dx.doi.org/10.1016/j.physleta.2007.04.059	http://dx.doi.org/10.1016/j.physleta.2007.04.059	PROPN
ap-2086	162	1	http://dx.doi.org/10.1103/physreva.79.052316	http://dx.doi.org/10.1103/physreva.79.052316	PROPN
ap-2086	163	1	http://dx.doi.org/10.1142/s0219749912500566	http://dx.doi.org/10.1142/s0219749912500566	PROPN
ap-2086	163	2	acta	acta	PROPN
ap-2086	163	3	polytechnica	polytechnica	PROPN
ap-2086	163	4	54(2):124–126	54(2):124–126	PROPN
ap-2086	163	5	,	,	PUNCT
ap-2086	163	6	2014	2014	NUM
ap-2086	163	7	1	1	NUM
ap-2086	163	8	introduction	introduction	NOUN
ap-2086	163	9	2	2	NUM
ap-2086	163	10	the	the	DET
ap-2086	163	11	two	two	NUM
ap-2086	163	12	approaches	approach	NOUN
ap-2086	163	13	3	3	NUM
ap-2086	163	14	equivalence	equivalence	NOUN
ap-2086	163	15	4	4	NUM
ap-2086	163	16	a	a	DET
ap-2086	163	17	parallel	parallel	ADJ
ap-2086	163	18	problem	problem	NOUN
ap-2086	163	19	5	5	NUM
ap-2086	163	20	concluding	conclude	VERB
ap-2086	163	21	remarks	remark	NOUN
ap-2086	163	22	acknowledgements	acknowledgement	NOUN
ap-2086	163	23	references	reference	NOUN