id	sid	tid	token	lemma	pos
ap-7656	1	1	acta	acta	PROPN
ap-7656	1	2	polytechnica	polytechnica	PROPN
ap-7656	1	3	https://doi.org/10.14311/ap.2022.62.0222	https://doi.org/10.14311/ap.2022.62.0222	PROPN
ap-7656	1	4	acta	acta	PROPN
ap-7656	1	5	polytechnica	polytechnica	PROPN
ap-7656	2	1	62(1):222–227	62(1):222–227	PROPN
ap-7656	2	2	,	,	PUNCT
ap-7656	2	3	2022	2022	NUM
ap-7656	2	4	©	©	ADP
ap-7656	2	5	2022	2022	NUM
ap-7656	2	6	the	the	DET
ap-7656	2	7	author(s	author(s	NOUN
ap-7656	2	8	)	)	PUNCT
ap-7656	2	9	.	.	PUNCT
ap-7656	3	1	licensed	license	VERB
ap-7656	3	2	under	under	ADP
ap-7656	3	3	a	a	DET
ap-7656	3	4	cc	cc	NOUN
ap-7656	3	5	-	-	PUNCT
ap-7656	3	6	by	by	ADP
ap-7656	3	7	4.0	4.0	NUM
ap-7656	3	8	licence	licence	NOUN
ap-7656	3	9	published	publish	VERB
ap-7656	3	10	by	by	ADP
ap-7656	3	11	the	the	DET
ap-7656	3	12	czech	czech	PROPN
ap-7656	3	13	technical	technical	PROPN
ap-7656	3	14	university	university	PROPN
ap-7656	3	15	in	in	ADP
ap-7656	3	16	prague	prague	PROPN
ap-7656	3	17	a	a	DET
ap-7656	3	18	note	note	NOUN
ap-7656	3	19	on	on	ADP
ap-7656	3	20	entanglement	entanglement	NOUN
ap-7656	3	21	classification	classification	NOUN
ap-7656	3	22	for	for	ADP
ap-7656	3	23	tripartite	tripartite	ADJ
ap-7656	3	24	mixed	mixed	ADJ
ap-7656	3	25	states	state	NOUN
ap-7656	3	26	hui	hui	PROPN
ap-7656	3	27	zhaoa	zhaoa	PROPN
ap-7656	3	28	,	,	PUNCT
ap-7656	3	29	yu	yu	PROPN
ap-7656	3	30	-	-	PUNCT
ap-7656	3	31	qiu	qiu	PROPN
ap-7656	3	32	liua	liua	NOUN
ap-7656	3	33	,	,	PUNCT
ap-7656	3	34	zhi	zhi	PROPN
ap-7656	3	35	-	-	PROPN
ap-7656	3	36	xi	xi	ADP
ap-7656	3	37	wangb	wangb	PROPN
ap-7656	3	38	,	,	PUNCT
ap-7656	3	39	shao	shao	PROPN
ap-7656	3	40	-	-	PUNCT
ap-7656	3	41	ming	ming	PROPN
ap-7656	3	42	feib,∗	feib,∗	PROPN
ap-7656	4	1	a	a	DET
ap-7656	4	2	beijing	beijing	PROPN
ap-7656	4	3	university	university	PROPN
ap-7656	4	4	of	of	ADP
ap-7656	4	5	technology	technology	NOUN
ap-7656	4	6	,	,	PUNCT
ap-7656	4	7	faculty	faculty	NOUN
ap-7656	4	8	of	of	ADP
ap-7656	4	9	science	science	NOUN
ap-7656	4	10	,	,	PUNCT
ap-7656	4	11	beijing	beijing	PROPN
ap-7656	4	12	100124	100124	NUM
ap-7656	4	13	,	,	PUNCT
ap-7656	4	14	china	china	PROPN
ap-7656	4	15	b	b	PROPN
ap-7656	4	16	capital	capital	PROPN
ap-7656	4	17	normal	normal	ADJ
ap-7656	4	18	university	university	NOUN
ap-7656	4	19	,	,	PUNCT
ap-7656	4	20	school	school	NOUN
ap-7656	4	21	of	of	ADP
ap-7656	4	22	mathematical	mathematical	ADJ
ap-7656	4	23	sciences	sciences	PROPN
ap-7656	4	24	,	,	PUNCT
ap-7656	4	25	beijing	beijing	PROPN
ap-7656	4	26	100037	100037	NUM
ap-7656	4	27	,	,	PUNCT
ap-7656	4	28	china	china	PROPN
ap-7656	4	29	∗	∗	PROPN
ap-7656	4	30	corresponding	correspond	VERB
ap-7656	4	31	author	author	NOUN
ap-7656	4	32	:	:	PUNCT
ap-7656	4	33	feishm@cnu.edu.cn	feishm@cnu.edu.cn	NOUN
ap-7656	4	34	abstract	abstract	NOUN
ap-7656	4	35	.	.	PUNCT
ap-7656	5	1	we	we	PRON
ap-7656	5	2	study	study	VERB
ap-7656	5	3	the	the	DET
ap-7656	5	4	classification	classification	NOUN
ap-7656	5	5	of	of	ADP
ap-7656	5	6	entanglement	entanglement	NOUN
ap-7656	5	7	in	in	ADP
ap-7656	5	8	tripartite	tripartite	ADJ
ap-7656	5	9	systems	system	NOUN
ap-7656	5	10	by	by	ADP
ap-7656	5	11	using	use	VERB
ap-7656	5	12	bell	bell	NOUN
ap-7656	5	13	-	-	PUNCT
ap-7656	5	14	type	type	NOUN
ap-7656	5	15	inequalities	inequality	NOUN
ap-7656	5	16	and	and	CCONJ
ap-7656	5	17	principal	principal	ADJ
ap-7656	5	18	basis	basis	NOUN
ap-7656	5	19	.	.	PUNCT
ap-7656	6	1	by	by	ADP
ap-7656	6	2	using	use	VERB
ap-7656	6	3	bell	bell	NOUN
ap-7656	6	4	functions	function	NOUN
ap-7656	6	5	and	and	CCONJ
ap-7656	6	6	the	the	DET
ap-7656	6	7	generalized	generalized	ADJ
ap-7656	6	8	three	three	NUM
ap-7656	6	9	dimensional	dimensional	ADJ
ap-7656	6	10	pauli	pauli	PROPN
ap-7656	6	11	operators	operator	NOUN
ap-7656	6	12	,	,	PUNCT
ap-7656	6	13	we	we	PRON
ap-7656	6	14	present	present	VERB
ap-7656	6	15	a	a	DET
ap-7656	6	16	set	set	NOUN
ap-7656	6	17	of	of	ADP
ap-7656	6	18	bell	bell	NOUN
ap-7656	6	19	inequalities	inequality	NOUN
ap-7656	6	20	which	which	PRON
ap-7656	6	21	classifies	classify	VERB
ap-7656	6	22	the	the	DET
ap-7656	6	23	entanglement	entanglement	NOUN
ap-7656	6	24	of	of	ADP
ap-7656	6	25	triqutrit	triqutrit	NOUN
ap-7656	6	26	fully	fully	ADV
ap-7656	6	27	separable	separable	ADJ
ap-7656	6	28	and	and	CCONJ
ap-7656	6	29	bi	bi	ADJ
ap-7656	6	30	-	-	ADJ
ap-7656	6	31	separable	separable	ADJ
ap-7656	6	32	mixed	mixed	ADJ
ap-7656	6	33	states	state	NOUN
ap-7656	6	34	.	.	PUNCT
ap-7656	7	1	by	by	ADP
ap-7656	7	2	using	use	VERB
ap-7656	7	3	the	the	DET
ap-7656	7	4	correlation	correlation	NOUN
ap-7656	7	5	tensors	tensor	NOUN
ap-7656	7	6	in	in	ADP
ap-7656	7	7	the	the	DET
ap-7656	7	8	principal	principal	ADJ
ap-7656	7	9	basis	basis	NOUN
ap-7656	7	10	representation	representation	NOUN
ap-7656	7	11	of	of	ADP
ap-7656	7	12	density	density	NOUN
ap-7656	7	13	matrices	matrix	NOUN
ap-7656	7	14	,	,	PUNCT
ap-7656	7	15	we	we	PRON
ap-7656	7	16	obtain	obtain	VERB
ap-7656	7	17	separability	separability	NOUN
ap-7656	7	18	criteria	criterion	NOUN
ap-7656	7	19	for	for	ADP
ap-7656	7	20	fully	fully	ADV
ap-7656	7	21	separable	separable	ADJ
ap-7656	7	22	and	and	CCONJ
ap-7656	7	23	bi	bi	ADJ
ap-7656	7	24	-	-	ADJ
ap-7656	7	25	separable	separable	ADJ
ap-7656	7	26	2	2	NUM
ap-7656	7	27	⊗	⊗	PROPN
ap-7656	7	28	2	2	NUM
ap-7656	7	29	⊗	⊗	NUM
ap-7656	7	30	3	3	NUM
ap-7656	7	31	quantum	quantum	NOUN
ap-7656	7	32	mixed	mix	VERB
ap-7656	7	33	states	state	NOUN
ap-7656	7	34	.	.	PUNCT
ap-7656	8	1	detailed	detailed	ADJ
ap-7656	8	2	example	example	NOUN
ap-7656	8	3	is	be	AUX
ap-7656	8	4	given	give	VERB
ap-7656	8	5	to	to	PART
ap-7656	8	6	illustrate	illustrate	VERB
ap-7656	8	7	our	our	PRON
ap-7656	8	8	criteria	criterion	NOUN
ap-7656	8	9	in	in	ADP
ap-7656	8	10	classifying	classify	VERB
ap-7656	8	11	the	the	DET
ap-7656	8	12	tripartite	tripartite	ADJ
ap-7656	8	13	entanglement	entanglement	NOUN
ap-7656	8	14	.	.	PUNCT
ap-7656	9	1	keywords	keyword	NOUN
ap-7656	9	2	:	:	PUNCT
ap-7656	9	3	bell	bell	NOUN
ap-7656	9	4	inequalities	inequality	NOUN
ap-7656	9	5	,	,	PUNCT
ap-7656	9	6	separability	separability	NOUN
ap-7656	9	7	,	,	PUNCT
ap-7656	9	8	principal	principal	ADJ
ap-7656	9	9	basis	basis	NOUN
ap-7656	9	10	.	.	PUNCT
ap-7656	10	1	1	1	X
ap-7656	10	2	.	.	X
ap-7656	10	3	introduction	introduction	NOUN
ap-7656	10	4	one	one	NUM
ap-7656	10	5	of	of	ADP
ap-7656	10	6	the	the	DET
ap-7656	10	7	most	most	ADV
ap-7656	10	8	remarkable	remarkable	ADJ
ap-7656	10	9	features	feature	NOUN
ap-7656	10	10	that	that	PRON
ap-7656	10	11	distinguishes	distinguish	VERB
ap-7656	10	12	quantum	quantum	ADJ
ap-7656	10	13	mechanics	mechanic	NOUN
ap-7656	10	14	from	from	ADP
ap-7656	10	15	classical	classical	ADJ
ap-7656	10	16	mechanics	mechanic	NOUN
ap-7656	10	17	is	be	AUX
ap-7656	10	18	the	the	DET
ap-7656	10	19	quantum	quantum	ADJ
ap-7656	10	20	entanglement	entanglement	NOUN
ap-7656	10	21	.	.	PUNCT
ap-7656	11	1	entanglement	entanglement	NOUN
ap-7656	11	2	was	be	AUX
ap-7656	11	3	first	first	ADV
ap-7656	11	4	recognized	recognize	VERB
ap-7656	11	5	by	by	ADP
ap-7656	11	6	epr	epr	PROPN
ap-7656	12	1	[	[	X
ap-7656	12	2	1	1	NUM
ap-7656	12	3	]	]	PUNCT
ap-7656	12	4	,	,	PUNCT
ap-7656	12	5	with	with	ADP
ap-7656	12	6	significant	significant	ADJ
ap-7656	12	7	progress	progress	NOUN
ap-7656	12	8	made	make	VERB
ap-7656	12	9	by	by	ADP
ap-7656	12	10	bell	bell	NOUN
ap-7656	12	11	[	[	X
ap-7656	12	12	2	2	NUM
ap-7656	12	13	]	]	PUNCT
ap-7656	12	14	toward	toward	ADP
ap-7656	12	15	the	the	DET
ap-7656	12	16	resolution	resolution	NOUN
ap-7656	12	17	of	of	ADP
ap-7656	12	18	the	the	DET
ap-7656	12	19	epr	epr	PROPN
ap-7656	12	20	problem	problem	NOUN
ap-7656	12	21	.	.	PUNCT
ap-7656	13	1	since	since	SCONJ
ap-7656	13	2	bell	bell	PROPN
ap-7656	13	3	’s	’s	PART
ap-7656	13	4	work	work	NOUN
ap-7656	13	5	,	,	PUNCT
ap-7656	13	6	derivation	derivation	NOUN
ap-7656	13	7	of	of	ADP
ap-7656	13	8	new	new	ADJ
ap-7656	13	9	bell	bell	NOUN
ap-7656	13	10	-	-	PUNCT
ap-7656	13	11	like	like	ADJ
ap-7656	13	12	inequalities	inequality	NOUN
ap-7656	13	13	has	have	AUX
ap-7656	13	14	been	be	AUX
ap-7656	13	15	one	one	NUM
ap-7656	13	16	of	of	ADP
ap-7656	13	17	the	the	DET
ap-7656	13	18	important	important	ADJ
ap-7656	13	19	and	and	CCONJ
ap-7656	13	20	challenging	challenging	ADJ
ap-7656	13	21	subjects	subject	NOUN
ap-7656	13	22	.	.	PUNCT
ap-7656	14	1	chsh	chsh	PROPN
ap-7656	14	2	generalized	generalize	VERB
ap-7656	14	3	the	the	DET
ap-7656	14	4	original	original	ADJ
ap-7656	14	5	bell	bell	NOUN
ap-7656	14	6	inequalities	inequality	NOUN
ap-7656	14	7	to	to	ADP
ap-7656	14	8	a	a	DET
ap-7656	14	9	more	more	ADV
ap-7656	14	10	general	general	ADJ
ap-7656	14	11	case	case	NOUN
ap-7656	14	12	for	for	ADP
ap-7656	14	13	two	two	NUM
ap-7656	14	14	observers	observer	NOUN
ap-7656	14	15	[	[	X
ap-7656	14	16	3	3	NUM
ap-7656	14	17	]	]	PUNCT
ap-7656	14	18	.	.	PUNCT
ap-7656	15	1	in	in	ADP
ap-7656	15	2	[	[	X
ap-7656	15	3	4	4	X
ap-7656	15	4	]	]	PUNCT
ap-7656	15	5	the	the	DET
ap-7656	15	6	authors	author	NOUN
ap-7656	15	7	proposed	propose	VERB
ap-7656	15	8	an	an	DET
ap-7656	15	9	estimation	estimation	NOUN
ap-7656	15	10	of	of	ADP
ap-7656	15	11	quantum	quantum	ADJ
ap-7656	15	12	entanglement	entanglement	NOUN
ap-7656	15	13	by	by	ADP
ap-7656	15	14	measuring	measure	VERB
ap-7656	15	15	the	the	DET
ap-7656	15	16	maximum	maximum	ADJ
ap-7656	15	17	violation	violation	NOUN
ap-7656	15	18	of	of	ADP
ap-7656	15	19	the	the	DET
ap-7656	15	20	bell	bell	PROPN
ap-7656	15	21	inequality	inequality	NOUN
ap-7656	15	22	without	without	ADP
ap-7656	15	23	information	information	NOUN
ap-7656	15	24	of	of	ADP
ap-7656	15	25	the	the	DET
ap-7656	15	26	reduced	reduce	VERB
ap-7656	15	27	density	density	NOUN
ap-7656	15	28	matrices	matrix	NOUN
ap-7656	15	29	.	.	PUNCT
ap-7656	16	1	in	in	ADP
ap-7656	16	2	[	[	X
ap-7656	16	3	5	5	NUM
ap-7656	16	4	]	]	SYM
ap-7656	16	5	series	series	NOUN
ap-7656	16	6	of	of	ADP
ap-7656	16	7	bell	bell	PROPN
ap-7656	16	8	inequalities	inequality	NOUN
ap-7656	16	9	for	for	ADP
ap-7656	16	10	multipartite	multipartite	ADJ
ap-7656	16	11	states	state	NOUN
ap-7656	16	12	have	have	AUX
ap-7656	16	13	been	be	AUX
ap-7656	16	14	presented	present	VERB
ap-7656	16	15	with	with	ADP
ap-7656	16	16	sufficient	sufficient	ADJ
ap-7656	16	17	and	and	CCONJ
ap-7656	16	18	necessary	necessary	ADJ
ap-7656	16	19	conditions	condition	NOUN
ap-7656	16	20	to	to	PART
ap-7656	16	21	detect	detect	VERB
ap-7656	16	22	certain	certain	ADJ
ap-7656	16	23	entanglement	entanglement	NOUN
ap-7656	16	24	.	.	PUNCT
ap-7656	17	1	there	there	PRON
ap-7656	17	2	have	have	AUX
ap-7656	17	3	been	be	AUX
ap-7656	17	4	many	many	ADJ
ap-7656	17	5	important	important	ADJ
ap-7656	17	6	generalizations	generalization	NOUN
ap-7656	17	7	and	and	CCONJ
ap-7656	17	8	interesting	interesting	ADJ
ap-7656	17	9	applications	application	NOUN
ap-7656	17	10	of	of	ADP
ap-7656	17	11	bell	bell	NOUN
ap-7656	17	12	inequalities	inequality	NOUN
ap-7656	17	13	[	[	X
ap-7656	17	14	6–8	6–8	X
ap-7656	17	15	]	]	X
ap-7656	17	16	.	.	PUNCT
ap-7656	18	1	by	by	ADP
ap-7656	18	2	calculating	calculate	VERB
ap-7656	18	3	the	the	DET
ap-7656	18	4	measures	measure	NOUN
ap-7656	18	5	of	of	ADP
ap-7656	18	6	entanglement	entanglement	NOUN
ap-7656	18	7	and	and	CCONJ
ap-7656	18	8	the	the	DET
ap-7656	18	9	quantum	quantum	ADJ
ap-7656	18	10	violation	violation	NOUN
ap-7656	18	11	of	of	ADP
ap-7656	18	12	the	the	DET
ap-7656	18	13	bell	bell	NOUN
ap-7656	18	14	-	-	PUNCT
ap-7656	18	15	type	type	NOUN
ap-7656	18	16	inequality	inequality	NOUN
ap-7656	18	17	,	,	PUNCT
ap-7656	18	18	a	a	DET
ap-7656	18	19	relationship	relationship	NOUN
ap-7656	18	20	between	between	ADP
ap-7656	18	21	the	the	DET
ap-7656	18	22	entanglement	entanglement	NOUN
ap-7656	18	23	measure	measure	NOUN
ap-7656	18	24	and	and	CCONJ
ap-7656	18	25	the	the	DET
ap-7656	18	26	amount	amount	NOUN
ap-7656	18	27	of	of	ADP
ap-7656	18	28	quantum	quantum	ADJ
ap-7656	18	29	violation	violation	NOUN
ap-7656	18	30	was	be	AUX
ap-7656	18	31	derived	derive	VERB
ap-7656	18	32	in	in	ADP
ap-7656	18	33	[	[	X
ap-7656	18	34	9	9	NUM
ap-7656	18	35	]	]	PUNCT
ap-7656	18	36	.	.	PUNCT
ap-7656	19	1	however	however	ADV
ap-7656	19	2	,	,	PUNCT
ap-7656	19	3	for	for	ADP
ap-7656	19	4	high	high	ADJ
ap-7656	19	5	-	-	PUNCT
ap-7656	19	6	dimensional	dimensional	ADJ
ap-7656	19	7	multiple	multiple	ADJ
ap-7656	19	8	quantum	quantum	NOUN
ap-7656	19	9	systems	system	NOUN
ap-7656	19	10	the	the	DET
ap-7656	19	11	results	result	NOUN
ap-7656	19	12	for	for	ADP
ap-7656	19	13	such	such	ADJ
ap-7656	19	14	relationships	relationship	NOUN
ap-7656	19	15	between	between	ADP
ap-7656	19	16	the	the	DET
ap-7656	19	17	entanglement	entanglement	NOUN
ap-7656	19	18	and	and	CCONJ
ap-7656	19	19	the	the	DET
ap-7656	19	20	nonlocal	nonlocal	ADJ
ap-7656	19	21	violation	violation	NOUN
ap-7656	19	22	are	be	AUX
ap-7656	19	23	still	still	ADV
ap-7656	19	24	far	far	ADV
ap-7656	19	25	from	from	ADP
ap-7656	19	26	being	be	AUX
ap-7656	19	27	satisfied	satisfied	ADJ
ap-7656	19	28	.	.	PUNCT
ap-7656	20	1	in	in	ADP
ap-7656	20	2	[	[	X
ap-7656	20	3	10	10	NUM
ap-7656	20	4	]	]	PUNCT
ap-7656	20	5	,	,	PUNCT
ap-7656	20	6	an	an	DET
ap-7656	20	7	upper	upper	ADJ
ap-7656	20	8	bound	bind	VERB
ap-7656	20	9	on	on	ADP
ap-7656	20	10	fully	fully	ADV
ap-7656	20	11	entangled	entangle	VERB
ap-7656	20	12	fraction	fraction	NOUN
ap-7656	20	13	for	for	ADP
ap-7656	20	14	arbitrary	arbitrary	ADJ
ap-7656	20	15	dimensional	dimensional	ADJ
ap-7656	20	16	states	state	NOUN
ap-7656	20	17	has	have	AUX
ap-7656	20	18	been	be	AUX
ap-7656	20	19	derived	derive	VERB
ap-7656	20	20	by	by	ADP
ap-7656	20	21	using	use	VERB
ap-7656	20	22	the	the	DET
ap-7656	20	23	principal	principal	ADJ
ap-7656	20	24	basis	basis	NOUN
ap-7656	20	25	representation	representation	NOUN
ap-7656	20	26	of	of	ADP
ap-7656	20	27	density	density	NOUN
ap-7656	20	28	matrices	matrix	NOUN
ap-7656	20	29	.	.	PUNCT
ap-7656	21	1	based	base	VERB
ap-7656	21	2	on	on	ADP
ap-7656	21	3	the	the	DET
ap-7656	21	4	norms	norm	NOUN
ap-7656	21	5	of	of	ADP
ap-7656	21	6	correlation	correlation	NOUN
ap-7656	21	7	vectors	vector	NOUN
ap-7656	21	8	,	,	PUNCT
ap-7656	21	9	the	the	DET
ap-7656	21	10	authors	author	NOUN
ap-7656	21	11	in	in	ADP
ap-7656	21	12	[	[	X
ap-7656	21	13	11	11	NUM
ap-7656	21	14	]	]	PUNCT
ap-7656	21	15	presented	present	VERB
ap-7656	21	16	an	an	DET
ap-7656	21	17	approach	approach	NOUN
ap-7656	21	18	to	to	PART
ap-7656	21	19	detect	detect	VERB
ap-7656	21	20	entanglement	entanglement	NOUN
ap-7656	21	21	in	in	ADP
ap-7656	21	22	arbitrary	arbitrary	ADJ
ap-7656	21	23	dimensional	dimensional	ADJ
ap-7656	21	24	quantum	quantum	NOUN
ap-7656	21	25	systems	system	NOUN
ap-7656	21	26	.	.	PUNCT
ap-7656	22	1	separability	separability	NOUN
ap-7656	22	2	criteria	criterion	NOUN
ap-7656	22	3	for	for	ADP
ap-7656	22	4	both	both	CCONJ
ap-7656	22	5	bipartite	bipartite	NOUN
ap-7656	22	6	and	and	CCONJ
ap-7656	22	7	multipartite	multipartite	ADJ
ap-7656	22	8	quantum	quantum	ADJ
ap-7656	22	9	states	state	NOUN
ap-7656	22	10	was	be	AUX
ap-7656	22	11	also	also	ADV
ap-7656	22	12	derived	derive	VERB
ap-7656	22	13	in	in	ADP
ap-7656	22	14	terms	term	NOUN
ap-7656	22	15	of	of	ADP
ap-7656	22	16	the	the	DET
ap-7656	22	17	correlation	correlation	NOUN
ap-7656	22	18	matrices	matrix	NOUN
ap-7656	22	19	[	[	X
ap-7656	22	20	12	12	NUM
ap-7656	22	21	]	]	PUNCT
ap-7656	22	22	.	.	PUNCT
ap-7656	23	1	in	in	ADP
ap-7656	23	2	this	this	DET
ap-7656	23	3	paper	paper	NOUN
ap-7656	23	4	by	by	ADP
ap-7656	23	5	using	use	VERB
ap-7656	23	6	the	the	DET
ap-7656	23	7	bell	bell	NOUN
ap-7656	23	8	function	function	NOUN
ap-7656	23	9	and	and	CCONJ
ap-7656	23	10	the	the	DET
ap-7656	23	11	generalized	generalized	ADJ
ap-7656	23	12	three	three	NUM
ap-7656	23	13	dimensional	dimensional	ADJ
ap-7656	23	14	pauli	pauli	PROPN
ap-7656	23	15	operators	operator	NOUN
ap-7656	23	16	,	,	PUNCT
ap-7656	23	17	we	we	PRON
ap-7656	23	18	derive	derive	VERB
ap-7656	23	19	a	a	DET
ap-7656	23	20	quantum	quantum	NOUN
ap-7656	23	21	upper	upper	NOUN
ap-7656	23	22	bound	bind	VERB
ap-7656	23	23	for	for	ADP
ap-7656	23	24	3	3	NUM
ap-7656	23	25	⊗	⊗	PROPN
ap-7656	23	26	3	3	NUM
ap-7656	23	27	⊗	⊗	PROPN
ap-7656	23	28	3	3	NUM
ap-7656	23	29	quantum	quantum	NOUN
ap-7656	23	30	systems	system	NOUN
ap-7656	23	31	.	.	PUNCT
ap-7656	24	1	we	we	PRON
ap-7656	24	2	present	present	VERB
ap-7656	24	3	a	a	DET
ap-7656	24	4	classification	classification	NOUN
ap-7656	24	5	of	of	ADP
ap-7656	24	6	entanglement	entanglement	NOUN
ap-7656	24	7	for	for	ADP
ap-7656	24	8	triqutrit	triqutrit	NOUN
ap-7656	24	9	mixed	mix	VERB
ap-7656	24	10	states	state	NOUN
ap-7656	24	11	by	by	ADP
ap-7656	24	12	a	a	DET
ap-7656	24	13	set	set	NOUN
ap-7656	24	14	of	of	ADP
ap-7656	24	15	bell	bell	NOUN
ap-7656	24	16	inequalities	inequality	NOUN
ap-7656	24	17	.	.	PUNCT
ap-7656	25	1	these	these	DET
ap-7656	25	2	inequalities	inequality	NOUN
ap-7656	25	3	can	can	AUX
ap-7656	25	4	distinguish	distinguish	VERB
ap-7656	25	5	fully	fully	ADV
ap-7656	25	6	separable	separable	ADJ
ap-7656	25	7	and	and	CCONJ
ap-7656	25	8	bi	bi	ADJ
ap-7656	25	9	-	-	ADJ
ap-7656	25	10	separable	separable	ADJ
ap-7656	25	11	states	state	NOUN
ap-7656	25	12	.	.	PUNCT
ap-7656	26	1	moreover	moreover	ADV
ap-7656	26	2	,	,	PUNCT
ap-7656	26	3	we	we	PRON
ap-7656	26	4	propose	propose	VERB
ap-7656	26	5	criteria	criterion	NOUN
ap-7656	26	6	to	to	PART
ap-7656	26	7	detect	detect	VERB
ap-7656	26	8	classification	classification	NOUN
ap-7656	26	9	of	of	ADP
ap-7656	26	10	entanglement	entanglement	NOUN
ap-7656	26	11	for	for	ADP
ap-7656	26	12	2	2	NUM
ap-7656	26	13	⊗	⊗	PROPN
ap-7656	26	14	2	2	NUM
ap-7656	26	15	⊗	⊗	NUM
ap-7656	26	16	3	3	NUM
ap-7656	26	17	mixed	mixed	ADJ
ap-7656	26	18	states	state	NOUN
ap-7656	26	19	with	with	ADP
ap-7656	26	20	correlation	correlation	NOUN
ap-7656	26	21	tensor	tensor	NOUN
ap-7656	26	22	matrices	matrix	NOUN
ap-7656	26	23	in	in	ADP
ap-7656	26	24	the	the	DET
ap-7656	26	25	principal	principal	ADJ
ap-7656	26	26	basis	basis	NOUN
ap-7656	26	27	representation	representation	NOUN
ap-7656	26	28	of	of	ADP
ap-7656	26	29	density	density	NOUN
ap-7656	26	30	matrices	matrix	NOUN
ap-7656	26	31	.	.	PUNCT
ap-7656	27	1	2	2	X
ap-7656	27	2	.	.	X
ap-7656	27	3	entanglement	entanglement	NOUN
ap-7656	27	4	identification	identification	NOUN
ap-7656	27	5	with	with	ADP
ap-7656	27	6	bell	bell	NOUN
ap-7656	27	7	inequalities	inequality	NOUN
ap-7656	27	8	we	we	PRON
ap-7656	27	9	first	first	ADV
ap-7656	27	10	consider	consider	VERB
ap-7656	27	11	relations	relation	NOUN
ap-7656	27	12	between	between	ADP
ap-7656	27	13	entanglement	entanglement	NOUN
ap-7656	27	14	and	and	CCONJ
ap-7656	27	15	non	non	ADJ
ap-7656	27	16	-	-	NOUN
ap-7656	27	17	locality	locality	NOUN
ap-7656	27	18	for	for	ADP
ap-7656	27	19	3	3	NUM
ap-7656	27	20	⊗	⊗	PROPN
ap-7656	27	21	3	3	NUM
ap-7656	27	22	⊗	⊗	PROPN
ap-7656	27	23	3	3	NUM
ap-7656	27	24	quantum	quantum	NOUN
ap-7656	27	25	systems	system	NOUN
ap-7656	27	26	.	.	PUNCT
ap-7656	28	1	consider	consider	VERB
ap-7656	28	2	three	three	NUM
ap-7656	28	3	observers	observer	NOUN
ap-7656	28	4	who	who	PRON
ap-7656	28	5	may	may	AUX
ap-7656	28	6	choose	choose	VERB
ap-7656	28	7	independently	independently	ADV
ap-7656	28	8	between	between	ADP
ap-7656	28	9	two	two	NUM
ap-7656	28	10	dichotomic	dichotomic	ADJ
ap-7656	28	11	observables	observable	NOUN
ap-7656	28	12	denoted	denote	VERB
ap-7656	28	13	by	by	ADP
ap-7656	28	14	ai	ai	PROPN
ap-7656	28	15	and	and	CCONJ
ap-7656	28	16	bi	bi	NOUN
ap-7656	28	17	for	for	ADP
ap-7656	28	18	the	the	DET
ap-7656	28	19	i	i	PROPN
ap-7656	28	20	-	-	PUNCT
ap-7656	28	21	th	th	X
ap-7656	28	22	observer	observer	NOUN
ap-7656	28	23	,	,	PUNCT
ap-7656	28	24	i	i	PRON
ap-7656	28	25	=	=	NOUN
ap-7656	28	26	1	1	NUM
ap-7656	28	27	,	,	PUNCT
ap-7656	28	28	2	2	NUM
ap-7656	28	29	,	,	PUNCT
ap-7656	28	30	3	3	NUM
ap-7656	28	31	.	.	X
ap-7656	29	1	let	let	AUX
ap-7656	29	2	v̂i	v̂i	PART
ap-7656	29	3	denote	denote	VERB
ap-7656	29	4	the	the	DET
ap-7656	29	5	measurement	measurement	NOUN
ap-7656	29	6	operator	operator	NOUN
ap-7656	29	7	associated	associate	VERB
ap-7656	29	8	with	with	ADP
ap-7656	29	9	the	the	DET
ap-7656	29	10	variable	variable	ADJ
ap-7656	29	11	vi	vi	PROPN
ap-7656	29	12	∈	∈	PROPN
ap-7656	29	13	{	{	PUNCT
ap-7656	29	14	ai	ai	NOUN
ap-7656	29	15	,	,	PUNCT
ap-7656	29	16	bi	bi	NOUN
ap-7656	29	17	}	}	PUNCT
ap-7656	29	18	of	of	ADP
ap-7656	29	19	i	i	PROPN
ap-7656	29	20	-	-	PUNCT
ap-7656	29	21	th	th	X
ap-7656	29	22	observer	observer	NOUN
ap-7656	29	23	.	.	PUNCT
ap-7656	30	1	we	we	PRON
ap-7656	30	2	choose	choose	VERB
ap-7656	30	3	a	a	DET
ap-7656	30	4	complete	complete	ADJ
ap-7656	30	5	set	set	NOUN
ap-7656	30	6	of	of	ADP
ap-7656	30	7	orthonormal	orthonormal	ADJ
ap-7656	30	8	basis	basis	NOUN
ap-7656	30	9	vectors	vector	NOUN
ap-7656	30	10	|k⟩	|k⟩	VERB
ap-7656	30	11	to	to	PART
ap-7656	30	12	describe	describe	VERB
ap-7656	30	13	an	an	DET
ap-7656	30	14	orthogonal	orthogonal	ADJ
ap-7656	30	15	measurement	measurement	NOUN
ap-7656	30	16	of	of	ADP
ap-7656	30	17	a	a	DET
ap-7656	30	18	given	give	VERB
ap-7656	30	19	variable	variable	NOUN
ap-7656	30	20	vi	vi	PROPN
ap-7656	30	21	.	.	PUNCT
ap-7656	31	1	the	the	DET
ap-7656	31	2	measurement	measurement	NOUN
ap-7656	31	3	outcomes	outcome	NOUN
ap-7656	31	4	are	be	AUX
ap-7656	31	5	indicated	indicate	VERB
ap-7656	31	6	by	by	ADP
ap-7656	31	7	a	a	DET
ap-7656	31	8	set	set	NOUN
ap-7656	31	9	of	of	ADP
ap-7656	31	10	eigenvalues	eigenvalue	NOUN
ap-7656	31	11	1	1	NUM
ap-7656	31	12	,	,	PUNCT
ap-7656	31	13	λ	λ	NOUN
ap-7656	31	14	,	,	PUNCT
ap-7656	31	15	λ2	λ2	NOUN
ap-7656	31	16	,	,	PUNCT
ap-7656	31	17	where	where	SCONJ
ap-7656	31	18	λ	λ	PROPN
ap-7656	31	19	=	=	SYM
ap-7656	31	20	exp	exp	PROPN
ap-7656	31	21	(	(	PUNCT
ap-7656	31	22	i2π	i2π	PROPN
ap-7656	31	23	3	3	NUM
ap-7656	31	24	)	)	PUNCT
ap-7656	31	25	is	be	AUX
ap-7656	31	26	a	a	DET
ap-7656	31	27	primitive	primitive	ADJ
ap-7656	31	28	third	third	ADJ
ap-7656	31	29	root	root	NOUN
ap-7656	31	30	of	of	ADP
ap-7656	31	31	unity	unity	NOUN
ap-7656	31	32	.	.	PUNCT
ap-7656	32	1	therefore	therefore	ADV
ap-7656	32	2	the	the	DET
ap-7656	32	3	measurement	measurement	NOUN
ap-7656	32	4	operator	operator	NOUN
ap-7656	32	5	can	can	AUX
ap-7656	32	6	be	be	AUX
ap-7656	32	7	represented	represent	VERB
ap-7656	32	8	by	by	ADP
ap-7656	32	9	v̂i	v̂i	ADV
ap-7656	32	10	=	=	SYM
ap-7656	32	11	∑2	∑2	NOUN
ap-7656	32	12	k=0	k=0	PROPN
ap-7656	32	13	λ	λ	PROPN
ap-7656	32	14	k|k⟩⟨k|	k|k⟩⟨k|	PROPN
ap-7656	32	15	.	.	PUNCT
ap-7656	33	1	inspired	inspire	VERB
ap-7656	33	2	by	by	ADP
ap-7656	33	3	the	the	DET
ap-7656	33	4	bell	bell	PROPN
ap-7656	33	5	function	function	NOUN
ap-7656	33	6	(	(	PUNCT
ap-7656	33	7	the	the	DET
ap-7656	33	8	expected	expect	VERB
ap-7656	33	9	value	value	NOUN
ap-7656	33	10	of	of	ADP
ap-7656	33	11	bell	bell	NOUN
ap-7656	33	12	operator	operator	NOUN
ap-7656	33	13	)	)	PUNCT
ap-7656	33	14	constructed	construct	VERB
ap-7656	33	15	in	in	ADP
ap-7656	33	16	[	[	X
ap-7656	33	17	13	13	NUM
ap-7656	33	18	]	]	PUNCT
ap-7656	33	19	,	,	PUNCT
ap-7656	33	20	we	we	PRON
ap-7656	33	21	introduce	introduce	VERB
ap-7656	33	22	the	the	DET
ap-7656	33	23	following	follow	VERB
ap-7656	33	24	bell	bell	NOUN
ap-7656	33	25	operator	operator	NOUN
ap-7656	33	26	,	,	PUNCT
ap-7656	33	27	b	b	X
ap-7656	33	28	=	=	SYM
ap-7656	33	29	2∑	2∑	NUM
ap-7656	33	30	j=1	j=1	NOUN
ap-7656	33	31	1	1	NUM
ap-7656	33	32	4(â1	4(â1	NUM
ap-7656	33	33	j	j	NOUN
ap-7656	34	1	⊗	⊗	PROPN
ap-7656	34	2	â2	â2	PROPN
ap-7656	35	1	j	j	PROPN
ap-7656	35	2	⊗	⊗	PROPN
ap-7656	35	3	â3	â3	PROPN
ap-7656	36	1	j	j	PROPN
ap-7656	37	1	+	+	NUM
ap-7656	37	2	λjâ1	λjâ1	X
ap-7656	37	3	j	j	PROPN
ap-7656	38	1	⊗	⊗	PROPN
ap-7656	38	2	b̂2	b̂2	PROPN
ap-7656	38	3	j	j	PROPN
ap-7656	38	4	⊗	⊗	PROPN
ap-7656	38	5	b̂3	b̂3	PROPN
ap-7656	39	1	j	j	PROPN
ap-7656	40	1	+	+	CCONJ
ap-7656	40	2	λjb̂1	λjb̂1	PROPN
ap-7656	40	3	j	j	PROPN
ap-7656	40	4	⊗	⊗	PROPN
ap-7656	40	5	â2	â2	PROPN
ap-7656	40	6	j	j	PROPN
ap-7656	40	7	⊗	⊗	PROPN
ap-7656	40	8	b̂3	b̂3	PROPN
ap-7656	40	9	j	j	PROPN
ap-7656	41	1	+	+	CCONJ
ap-7656	41	2	λjb̂1	λjb̂1	PROPN
ap-7656	41	3	j	j	PROPN
ap-7656	41	4	⊗	⊗	PROPN
ap-7656	41	5	b̂2	b̂2	PROPN
ap-7656	42	1	j	j	PROPN
ap-7656	42	2	⊗	⊗	PROPN
ap-7656	42	3	â3	â3	PROPN
ap-7656	42	4	j	j	PROPN
ap-7656	42	5	)	)	PUNCT
ap-7656	42	6	,	,	PUNCT
ap-7656	42	7	(	(	PUNCT
ap-7656	42	8	1	1	X
ap-7656	42	9	)	)	PUNCT
ap-7656	42	10	where	where	SCONJ
ap-7656	42	11	âi	âi	PUNCT
ap-7656	42	12	j	j	PROPN
ap-7656	42	13	(	(	PUNCT
ap-7656	42	14	b̂i	b̂i	PROPN
ap-7656	42	15	j	j	PROPN
ap-7656	42	16	)	)	PUNCT
ap-7656	42	17	denotes	denote	VERB
ap-7656	42	18	the	the	DET
ap-7656	42	19	j	j	PROPN
ap-7656	42	20	-	-	PUNCT
ap-7656	42	21	th	th	VERB
ap-7656	42	22	power	power	NOUN
ap-7656	42	23	of	of	ADP
ap-7656	42	24	âi	âi	PRON
ap-7656	42	25	(	(	PUNCT
ap-7656	42	26	b̂i	b̂i	PROPN
ap-7656	42	27	)	)	PUNCT
ap-7656	42	28	.	.	PUNCT
ap-7656	43	1	next	next	ADV
ap-7656	43	2	we	we	PRON
ap-7656	43	3	construct	construct	VERB
ap-7656	43	4	three	three	NUM
ap-7656	43	5	bell	bell	NOUN
ap-7656	43	6	operators	operator	NOUN
ap-7656	43	7	in	in	ADP
ap-7656	43	8	terms	term	NOUN
ap-7656	43	9	of	of	ADP
ap-7656	43	10	eq	eq	PROPN
ap-7656	43	11	.	.	PUNCT
ap-7656	44	1	(	(	PUNCT
ap-7656	44	2	1	1	NUM
ap-7656	44	3	)	)	PUNCT
ap-7656	44	4	.	.	PUNCT
ap-7656	45	1	consider	consider	VERB
ap-7656	45	2	three	three	NUM
ap-7656	45	3	dimensional	dimensional	ADJ
ap-7656	45	4	pauli	pauli	PROPN
ap-7656	45	5	opera222	opera222	PROPN
ap-7656	45	6	https://doi.org/10.14311/ap.2022.62.0222	https://doi.org/10.14311/ap.2022.62.0222	PROPN
ap-7656	45	7	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7656	45	8	https://www.cvut.cz/en	https://www.cvut.cz/en	PROPN
ap-7656	45	9	vol	vol	NOUN
ap-7656	45	10	.	.	PROPN
ap-7656	46	1	62	62	NUM
ap-7656	46	2	no	no	INTJ
ap-7656	46	3	.	.	PUNCT
ap-7656	47	1	1/2022	1/2022	NUM
ap-7656	47	2	a	a	DET
ap-7656	47	3	note	note	NOUN
ap-7656	47	4	on	on	ADP
ap-7656	47	5	entanglement	entanglement	NOUN
ap-7656	47	6	classification	classification	NOUN
ap-7656	47	7	for	for	ADP
ap-7656	47	8	tripartite	tripartite	ADJ
ap-7656	47	9	.	.	PUNCT
ap-7656	47	10	.	.	PUNCT
ap-7656	47	11	.	.	PUNCT
ap-7656	48	1	tors	tor	NOUN
ap-7656	49	1	[	[	X
ap-7656	49	2	14	14	NUM
ap-7656	49	3	]	]	PUNCT
ap-7656	49	4	x̂	x̂	NOUN
ap-7656	49	5	and	and	CCONJ
ap-7656	49	6	ẑ	ẑ	NUM
ap-7656	49	7	which	which	PRON
ap-7656	49	8	satisfy	satisfy	VERB
ap-7656	49	9	x̂|k⟩	x̂|k⟩	PROPN
ap-7656	50	1	=	=	PUNCT
ap-7656	50	2	|k	|k	NOUN
ap-7656	51	1	+	+	CCONJ
ap-7656	51	2	1⟩	1⟩	NUM
ap-7656	51	3	,	,	PUNCT
ap-7656	51	4	ẑ|k⟩	ẑ|k⟩	NOUN
ap-7656	51	5	=	=	SYM
ap-7656	51	6	λk|k⟩	λk|k⟩	NOUN
ap-7656	51	7	,	,	PUNCT
ap-7656	51	8	x̂3	x̂3	PUNCT
ap-7656	52	1	=	=	SYM
ap-7656	52	2	i	i	PROPN
ap-7656	52	3	,	,	PUNCT
ap-7656	52	4	ẑ3	ẑ3	PROPN
ap-7656	52	5	=	=	PUNCT
ap-7656	53	1	i	i	PROPN
ap-7656	53	2	,	,	PUNCT
ap-7656	53	3	where	where	SCONJ
ap-7656	53	4	i	i	PRON
ap-7656	53	5	denotes	denote	VERB
ap-7656	53	6	the	the	DET
ap-7656	53	7	identity	identity	NOUN
ap-7656	53	8	operator	operator	NOUN
ap-7656	53	9	.	.	PUNCT
ap-7656	54	1	therefore	therefore	ADV
ap-7656	54	2	,	,	PUNCT
ap-7656	54	3	if	if	SCONJ
ap-7656	54	4	we	we	PRON
ap-7656	54	5	replace	replace	VERB
ap-7656	54	6	âi	âi	PRON
ap-7656	54	7	and	and	CCONJ
ap-7656	54	8	b̂i	b̂i	PROPN
ap-7656	54	9	with	with	ADP
ap-7656	54	10	the	the	DET
ap-7656	54	11	following	follow	VERB
ap-7656	54	12	unitary	unitary	ADJ
ap-7656	54	13	operators	operator	NOUN
ap-7656	54	14	,	,	PUNCT
ap-7656	54	15	â1	â1	VERB
ap-7656	54	16	=	=	PUNCT
ap-7656	54	17	ẑ	ẑ	NUM
ap-7656	54	18	,	,	PUNCT
ap-7656	54	19	â2	â2	PUNCT
ap-7656	55	1	=	=	SYM
ap-7656	55	2	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	55	3	,	,	PUNCT
ap-7656	55	4	â3	â3	X
ap-7656	55	5	=	=	SYM
ap-7656	55	6	x̂ẑ2	x̂ẑ2	X
ap-7656	55	7	,	,	PUNCT
ap-7656	55	8	b̂1	b̂1	PROPN
ap-7656	55	9	=	=	SYM
ap-7656	55	10	ẑ	ẑ	NUM
ap-7656	55	11	,	,	PUNCT
ap-7656	55	12	b̂2	b̂2	X
ap-7656	55	13	=	=	SYM
ap-7656	55	14	x̂ẑ2	x̂ẑ2	PROPN
ap-7656	55	15	and	and	CCONJ
ap-7656	55	16	b̂3	b̂3	X
ap-7656	55	17	=	=	SYM
ap-7656	55	18	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	55	19	,	,	PUNCT
ap-7656	55	20	we	we	PRON
ap-7656	55	21	obtain	obtain	VERB
ap-7656	55	22	b1	b1	NOUN
ap-7656	55	23	=	=	SYM
ap-7656	56	1	2∑	2∑	NUM
ap-7656	56	2	j=1	j=1	NOUN
ap-7656	56	3	1	1	NUM
ap-7656	56	4	4	4	NUM
ap-7656	56	5	[	[	X
ap-7656	56	6	ẑj	ẑj	X
ap-7656	56	7	⊗	⊗	X
ap-7656	56	8	(	(	PUNCT
ap-7656	56	9	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	56	10	⊗	⊗	PROPN
ap-7656	56	11	(	(	PUNCT
ap-7656	56	12	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	56	13	+	+	CCONJ
ap-7656	56	14	λjẑj	λjẑj	PROPN
ap-7656	56	15	⊗	⊗	PROPN
ap-7656	56	16	(	(	PUNCT
ap-7656	56	17	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	56	18	⊗	⊗	PROPN
ap-7656	56	19	(	(	PUNCT
ap-7656	56	20	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	56	21	+	+	CCONJ
ap-7656	56	22	λjẑj	λjẑj	PROPN
ap-7656	56	23	⊗	⊗	PROPN
ap-7656	56	24	(	(	PUNCT
ap-7656	56	25	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	56	26	⊗	⊗	X
ap-7656	56	27	(	(	PUNCT
ap-7656	56	28	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	56	29	+	+	CCONJ
ap-7656	56	30	λjẑj	λjẑj	PROPN
ap-7656	56	31	⊗	⊗	PROPN
ap-7656	56	32	(	(	PUNCT
ap-7656	56	33	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	56	34	⊗	⊗	PROPN
ap-7656	56	35	(	(	PUNCT
ap-7656	56	36	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	56	37	]	]	X
ap-7656	56	38	.	.	PUNCT
ap-7656	57	1	(	(	PUNCT
ap-7656	57	2	2	2	X
ap-7656	57	3	)	)	PUNCT
ap-7656	57	4	if	if	SCONJ
ap-7656	57	5	we	we	PRON
ap-7656	57	6	choose	choose	VERB
ap-7656	57	7	unitary	unitary	ADJ
ap-7656	57	8	operators	operator	NOUN
ap-7656	57	9	as	as	SCONJ
ap-7656	57	10	follows	follow	VERB
ap-7656	57	11	,	,	PUNCT
ap-7656	57	12	â1	â1	PRON
ap-7656	57	13	=	=	SYM
ap-7656	57	14	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	57	15	,	,	PUNCT
ap-7656	57	16	â2	â2	NOUN
ap-7656	57	17	=	=	PUNCT
ap-7656	58	1	x̂ẑ2	x̂ẑ2	PROPN
ap-7656	58	2	,	,	PUNCT
ap-7656	58	3	â3	â3	X
ap-7656	58	4	=	=	SYM
ap-7656	58	5	ẑ	ẑ	NUM
ap-7656	58	6	,	,	PUNCT
ap-7656	58	7	b̂1	b̂1	PROPN
ap-7656	58	8	=	=	SYM
ap-7656	59	1	x̂ẑ2	x̂ẑ2	PROPN
ap-7656	59	2	,	,	PUNCT
ap-7656	59	3	b̂2	b̂2	PROPN
ap-7656	59	4	=	=	SYM
ap-7656	59	5	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	59	6	and	and	CCONJ
ap-7656	59	7	b̂3	b̂3	X
ap-7656	59	8	=	=	SYM
ap-7656	59	9	ẑ	ẑ	NUM
ap-7656	59	10	,	,	PUNCT
ap-7656	59	11	we	we	PRON
ap-7656	59	12	have	have	VERB
ap-7656	59	13	b2	b2	NOUN
ap-7656	59	14	=	=	SYM
ap-7656	59	15	2∑	2∑	NUM
ap-7656	59	16	j=1	j=1	NOUN
ap-7656	59	17	1	1	NUM
ap-7656	59	18	4	4	NUM
ap-7656	59	19	[	[	X
ap-7656	59	20	(	(	PUNCT
ap-7656	59	21	ω2x̂ẑ)j	ω2x̂ẑ)j	NUM
ap-7656	59	22	⊗	⊗	PROPN
ap-7656	59	23	(	(	PUNCT
ap-7656	59	24	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	59	25	⊗	⊗	PROPN
ap-7656	59	26	ẑj	ẑj	PROPN
ap-7656	60	1	+	+	CCONJ
ap-7656	60	2	λj(λ2x̂ẑ)j	λj(λ2x̂ẑ)j	X
ap-7656	60	3	⊗	⊗	NOUN
ap-7656	60	4	(	(	PUNCT
ap-7656	60	5	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	60	6	⊗	⊗	PROPN
ap-7656	60	7	ẑj	ẑj	PROPN
ap-7656	60	8	)	)	PUNCT
ap-7656	61	1	+	+	CCONJ
ap-7656	62	1	λj(x̂ẑ2)j	λj(x̂ẑ2)j	PROPN
ap-7656	62	2	⊗	⊗	PROPN
ap-7656	62	3	(	(	PUNCT
ap-7656	62	4	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	62	5	⊗	⊗	PROPN
ap-7656	62	6	(	(	PUNCT
ap-7656	62	7	ẑ)j	ẑ)j	PROPN
ap-7656	62	8	+	+	NUM
ap-7656	63	1	λj(x̂ẑ2)j	λj(x̂ẑ2)j	PROPN
ap-7656	63	2	⊗	⊗	PROPN
ap-7656	63	3	(	(	PUNCT
ap-7656	63	4	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	63	5	⊗	⊗	X
ap-7656	63	6	(	(	PUNCT
ap-7656	63	7	ẑ)j	ẑ)j	PROPN
ap-7656	63	8	]	]	X
ap-7656	63	9	.	.	PUNCT
ap-7656	64	1	(	(	PUNCT
ap-7656	64	2	3	3	X
ap-7656	64	3	)	)	PUNCT
ap-7656	64	4	taking	take	VERB
ap-7656	64	5	â1	â1	PRON
ap-7656	64	6	=	=	PUNCT
ap-7656	64	7	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	64	8	,	,	PUNCT
ap-7656	64	9	â2	â2	PROPN
ap-7656	64	10	=	=	PUNCT
ap-7656	64	11	ẑ	ẑ	NUM
ap-7656	64	12	,	,	PUNCT
ap-7656	64	13	â3	â3	X
ap-7656	64	14	=	=	SYM
ap-7656	64	15	x̂ẑ2	x̂ẑ2	X
ap-7656	64	16	,	,	PUNCT
ap-7656	64	17	b̂1	b̂1	X
ap-7656	64	18	=	=	SYM
ap-7656	64	19	x̂ẑ2	x̂ẑ2	PROPN
ap-7656	64	20	,	,	PUNCT
ap-7656	64	21	b̂2	b̂2	X
ap-7656	64	22	=	=	SYM
ap-7656	64	23	ẑ	ẑ	NUM
ap-7656	64	24	and	and	CCONJ
ap-7656	64	25	b̂3	b̂3	PROPN
ap-7656	64	26	=	=	SYM
ap-7656	64	27	λ2x̂ẑ	λ2x̂ẑ	PROPN
ap-7656	64	28	,	,	PUNCT
ap-7656	64	29	we	we	PRON
ap-7656	64	30	have	have	VERB
ap-7656	65	1	b3	b3	NOUN
ap-7656	65	2	=	=	SYM
ap-7656	65	3	2∑	2∑	NUM
ap-7656	65	4	j=1	j=1	NOUN
ap-7656	65	5	1	1	NUM
ap-7656	65	6	4	4	NUM
ap-7656	65	7	[	[	X
ap-7656	65	8	(	(	PUNCT
ap-7656	65	9	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	65	10	⊗	⊗	PROPN
ap-7656	65	11	ẑj	ẑj	PROPN
ap-7656	65	12	⊗	⊗	X
ap-7656	65	13	(	(	PUNCT
ap-7656	65	14	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	65	15	+	+	CCONJ
ap-7656	65	16	λj(λ2x̂ẑ)j	λj(λ2x̂ẑ)j	PROPN
ap-7656	66	1	⊗	⊗	NOUN
ap-7656	66	2	(	(	PUNCT
ap-7656	66	3	ẑ)j	ẑ)j	PROPN
ap-7656	66	4	⊗	⊗	PROPN
ap-7656	66	5	(	(	PUNCT
ap-7656	66	6	λ2x̂ẑ)j	λ2x̂ẑ)j	NOUN
ap-7656	66	7	)	)	PUNCT
ap-7656	66	8	+	+	CCONJ
ap-7656	67	1	λj(x̂ẑ2)j	λj(x̂ẑ2)j	PROPN
ap-7656	67	2	⊗	⊗	X
ap-7656	67	3	ẑj	ẑj	PROPN
ap-7656	68	1	⊗	⊗	NUM
ap-7656	68	2	(	(	PUNCT
ap-7656	68	3	λ2x̂ẑ)j	λ2x̂ẑ)j	X
ap-7656	69	1	+	+	CCONJ
ap-7656	69	2	λj(x̂ẑ2)j	λj(x̂ẑ2)j	PROPN
ap-7656	69	3	⊗	⊗	X
ap-7656	69	4	ẑj	ẑj	PROPN
ap-7656	70	1	⊗	⊗	X
ap-7656	70	2	(	(	PUNCT
ap-7656	70	3	x̂ẑ2)j	x̂ẑ2)j	PROPN
ap-7656	70	4	]	]	X
ap-7656	70	5	.	.	PUNCT
ap-7656	71	1	(	(	PUNCT
ap-7656	71	2	4	4	X
ap-7656	71	3	)	)	PUNCT
ap-7656	71	4	concerning	concern	VERB
ap-7656	71	5	the	the	DET
ap-7656	71	6	bounds	bound	NOUN
ap-7656	71	7	on	on	ADP
ap-7656	71	8	the	the	DET
ap-7656	71	9	mean	mean	ADJ
ap-7656	71	10	values	value	NOUN
ap-7656	71	11	|⟨bi⟩|	|⟨bi⟩|	NUM
ap-7656	71	12	of	of	ADP
ap-7656	71	13	the	the	DET
ap-7656	71	14	operators	operator	NOUN
ap-7656	71	15	bi	bi	PROPN
ap-7656	71	16	,	,	PUNCT
ap-7656	71	17	i	i	NOUN
ap-7656	71	18	=	=	NOUN
ap-7656	71	19	1	1	NUM
ap-7656	71	20	,	,	PUNCT
ap-7656	71	21	2	2	NUM
ap-7656	71	22	,	,	PUNCT
ap-7656	71	23	3	3	NUM
ap-7656	71	24	,	,	PUNCT
ap-7656	71	25	we	we	PRON
ap-7656	71	26	have	have	VERB
ap-7656	71	27	the	the	DET
ap-7656	71	28	following	follow	VERB
ap-7656	71	29	conclusions	conclusion	NOUN
ap-7656	71	30	.	.	PUNCT
ap-7656	72	1	theorem	theorem	NOUN
ap-7656	72	2	1	1	NUM
ap-7656	72	3	.	.	PUNCT
ap-7656	73	1	for	for	ADP
ap-7656	73	2	3	3	NUM
ap-7656	73	3	⊗	⊗	PROPN
ap-7656	73	4	3	3	NUM
ap-7656	73	5	⊗	⊗	NUM
ap-7656	73	6	3	3	NUM
ap-7656	73	7	mixed	mixed	ADJ
ap-7656	73	8	states	state	NOUN
ap-7656	73	9	,	,	PUNCT
ap-7656	73	10	we	we	PRON
ap-7656	73	11	have	have	VERB
ap-7656	73	12	the	the	DET
ap-7656	73	13	inequality	inequality	NOUN
ap-7656	73	14	,	,	PUNCT
ap-7656	73	15	|⟨bi⟩|	|⟨bi⟩|	ADJ
ap-7656	73	16	≤	≤	NUM
ap-7656	73	17	5	5	NUM
ap-7656	73	18	4	4	NUM
ap-7656	73	19	,	,	PUNCT
ap-7656	73	20	i	i	PRON
ap-7656	73	21	=	=	NOUN
ap-7656	73	22	1	1	NUM
ap-7656	73	23	,	,	PUNCT
ap-7656	73	24	2	2	NUM
ap-7656	73	25	,	,	PUNCT
ap-7656	73	26	3	3	NUM
ap-7656	73	27	.	.	X
ap-7656	73	28	proof	proof	NOUN
ap-7656	73	29	due	due	ADP
ap-7656	73	30	to	to	ADP
ap-7656	73	31	the	the	DET
ap-7656	73	32	linear	linear	ADJ
ap-7656	73	33	property	property	NOUN
ap-7656	73	34	of	of	ADP
ap-7656	73	35	the	the	DET
ap-7656	73	36	average	average	ADJ
ap-7656	73	37	values	value	NOUN
ap-7656	73	38	,	,	PUNCT
ap-7656	73	39	it	it	PRON
ap-7656	73	40	is	be	AUX
ap-7656	73	41	sufficient	sufficient	ADJ
ap-7656	73	42	to	to	PART
ap-7656	73	43	consider	consider	VERB
ap-7656	73	44	pure	pure	ADJ
ap-7656	73	45	states	state	NOUN
ap-7656	73	46	.	.	PUNCT
ap-7656	74	1	any	any	DET
ap-7656	74	2	triqutrit	triqutrit	NOUN
ap-7656	74	3	pure	pure	ADJ
ap-7656	74	4	state	state	NOUN
ap-7656	74	5	can	can	AUX
ap-7656	74	6	be	be	AUX
ap-7656	74	7	written	write	VERB
ap-7656	74	8	as	as	ADP
ap-7656	74	9	,	,	PUNCT
ap-7656	74	10	|ψ⟩	|ψ⟩	PROPN
ap-7656	74	11	=	=	NOUN
ap-7656	74	12	c1|000⟩	c1|000⟩	NOUN
ap-7656	74	13	+	+	CCONJ
ap-7656	74	14	c2|011⟩	c2|011⟩	NOUN
ap-7656	74	15	+	+	CCONJ
ap-7656	74	16	c3|012⟩	c3|012⟩	NOUN
ap-7656	74	17	+	+	CCONJ
ap-7656	74	18	c4|021⟩	c4|021⟩	VERB
ap-7656	74	19	+	+	CCONJ
ap-7656	74	20	c5|022⟩	c5|022⟩	ADJ
ap-7656	74	21	+	+	CCONJ
ap-7656	74	22	c6|101⟩	c6|101⟩	VERB
ap-7656	74	23	+	+	X
ap-7656	74	24	c7|102⟩	c7|102⟩	ADJ
ap-7656	75	1	+	+	CCONJ
ap-7656	75	2	c8|110⟩	c8|110⟩	NOUN
ap-7656	75	3	+	+	CCONJ
ap-7656	75	4	c9|111⟩	c9|111⟩	VERB
ap-7656	75	5	+	+	CCONJ
ap-7656	75	6	c10|120⟩	c10|120⟩	ADJ
ap-7656	75	7	+	+	CCONJ
ap-7656	75	8	c11|122⟩	c11|122⟩	NOUN
ap-7656	76	1	+	+	CCONJ
ap-7656	76	2	c12|201⟩	c12|201⟩	NOUN
ap-7656	77	1	+	+	CCONJ
ap-7656	78	1	c13|202⟩	c13|202⟩	ADJ
ap-7656	78	2	+	+	NUM
ap-7656	78	3	c14|210⟩	c14|210⟩	NOUN
ap-7656	78	4	+	+	CCONJ
ap-7656	78	5	c15|212⟩	c15|212⟩	NOUN
ap-7656	78	6	+	+	CCONJ
ap-7656	78	7	c16|220⟩	c16|220⟩	ADJ
ap-7656	78	8	+	+	CCONJ
ap-7656	78	9	c17|221⟩	c17|221⟩	ADJ
ap-7656	78	10	+	+	CCONJ
ap-7656	78	11	c18|222⟩	c18|222⟩	PROPN
ap-7656	78	12	,	,	PUNCT
ap-7656	78	13	(	(	PUNCT
ap-7656	78	14	5	5	NUM
ap-7656	78	15	)	)	PUNCT
ap-7656	78	16	where	where	SCONJ
ap-7656	78	17	c5	c5	PROPN
ap-7656	78	18	,	,	PUNCT
ap-7656	78	19	c11	c11	NOUN
ap-7656	78	20	,	,	PUNCT
ap-7656	78	21	c13	c13	PROPN
ap-7656	78	22	,	,	PUNCT
ap-7656	78	23	c15	c15	PROPN
ap-7656	78	24	,	,	PUNCT
ap-7656	78	25	c16	c16	PROPN
ap-7656	78	26	,	,	PUNCT
ap-7656	78	27	c17	c17	NOUN
ap-7656	78	28	and	and	CCONJ
ap-7656	78	29	c18	c18	NOUN
ap-7656	78	30	are	be	AUX
ap-7656	78	31	real	real	ADJ
ap-7656	78	32	and	and	CCONJ
ap-7656	78	33	nonnegative	nonnegative	ADJ
ap-7656	78	34	,	,	PUNCT
ap-7656	78	35	|c1|	|c1|	NOUN
ap-7656	78	36	≥	≥	NUM
ap-7656	78	37	|ci|	|ci|	PROPN
ap-7656	78	38	for	for	ADP
ap-7656	78	39	i	i	PRON
ap-7656	78	40	=	=	NOUN
ap-7656	78	41	1	1	NUM
ap-7656	78	42	,	,	PUNCT
ap-7656	78	43	2	2	NUM
ap-7656	78	44	,	,	PUNCT
ap-7656	78	45	.	.	PUNCT
ap-7656	78	46	.	.	PUNCT
ap-7656	79	1	.	.	PUNCT
ap-7656	80	1	,	,	PUNCT
ap-7656	80	2	18	18	NUM
ap-7656	80	3	,	,	PUNCT
ap-7656	80	4	|c9|	|c9|	NOUN
ap-7656	80	5	≥	≥	NOUN
ap-7656	80	6	|c18|	|c18|	ADV
ap-7656	80	7	and	and	CCONJ
ap-7656	80	8	∑18	∑18	ADJ
ap-7656	81	1	i=1	i=1	PRON
ap-7656	81	2	|ci|2	|ci|2	PROPN
ap-7656	81	3	=	=	SYM
ap-7656	81	4	1	1	X
ap-7656	81	5	.	.	PUNCT
ap-7656	82	1	therefore	therefore	ADV
ap-7656	82	2	,	,	PUNCT
ap-7656	82	3	|⟨b1⟩|	|⟨b1⟩|	PROPN
ap-7656	82	4	=	=	PRON
ap-7656	82	5	|14(−c1c2	|14(−c1c2	PROPN
ap-7656	83	1	+	+	NUM
ap-7656	83	2	5c1c5	5c1c5	NUM
ap-7656	83	3	−	−	NOUN
ap-7656	83	4	c2c5	c2c5	PROPN
ap-7656	83	5	−	−	PROPN
ap-7656	83	6	c6c10	c6c10	ADJ
ap-7656	83	7	+	+	CCONJ
ap-7656	83	8	2c7c8	2c7c8	NUM
ap-7656	83	9	+	+	CCONJ
ap-7656	83	10	2c9c11	2c9c11	NUM
ap-7656	83	11	+	+	CCONJ
ap-7656	83	12	2c12c15	2c12c15	NOUN
ap-7656	83	13	+	+	NUM
ap-7656	83	14	5c12c16	5c12c16	PROPN
ap-7656	83	15	−	−	PROPN
ap-7656	83	16	c13c14	c13c14	NOUN
ap-7656	83	17	−	−	NOUN
ap-7656	83	18	c13c17	c13c17	NOUN
ap-7656	83	19	−	−	PROPN
ap-7656	83	20	4c14c17	4c14c17	NOUN
ap-7656	83	21	+	+	CCONJ
ap-7656	83	22	5c15c16)|	5c15c16)|	NUM
ap-7656	83	23	≤1	≤1	ADJ
ap-7656	83	24	8	8	NUM
ap-7656	83	25	×	×	NOUN
ap-7656	83	26	10	10	NUM
ap-7656	83	27	×	×	NOUN
ap-7656	83	28	18∑	18∑	PROPN
ap-7656	84	1	i=1	i=1	PROPN
ap-7656	84	2	c2	c2	PROPN
ap-7656	84	3	i	i	PRON
ap-7656	84	4	=	=	NOUN
ap-7656	84	5	5	5	NUM
ap-7656	84	6	4	4	NUM
ap-7656	84	7	.	.	PUNCT
ap-7656	85	1	(	(	PUNCT
ap-7656	85	2	6	6	NUM
ap-7656	85	3	)	)	PUNCT
ap-7656	85	4	similarly	similarly	ADV
ap-7656	85	5	one	one	PRON
ap-7656	85	6	can	can	AUX
ap-7656	85	7	prove	prove	VERB
ap-7656	85	8	that	that	SCONJ
ap-7656	85	9	|⟨bi⟩|	|⟨bi⟩|	ADJ
ap-7656	85	10	≤	≤	NUM
ap-7656	85	11	5	5	NUM
ap-7656	85	12	4	4	NUM
ap-7656	85	13	for	for	ADP
ap-7656	85	14	i	i	PRON
ap-7656	85	15	=	=	SYM
ap-7656	85	16	2	2	NUM
ap-7656	85	17	,	,	PUNCT
ap-7656	85	18	3	3	NUM
ap-7656	85	19	.	.	PUNCT
ap-7656	85	20	□	□	PUNCT
ap-7656	85	21	theorem	theorem	NOUN
ap-7656	85	22	2	2	NUM
ap-7656	85	23	.	.	PUNCT
ap-7656	86	1	if	if	SCONJ
ap-7656	86	2	a	a	DET
ap-7656	86	3	triqutrit	triqutrit	NOUN
ap-7656	86	4	mixed	mix	VERB
ap-7656	86	5	state	state	NOUN
ap-7656	86	6	ρ	ρ	PROPN
ap-7656	86	7	is	be	AUX
ap-7656	86	8	fully	fully	ADV
ap-7656	86	9	separable	separable	ADJ
ap-7656	86	10	,	,	PUNCT
ap-7656	86	11	then	then	ADV
ap-7656	86	12	|⟨bi⟩|	|⟨bi⟩|	PROPN
ap-7656	86	13	=	=	SYM
ap-7656	86	14	0	0	NUM
ap-7656	86	15	,	,	PUNCT
ap-7656	86	16	i	i	PRON
ap-7656	86	17	=	=	NOUN
ap-7656	86	18	1	1	NUM
ap-7656	86	19	,	,	PUNCT
ap-7656	86	20	2	2	NUM
ap-7656	86	21	,	,	PUNCT
ap-7656	86	22	3	3	NUM
ap-7656	86	23	.	.	PUNCT
ap-7656	87	1	the	the	DET
ap-7656	87	2	proof	proof	NOUN
ap-7656	87	3	is	be	AUX
ap-7656	87	4	straightforward	straightforward	ADJ
ap-7656	87	5	.	.	PUNCT
ap-7656	88	1	due	due	ADP
ap-7656	88	2	to	to	ADP
ap-7656	88	3	the	the	DET
ap-7656	88	4	linear	linear	ADJ
ap-7656	88	5	property	property	NOUN
ap-7656	88	6	of	of	ADP
ap-7656	88	7	the	the	DET
ap-7656	88	8	average	average	ADJ
ap-7656	88	9	values	value	NOUN
ap-7656	88	10	,	,	PUNCT
ap-7656	88	11	it	it	PRON
ap-7656	88	12	is	be	AUX
ap-7656	88	13	sufficient	sufficient	ADJ
ap-7656	88	14	to	to	PART
ap-7656	88	15	consider	consider	VERB
ap-7656	88	16	pure	pure	ADJ
ap-7656	88	17	states	state	NOUN
ap-7656	88	18	again	again	ADV
ap-7656	88	19	.	.	PUNCT
ap-7656	89	1	a	a	DET
ap-7656	89	2	fully	fully	ADV
ap-7656	89	3	separable	separable	ADJ
ap-7656	89	4	pure	pure	ADJ
ap-7656	89	5	state	state	NOUN
ap-7656	89	6	can	can	AUX
ap-7656	89	7	be	be	AUX
ap-7656	89	8	written	write	VERB
ap-7656	89	9	as	as	ADP
ap-7656	89	10	under	under	ADP
ap-7656	89	11	suitable	suitable	ADJ
ap-7656	89	12	bases	basis	NOUN
ap-7656	89	13	,	,	PUNCT
ap-7656	89	14	|ψ⟩	|ψ⟩	PROPN
ap-7656	89	15	=	=	PUNCT
ap-7656	89	16	|0⟩	|0⟩	PROPN
ap-7656	89	17	⊗	⊗	PROPN
ap-7656	89	18	|0⟩	|0⟩	PROPN
ap-7656	89	19	⊗	⊗	PROPN
ap-7656	89	20	|0⟩	|0⟩	PROPN
ap-7656	89	21	⊗	⊗	PROPN
ap-7656	89	22	|0⟩.	|0⟩.	PROPN
ap-7656	89	23	therefore	therefore	ADV
ap-7656	89	24	|⟨bi⟩|	|⟨bi⟩|	PUNCT
ap-7656	89	25	=	=	NOUN
ap-7656	89	26	|tr(ρbi)|	|tr(ρbi)|	NOUN
ap-7656	90	1	=	=	SYM
ap-7656	90	2	0	0	X
ap-7656	90	3	.	.	PUNCT
ap-7656	90	4	theorem	theorem	NOUN
ap-7656	90	5	3	3	NUM
ap-7656	90	6	.	.	X
ap-7656	90	7	for	for	ADP
ap-7656	90	8	bi	bi	ADJ
ap-7656	90	9	-	-	ADJ
ap-7656	90	10	separable	separable	ADJ
ap-7656	90	11	states	state	NOUN
ap-7656	90	12	ρi|jk	ρi|jk	PROPN
ap-7656	90	13	under	under	ADP
ap-7656	90	14	bipartition	bipartition	NOUN
ap-7656	90	15	i	i	PRON
ap-7656	90	16	and	and	CCONJ
ap-7656	90	17	jk	jk	PROPN
ap-7656	90	18	,	,	PUNCT
ap-7656	90	19	i	i	PROPN
ap-7656	90	20	̸=	̸=	PROPN
ap-7656	90	21	j	j	PROPN
ap-7656	90	22	̸=	̸=	PROPN
ap-7656	90	23	k	k	PROPN
ap-7656	90	24	∈	∈	PROPN
ap-7656	90	25	{	{	PUNCT
ap-7656	90	26	1	1	NUM
ap-7656	90	27	,	,	PUNCT
ap-7656	90	28	2	2	NUM
ap-7656	90	29	,	,	PUNCT
ap-7656	90	30	3	3	NUM
ap-7656	90	31	}	}	PUNCT
ap-7656	90	32	,	,	PUNCT
ap-7656	90	33	we	we	PRON
ap-7656	90	34	have	have	VERB
ap-7656	90	35	|⟨b1⟩|	|⟨b1⟩|	PROPN
ap-7656	90	36	≤	≤	X
ap-7656	90	37	3	3	NUM
ap-7656	90	38	4	4	NUM
ap-7656	90	39	,	,	PUNCT
ap-7656	90	40	|⟨b2⟩|	|⟨b2⟩|	ADV
ap-7656	90	41	=	=	SYM
ap-7656	90	42	0	0	NUM
ap-7656	90	43	,	,	PUNCT
ap-7656	90	44	|⟨b3⟩|	|⟨b3⟩|	X
ap-7656	90	45	=	=	SYM
ap-7656	90	46	0	0	NUM
ap-7656	90	47	,	,	PUNCT
ap-7656	90	48	|⟨b1⟩|	|⟨b1⟩|	NOUN
ap-7656	90	49	=	=	SYM
ap-7656	90	50	0	0	NUM
ap-7656	90	51	,	,	PUNCT
ap-7656	90	52	|⟨b2⟩|	|⟨b2⟩|	ADV
ap-7656	90	53	≤	≤	ADV
ap-7656	90	54	3	3	NUM
ap-7656	90	55	4	4	NUM
ap-7656	90	56	,	,	PUNCT
ap-7656	90	57	|⟨b3⟩|	|⟨b3⟩|	X
ap-7656	90	58	=	=	SYM
ap-7656	90	59	0	0	NUM
ap-7656	90	60	,	,	PUNCT
ap-7656	90	61	|⟨b1⟩|	|⟨b1⟩|	NOUN
ap-7656	90	62	=	=	SYM
ap-7656	90	63	0	0	NUM
ap-7656	90	64	,	,	PUNCT
ap-7656	90	65	|⟨b2⟩|	|⟨b2⟩|	PROPN
ap-7656	90	66	=	=	SYM
ap-7656	90	67	0	0	NUM
ap-7656	90	68	,	,	PUNCT
ap-7656	90	69	|⟨b3⟩|	|⟨b3⟩|	ADJ
ap-7656	90	70	≤	≤	ADJ
ap-7656	90	71	3	3	NUM
ap-7656	90	72	4	4	NUM
ap-7656	90	73	,	,	PUNCT
ap-7656	90	74	for	for	ADP
ap-7656	90	75	ρ1|23	ρ1|23	PROPN
ap-7656	90	76	,	,	PUNCT
ap-7656	90	77	ρ3|12	ρ3|12	PROPN
ap-7656	90	78	and	and	CCONJ
ap-7656	90	79	ρ2|13	ρ2|13	PROPN
ap-7656	90	80	,	,	PUNCT
ap-7656	90	81	respectively	respectively	ADV
ap-7656	90	82	.	.	PUNCT
ap-7656	91	1	proof	proof	NOUN
ap-7656	91	2	it	it	PRON
ap-7656	91	3	is	be	AUX
ap-7656	91	4	sufficient	sufficient	ADJ
ap-7656	91	5	to	to	PART
ap-7656	91	6	consider	consider	VERB
ap-7656	91	7	pure	pure	ADJ
ap-7656	91	8	states	state	NOUN
ap-7656	91	9	only	only	ADV
ap-7656	91	10	.	.	PUNCT
ap-7656	92	1	every	every	DET
ap-7656	92	2	bi	bi	ADJ
ap-7656	92	3	-	-	ADJ
ap-7656	92	4	separable	separable	ADJ
ap-7656	92	5	pure	pure	ADJ
ap-7656	92	6	state	state	NOUN
ap-7656	92	7	ρ1|23	ρ1|23	PROPN
ap-7656	92	8	can	can	AUX
ap-7656	92	9	be	be	AUX
ap-7656	92	10	written	write	VERB
ap-7656	92	11	as	as	ADP
ap-7656	92	12	via	via	ADP
ap-7656	92	13	a	a	DET
ap-7656	92	14	suitable	suitable	ADJ
ap-7656	92	15	choice	choice	NOUN
ap-7656	92	16	of	of	ADP
ap-7656	92	17	bases	basis	NOUN
ap-7656	92	18	[	[	X
ap-7656	92	19	15	15	NUM
ap-7656	92	20	]	]	PUNCT
ap-7656	92	21	,	,	PUNCT
ap-7656	92	22	|ψ⟩	|ψ⟩	PROPN
ap-7656	92	23	=	=	PUNCT
ap-7656	92	24	|0⟩	|0⟩	PROPN
ap-7656	92	25	⊗	⊗	PROPN
ap-7656	92	26	(	(	PUNCT
ap-7656	92	27	c0|00⟩	c0|00⟩	NOUN
ap-7656	92	28	+	+	CCONJ
ap-7656	92	29	c1|11⟩	c1|11⟩	NOUN
ap-7656	92	30	+	+	X
ap-7656	92	31	c2|22⟩	c2|22⟩	NOUN
ap-7656	92	32	)	)	PUNCT
ap-7656	92	33	,	,	PUNCT
ap-7656	92	34	where	where	SCONJ
ap-7656	92	35	|c0|	|c0|	NOUN
ap-7656	92	36	≥	≥	NOUN
ap-7656	92	37	|c1|	|c1|	VERB
ap-7656	92	38	≥	≥	NUM
ap-7656	92	39	|c2|	|c2|	PROPN
ap-7656	92	40	and	and	CCONJ
ap-7656	92	41	∑2	∑2	PROPN
ap-7656	92	42	i=0	i=0	PROPN
ap-7656	92	43	|ci|2	|ci|2	PUNCT
ap-7656	92	44	=	=	SYM
ap-7656	92	45	1	1	X
ap-7656	92	46	.	.	PUNCT
ap-7656	93	1	therefore	therefore	ADV
ap-7656	93	2	,	,	PUNCT
ap-7656	93	3	we	we	PRON
ap-7656	93	4	have	have	VERB
ap-7656	93	5	by	by	ADP
ap-7656	93	6	direct	direct	ADJ
ap-7656	93	7	calculation	calculation	NOUN
ap-7656	93	8	,	,	PUNCT
ap-7656	93	9	|⟨b1⟩|	|⟨b1⟩|	PROPN
ap-7656	93	10	=	=	NOUN
ap-7656	93	11	|14(5c2c0	|14(5c2c0	NOUN
ap-7656	93	12	−	−	NOUN
ap-7656	94	1	c0c1	c0c1	SYM
ap-7656	94	2	−	−	NOUN
ap-7656	94	3	c1c2)|	c1c2)|	NOUN
ap-7656	95	1	≤1	≤1	PROPN
ap-7656	95	2	8(5	8(5	NUM
ap-7656	95	3	×	×	NOUN
ap-7656	95	4	(	(	PUNCT
ap-7656	95	5	c2	c2	PROPN
ap-7656	95	6	2	2	NUM
ap-7656	95	7	+	+	CCONJ
ap-7656	95	8	c2	c2	PROPN
ap-7656	95	9	0	0	NUM
ap-7656	95	10	)	)	PUNCT
ap-7656	96	1	+	+	CCONJ
ap-7656	96	2	(	(	PUNCT
ap-7656	96	3	c2	c2	PROPN
ap-7656	96	4	0	0	PUNCT
ap-7656	97	1	+	+	CCONJ
ap-7656	97	2	c2	c2	PROPN
ap-7656	97	3	1	1	NUM
ap-7656	97	4	)	)	PUNCT
ap-7656	97	5	×	×	NOUN
ap-7656	97	6	(	(	PUNCT
ap-7656	97	7	c2	c2	PROPN
ap-7656	97	8	1	1	NUM
ap-7656	97	9	+	+	CCONJ
ap-7656	97	10	c2	c2	PROPN
ap-7656	97	11	2	2	NUM
ap-7656	97	12	)	)	PUNCT
ap-7656	97	13	)	)	PUNCT
ap-7656	97	14	≤3	≤3	PROPN
ap-7656	97	15	4	4	NUM
ap-7656	97	16	.	.	PUNCT
ap-7656	98	1	it	it	PRON
ap-7656	98	2	is	be	AUX
ap-7656	98	3	straightforward	straightforward	ADJ
ap-7656	98	4	to	to	PART
ap-7656	98	5	prove	prove	VERB
ap-7656	98	6	similarly	similarly	ADV
ap-7656	98	7	,	,	PUNCT
ap-7656	98	8	|⟨b2⟩|	|⟨b2⟩|	PROPN
ap-7656	98	9	=	=	SYM
ap-7656	98	10	0	0	NUM
ap-7656	98	11	and	and	CCONJ
ap-7656	98	12	|⟨b3⟩|	|⟨b3⟩|	X
ap-7656	98	13	=	=	SYM
ap-7656	98	14	0	0	PROPN
ap-7656	98	15	.	.	PUNCT
ap-7656	99	1	for	for	ADP
ap-7656	99	2	bi	bi	ADJ
ap-7656	99	3	-	-	ADJ
ap-7656	99	4	separable	separable	ADJ
ap-7656	99	5	states	state	NOUN
ap-7656	99	6	ρ3|12	ρ3|12	PROPN
ap-7656	99	7	and	and	CCONJ
ap-7656	99	8	ρ2|13	ρ2|13	PROPN
ap-7656	99	9	,	,	PUNCT
ap-7656	99	10	the	the	DET
ap-7656	99	11	results	result	NOUN
ap-7656	99	12	can	can	AUX
ap-7656	99	13	be	be	AUX
ap-7656	99	14	proved	prove	VERB
ap-7656	99	15	in	in	ADP
ap-7656	99	16	a	a	DET
ap-7656	99	17	similar	similar	ADJ
ap-7656	99	18	way	way	NOUN
ap-7656	99	19	.	.	PUNCT
ap-7656	100	1	□	□	PUNCT
ap-7656	100	2	the	the	DET
ap-7656	100	3	above	above	ADJ
ap-7656	100	4	relations	relation	NOUN
ap-7656	100	5	given	give	VERB
ap-7656	100	6	in	in	ADP
ap-7656	100	7	theorem	theorem	ADJ
ap-7656	100	8	1	1	NUM
ap-7656	100	9	-	-	SYM
ap-7656	100	10	3	3	NUM
ap-7656	100	11	give	give	VERB
ap-7656	100	12	rise	rise	NOUN
ap-7656	100	13	to	to	ADP
ap-7656	100	14	characterization	characterization	NOUN
ap-7656	100	15	of	of	ADP
ap-7656	100	16	quantum	quantum	ADJ
ap-7656	100	17	entanglement	entanglement	NOUN
ap-7656	100	18	based	base	VERB
ap-7656	100	19	on	on	ADP
ap-7656	100	20	the	the	DET
ap-7656	100	21	bell	bell	NOUN
ap-7656	100	22	-	-	PUNCT
ap-7656	100	23	type	type	NOUN
ap-7656	100	24	violations	violation	NOUN
ap-7656	100	25	.	.	PUNCT
ap-7656	101	1	if	if	SCONJ
ap-7656	101	2	we	we	PRON
ap-7656	101	3	consider	consider	VERB
ap-7656	101	4	|⟨bi⟩|	|⟨bi⟩|	ADV
ap-7656	101	5	,	,	PUNCT
ap-7656	101	6	i	i	PRON
ap-7656	101	7	=	=	NOUN
ap-7656	101	8	1	1	NUM
ap-7656	101	9	,	,	PUNCT
ap-7656	101	10	2	2	NUM
ap-7656	101	11	,	,	PUNCT
ap-7656	101	12	3	3	NUM
ap-7656	101	13	,	,	PUNCT
ap-7656	101	14	to	to	PART
ap-7656	101	15	be	be	AUX
ap-7656	101	16	three	three	NUM
ap-7656	101	17	coordinates	coordinate	NOUN
ap-7656	101	18	,	,	PUNCT
ap-7656	101	19	then	then	ADV
ap-7656	101	20	all	all	DET
ap-7656	101	21	the	the	DET
ap-7656	101	22	triqutrit	triqutrit	NOUN
ap-7656	101	23	states	state	NOUN
ap-7656	101	24	are	be	AUX
ap-7656	101	25	confined	confine	VERB
ap-7656	101	26	in	in	ADP
ap-7656	101	27	a	a	DET
ap-7656	101	28	cube	cube	NOUN
ap-7656	101	29	with	with	ADP
ap-7656	101	30	size	size	NOUN
ap-7656	101	31	5	5	NUM
ap-7656	101	32	4	4	NUM
ap-7656	101	33	×	×	NOUN
ap-7656	101	34	5	5	NUM
ap-7656	101	35	4	4	NUM
ap-7656	101	36	×	×	NOUN
ap-7656	101	37	5	5	NUM
ap-7656	101	38	4	4	NUM
ap-7656	101	39	.	.	PUNCT
ap-7656	102	1	the	the	DET
ap-7656	102	2	bi	bi	ADJ
ap-7656	102	3	-	-	ADJ
ap-7656	102	4	separable	separable	ADJ
ap-7656	102	5	states	state	NOUN
ap-7656	102	6	are	be	AUX
ap-7656	102	7	confined	confine	VERB
ap-7656	102	8	in	in	ADP
ap-7656	102	9	a	a	DET
ap-7656	102	10	cube	cube	NOUN
ap-7656	102	11	with	with	ADP
ap-7656	102	12	size	size	NOUN
ap-7656	102	13	3	3	NUM
ap-7656	102	14	4	4	NUM
ap-7656	102	15	×	×	NOUN
ap-7656	102	16	3	3	NUM
ap-7656	102	17	4	4	NUM
ap-7656	102	18	×	×	NOUN
ap-7656	102	19	3	3	NUM
ap-7656	102	20	4	4	NUM
ap-7656	102	21	,	,	PUNCT
ap-7656	102	22	see	see	VERB
ap-7656	102	23	figure	figure	NOUN
ap-7656	102	24	1	1	NUM
ap-7656	102	25	.	.	NUM
ap-7656	102	26	223	223	NUM
ap-7656	103	1	h.	h.	PROPN
ap-7656	103	2	zhao	zhao	PROPN
ap-7656	103	3	,	,	PUNCT
ap-7656	103	4	y.-q	y.-q	PROPN
ap-7656	103	5	.	.	PUNCT
ap-7656	104	1	liu	liu	PROPN
ap-7656	104	2	,	,	PUNCT
ap-7656	104	3	z.-x	z.-x	PROPN
ap-7656	104	4	.	.	PUNCT
ap-7656	105	1	wang	wang	PROPN
ap-7656	105	2	,	,	PUNCT
ap-7656	105	3	s.-m	s.-m	PROPN
ap-7656	105	4	.	.	PUNCT
ap-7656	106	1	fei	fei	PROPN
ap-7656	106	2	acta	acta	PROPN
ap-7656	106	3	polytechnica	polytechnica	PROPN
ap-7656	106	4	figure	figure	NOUN
ap-7656	106	5	1	1	NUM
ap-7656	106	6	.	.	PUNCT
ap-7656	107	1	all	all	DET
ap-7656	107	2	states	state	NOUN
ap-7656	107	3	lie	lie	VERB
ap-7656	107	4	in	in	ADP
ap-7656	107	5	the	the	DET
ap-7656	107	6	yellow	yellow	ADJ
ap-7656	107	7	cube	cube	NOUN
ap-7656	107	8	,	,	PUNCT
ap-7656	107	9	while	while	SCONJ
ap-7656	107	10	in	in	ADP
ap-7656	107	11	the	the	DET
ap-7656	107	12	green	green	PROPN
ap-7656	107	13	cube	cube	NOUN
ap-7656	107	14	are	be	AUX
ap-7656	107	15	bi	bi	ADJ
ap-7656	107	16	-	-	ADJ
ap-7656	107	17	separable	separable	ADJ
ap-7656	107	18	states	state	NOUN
ap-7656	107	19	.	.	PUNCT
ap-7656	108	1	3	3	X
ap-7656	108	2	.	.	X
ap-7656	108	3	entanglement	entanglement	NOUN
ap-7656	108	4	classification	classification	NOUN
ap-7656	108	5	under	under	ADP
ap-7656	108	6	principal	principal	ADJ
ap-7656	108	7	basis	basis	NOUN
ap-7656	108	8	consider	consider	VERB
ap-7656	108	9	the	the	DET
ap-7656	108	10	principal	principal	ADJ
ap-7656	108	11	basis	basis	NOUN
ap-7656	108	12	on	on	ADP
ap-7656	108	13	d	d	ADJ
ap-7656	108	14	-	-	ADJ
ap-7656	108	15	dimensional	dimensional	ADJ
ap-7656	108	16	hilbert	hilbert	NOUN
ap-7656	108	17	space	space	NOUN
ap-7656	108	18	h	h	NOUN
ap-7656	108	19	with	with	ADP
ap-7656	108	20	computational	computational	ADJ
ap-7656	108	21	basis	basis	NOUN
ap-7656	108	22	|i⟩	|i⟩	PROPN
ap-7656	108	23	,	,	PUNCT
ap-7656	108	24	i	i	PRON
ap-7656	108	25	=	=	NOUN
ap-7656	108	26	1	1	NUM
ap-7656	108	27	,	,	PUNCT
ap-7656	108	28	2	2	NUM
ap-7656	108	29	,	,	PUNCT
ap-7656	108	30	...	...	PUNCT
ap-7656	108	31	,	,	PUNCT
ap-7656	108	32	d.	d.	PROPN
ap-7656	108	33	let	let	VERB
ap-7656	108	34	eij	eij	PROPN
ap-7656	108	35	be	be	AUX
ap-7656	108	36	the	the	DET
ap-7656	108	37	d×d	d×d	PROPN
ap-7656	108	38	unit	unit	NOUN
ap-7656	108	39	matrix	matrix	NOUN
ap-7656	108	40	with	with	ADP
ap-7656	108	41	the	the	DET
ap-7656	108	42	only	only	ADJ
ap-7656	108	43	nonzero	nonzero	ADJ
ap-7656	108	44	entry	entry	NOUN
ap-7656	108	45	1	1	NUM
ap-7656	108	46	at	at	ADP
ap-7656	108	47	the	the	DET
ap-7656	108	48	position	position	NOUN
ap-7656	108	49	(	(	PUNCT
ap-7656	108	50	i	i	PROPN
ap-7656	108	51	,	,	PUNCT
ap-7656	108	52	j	j	PROPN
ap-7656	108	53	)	)	PUNCT
ap-7656	108	54	.	.	PUNCT
ap-7656	109	1	let	let	VERB
ap-7656	109	2	ω	ω	PRON
ap-7656	109	3	be	be	AUX
ap-7656	109	4	a	a	DET
ap-7656	109	5	fixed	fix	VERB
ap-7656	109	6	d	d	NOUN
ap-7656	109	7	-	-	PUNCT
ap-7656	109	8	th	th	X
ap-7656	109	9	primitive	primitive	ADJ
ap-7656	109	10	root	root	NOUN
ap-7656	109	11	of	of	ADP
ap-7656	109	12	unity	unity	NOUN
ap-7656	109	13	,	,	PUNCT
ap-7656	109	14	the	the	DET
ap-7656	109	15	principal	principal	ADJ
ap-7656	109	16	basis	basis	NOUN
ap-7656	109	17	is	be	AUX
ap-7656	109	18	given	give	VERB
ap-7656	109	19	by	by	ADP
ap-7656	109	20	aij	aij	PROPN
ap-7656	109	21	=	=	SYM
ap-7656	109	22	∑	∑	PROPN
ap-7656	109	23	m∈zd	m∈zd	PROPN
ap-7656	109	24	ωimem	ωimem	NUM
ap-7656	109	25	,	,	PUNCT
ap-7656	109	26	m+j	m+j	NUM
ap-7656	109	27	,	,	PUNCT
ap-7656	109	28	(	(	PUNCT
ap-7656	109	29	7	7	X
ap-7656	109	30	)	)	PUNCT
ap-7656	109	31	where	where	SCONJ
ap-7656	109	32	ωd	ωd	NOUN
ap-7656	109	33	=	=	NOUN
ap-7656	109	34	1	1	NUM
ap-7656	109	35	,	,	PUNCT
ap-7656	109	36	i	i	PRON
ap-7656	109	37	,	,	PUNCT
ap-7656	109	38	j	j	PROPN
ap-7656	109	39	∈	∈	PROPN
ap-7656	109	40	zd	zd	PROPN
ap-7656	109	41	and	and	CCONJ
ap-7656	109	42	zd	zd	PROPN
ap-7656	109	43	is	be	AUX
ap-7656	109	44	z	z	PROPN
ap-7656	109	45	modulo	modulo	PROPN
ap-7656	109	46	d.	d.	PROPN
ap-7656	109	47	the	the	DET
ap-7656	109	48	set	set	PROPN
ap-7656	109	49	{	{	PUNCT
ap-7656	109	50	aij	aij	PROPN
ap-7656	109	51	}	}	PUNCT
ap-7656	109	52	spans	span	NOUN
ap-7656	109	53	the	the	DET
ap-7656	109	54	principal	principal	ADJ
ap-7656	109	55	cartan	cartan	ADJ
ap-7656	109	56	subalgebra	subalgebra	NOUN
ap-7656	109	57	of	of	ADP
ap-7656	109	58	gl(d	gl(d	NUM
ap-7656	109	59	)	)	PUNCT
ap-7656	109	60	.	.	PUNCT
ap-7656	110	1	under	under	ADP
ap-7656	110	2	the	the	DET
ap-7656	110	3	stand	stand	VERB
ap-7656	110	4	inner	inner	ADJ
ap-7656	110	5	product	product	NOUN
ap-7656	110	6	(	(	PUNCT
ap-7656	110	7	x|y	x|y	X
ap-7656	110	8	)	)	PUNCT
ap-7656	110	9	=	=	SYM
ap-7656	110	10	tr(xy	tr(xy	PROPN
ap-7656	110	11	)	)	PUNCT
ap-7656	110	12	of	of	ADP
ap-7656	110	13	matrices	matrix	NOUN
ap-7656	110	14	x	x	PUNCT
ap-7656	110	15	and	and	CCONJ
ap-7656	110	16	y	y	PROPN
ap-7656	110	17	,	,	PUNCT
ap-7656	110	18	the	the	DET
ap-7656	110	19	dual	dual	ADJ
ap-7656	110	20	basis	basis	NOUN
ap-7656	110	21	of	of	ADP
ap-7656	110	22	the	the	DET
ap-7656	110	23	principal	principal	ADJ
ap-7656	110	24	basis	basis	NOUN
ap-7656	110	25	{	{	PUNCT
ap-7656	110	26	aij	aij	X
ap-7656	110	27	}	}	PUNCT
ap-7656	110	28	is	be	AUX
ap-7656	110	29	{	{	PUNCT
ap-7656	110	30	(	(	PUNCT
ap-7656	110	31	ωij	ωij	PROPN
ap-7656	110	32	/	/	SYM
ap-7656	110	33	d)a−i,−j	d)a−i,−j	PROPN
ap-7656	110	34	}	}	PUNCT
ap-7656	110	35	,	,	PUNCT
ap-7656	110	36	which	which	PRON
ap-7656	110	37	follows	follow	VERB
ap-7656	110	38	also	also	ADV
ap-7656	110	39	from	from	ADP
ap-7656	110	40	the	the	DET
ap-7656	110	41	algebraic	algebraic	ADJ
ap-7656	110	42	property	property	NOUN
ap-7656	110	43	of	of	ADP
ap-7656	110	44	the	the	DET
ap-7656	110	45	principal	principal	ADJ
ap-7656	110	46	matrices	matrix	NOUN
ap-7656	110	47	,	,	PUNCT
ap-7656	110	48	aijakl	aijakl	ADJ
ap-7656	110	49	=	=	SYM
ap-7656	110	50	ωjkai+k	ωjkai+k	NOUN
ap-7656	110	51	,	,	PUNCT
ap-7656	110	52	j+l	j+l	PROPN
ap-7656	110	53	.	.	PUNCT
ap-7656	111	1	namely	namely	ADV
ap-7656	111	2	,	,	PUNCT
ap-7656	111	3	a†	a†	X
ap-7656	111	4	i	i	PROPN
ap-7656	111	5	,	,	PUNCT
ap-7656	111	6	j	j	PROPN
ap-7656	111	7	=	=	PUNCT
ap-7656	111	8	ωija−i,−j	ωija−i,−j	NOUN
ap-7656	111	9	,	,	PUNCT
ap-7656	111	10	and	and	CCONJ
ap-7656	111	11	thus	thus	ADV
ap-7656	111	12	tr(aija	tr(aija	PROPN
ap-7656	111	13	†	†	X
ap-7656	111	14	kl	kl	PROPN
ap-7656	111	15	)	)	PUNCT
ap-7656	111	16	=	=	VERB
ap-7656	111	17	δikδjld	δikδjld	ADJ
ap-7656	112	1	[	[	X
ap-7656	112	2	10	10	NUM
ap-7656	112	3	]	]	PUNCT
ap-7656	112	4	.	.	PUNCT
ap-7656	113	1	next	next	ADV
ap-7656	113	2	we	we	PRON
ap-7656	113	3	consider	consider	VERB
ap-7656	113	4	the	the	DET
ap-7656	113	5	entanglement	entanglement	NOUN
ap-7656	113	6	of	of	ADP
ap-7656	113	7	2	2	NUM
ap-7656	113	8	⊗	⊗	NUM
ap-7656	113	9	2	2	NUM
ap-7656	113	10	⊗	⊗	PROPN
ap-7656	113	11	3	3	NUM
ap-7656	113	12	systems	system	NOUN
ap-7656	113	13	.	.	PUNCT
ap-7656	114	1	let	let	VERB
ap-7656	114	2	{	{	PUNCT
ap-7656	114	3	aij	aij	VERB
ap-7656	114	4	}	}	PUNCT
ap-7656	114	5	and	and	CCONJ
ap-7656	114	6	{	{	PUNCT
ap-7656	114	7	bij	bij	NOUN
ap-7656	114	8	}	}	PUNCT
ap-7656	114	9	be	be	VERB
ap-7656	114	10	the	the	DET
ap-7656	114	11	principal	principal	ADJ
ap-7656	114	12	bases	basis	NOUN
ap-7656	114	13	of	of	ADP
ap-7656	114	14	2	2	NUM
ap-7656	114	15	-	-	PUNCT
ap-7656	114	16	dimensional	dimensional	ADJ
ap-7656	114	17	and	and	CCONJ
ap-7656	114	18	3	3	NUM
ap-7656	114	19	-	-	PUNCT
ap-7656	114	20	dimensional	dimensional	ADJ
ap-7656	114	21	hilbert	hilbert	NOUN
ap-7656	114	22	space	space	NOUN
ap-7656	114	23	,	,	PUNCT
ap-7656	114	24	respectively	respectively	ADV
ap-7656	114	25	.	.	PUNCT
ap-7656	115	1	for	for	ADP
ap-7656	115	2	any	any	DET
ap-7656	115	3	quantum	quantum	ADJ
ap-7656	115	4	state	state	NOUN
ap-7656	115	5	ρ	ρ	PROPN
ap-7656	115	6	∈	∈	PROPN
ap-7656	115	7	h2	h2	NOUN
ap-7656	115	8	1	1	NUM
ap-7656	115	9	⊗h2	⊗h2	PROPN
ap-7656	115	10	2	2	NUM
ap-7656	115	11	⊗h3	⊗h3	NUM
ap-7656	115	12	3	3	NUM
ap-7656	115	13	,	,	PUNCT
ap-7656	115	14	ρ	ρ	PROPN
ap-7656	115	15	has	have	VERB
ap-7656	115	16	the	the	DET
ap-7656	115	17	principal	principal	ADJ
ap-7656	115	18	basis	basis	NOUN
ap-7656	115	19	representation	representation	NOUN
ap-7656	115	20	:	:	PUNCT
ap-7656	115	21	ρ	ρ	PROPN
ap-7656	115	22	=	=	SYM
ap-7656	115	23	1	1	NUM
ap-7656	115	24	12(i2	12(i2	NUM
ap-7656	115	25	⊗	⊗	PROPN
ap-7656	115	26	i2	i2	PROPN
ap-7656	115	27	⊗	⊗	PROPN
ap-7656	115	28	i3	i3	PROPN
ap-7656	115	29	+	+	CCONJ
ap-7656	115	30	∑	∑	PROPN
ap-7656	115	31	(	(	PUNCT
ap-7656	115	32	i	i	PROPN
ap-7656	115	33	,	,	PUNCT
ap-7656	115	34	j	j	PROPN
ap-7656	115	35	)	)	PUNCT
ap-7656	115	36	̸=(0,0	̸=(0,0	NOUN
ap-7656	115	37	)	)	PUNCT
ap-7656	115	38	uijaij	uijaij	NOUN
ap-7656	115	39	⊗	⊗	PROPN
ap-7656	115	40	i2	i2	PROPN
ap-7656	115	41	⊗	⊗	PROPN
ap-7656	115	42	i3	i3	PROPN
ap-7656	115	43	+	+	CCONJ
ap-7656	115	44	∑	∑	PROPN
ap-7656	115	45	(	(	PUNCT
ap-7656	115	46	k	k	X
ap-7656	115	47	,	,	PUNCT
ap-7656	115	48	l	l	NOUN
ap-7656	115	49	)	)	PUNCT
ap-7656	115	50	̸=(0,0	̸=(0,0	NOUN
ap-7656	115	51	)	)	PUNCT
ap-7656	115	52	vkli2	vkli2	NOUN
ap-7656	116	1	⊗	⊗	PROPN
ap-7656	116	2	akl	akl	PROPN
ap-7656	116	3	⊗	⊗	PROPN
ap-7656	116	4	i3	i3	PROPN
ap-7656	116	5	+	+	CCONJ
ap-7656	116	6	∑	∑	PROPN
ap-7656	116	7	(	(	PUNCT
ap-7656	116	8	s	s	PROPN
ap-7656	116	9	,	,	PUNCT
ap-7656	116	10	t)̸=(0,0	t)̸=(0,0	NOUN
ap-7656	116	11	)	)	PUNCT
ap-7656	116	12	wsti2	wsti2	NOUN
ap-7656	117	1	⊗	⊗	PROPN
ap-7656	117	2	i2	i2	PROPN
ap-7656	117	3	⊗	⊗	PROPN
ap-7656	117	4	bst	bst	PROPN
ap-7656	118	1	+	+	CCONJ
ap-7656	118	2	∑	∑	PROPN
ap-7656	118	3	(	(	PUNCT
ap-7656	118	4	i	i	PROPN
ap-7656	118	5	,	,	PUNCT
ap-7656	118	6	j),(k	j),(k	PROPN
ap-7656	118	7	,	,	PUNCT
ap-7656	118	8	l	l	NOUN
ap-7656	118	9	)	)	PUNCT
ap-7656	118	10	̸=(0,0	̸=(0,0	NOUN
ap-7656	118	11	)	)	PUNCT
ap-7656	118	12	xij	xij	PRON
ap-7656	118	13	,	,	PUNCT
ap-7656	118	14	klaij	klaij	ADJ
ap-7656	118	15	⊗	⊗	PROPN
ap-7656	118	16	akl	akl	PROPN
ap-7656	118	17	⊗	⊗	PROPN
ap-7656	118	18	i3	i3	PROPN
ap-7656	118	19	+	+	CCONJ
ap-7656	118	20	∑	∑	PROPN
ap-7656	118	21	(	(	PUNCT
ap-7656	118	22	i	i	PROPN
ap-7656	118	23	,	,	PUNCT
ap-7656	118	24	j),(s	j),(s	PROPN
ap-7656	118	25	,	,	PUNCT
ap-7656	118	26	t	t	PROPN
ap-7656	118	27	)	)	PUNCT
ap-7656	118	28	̸=(0,0	̸=(0,0	NOUN
ap-7656	118	29	)	)	PUNCT
ap-7656	118	30	yij	yij	NOUN
ap-7656	118	31	,	,	PUNCT
ap-7656	118	32	staij	staij	PROPN
ap-7656	118	33	⊗	⊗	PROPN
ap-7656	118	34	i2	i2	PROPN
ap-7656	118	35	⊗	⊗	PROPN
ap-7656	118	36	bst	bst	PROPN
ap-7656	119	1	+	+	CCONJ
ap-7656	119	2	∑	∑	PROPN
ap-7656	119	3	(	(	PUNCT
ap-7656	119	4	k	k	NOUN
ap-7656	119	5	,	,	PUNCT
ap-7656	119	6	l),(s	l),(s	PROPN
ap-7656	119	7	,	,	PUNCT
ap-7656	119	8	t	t	PROPN
ap-7656	119	9	)	)	PUNCT
ap-7656	119	10	̸=(0,0	̸=(0,0	NOUN
ap-7656	119	11	)	)	PUNCT
ap-7656	119	12	zkl	zkl	NOUN
ap-7656	119	13	,	,	PUNCT
ap-7656	119	14	sti2	sti2	PROPN
ap-7656	119	15	⊗	⊗	PROPN
ap-7656	119	16	akl	akl	PROPN
ap-7656	119	17	⊗	⊗	PROPN
ap-7656	119	18	bst	bst	PROPN
ap-7656	120	1	+	+	CCONJ
ap-7656	120	2	∑	∑	PROPN
ap-7656	120	3	(	(	PUNCT
ap-7656	120	4	i	i	PROPN
ap-7656	120	5	,	,	PUNCT
ap-7656	120	6	j),(k	j),(k	PROPN
ap-7656	120	7	,	,	PUNCT
ap-7656	120	8	l),(s	l),(s	PROPN
ap-7656	120	9	,	,	PUNCT
ap-7656	120	10	t	t	PROPN
ap-7656	120	11	)	)	PUNCT
ap-7656	120	12	̸=(0,0	̸=(0,0	NOUN
ap-7656	120	13	)	)	PUNCT
ap-7656	120	14	rij	rij	ADJ
ap-7656	120	15	,	,	PUNCT
ap-7656	120	16	kl	kl	PROPN
ap-7656	120	17	,	,	PUNCT
ap-7656	120	18	staij	staij	PROPN
ap-7656	120	19	⊗	⊗	PROPN
ap-7656	120	20	akl	akl	PROPN
ap-7656	120	21	⊗	⊗	PROPN
ap-7656	120	22	bst	bst	PROPN
ap-7656	120	23	)	)	PUNCT
ap-7656	120	24	,	,	PUNCT
ap-7656	120	25	(	(	PUNCT
ap-7656	120	26	8)	8)	NUM
ap-7656	120	27	where	where	SCONJ
ap-7656	120	28	i2	i2	PROPN
ap-7656	120	29	(	(	PUNCT
ap-7656	120	30	i3	i3	PROPN
ap-7656	120	31	)	)	PUNCT
ap-7656	120	32	denotes	denote	VERB
ap-7656	120	33	the	the	DET
ap-7656	120	34	two	two	NUM
ap-7656	120	35	(	(	PUNCT
ap-7656	120	36	three	three	NUM
ap-7656	120	37	)	)	PUNCT
ap-7656	120	38	dimensional	dimensional	ADJ
ap-7656	120	39	identity	identity	NOUN
ap-7656	120	40	matrix	matrix	NOUN
ap-7656	120	41	,	,	PUNCT
ap-7656	120	42	uij	uij	PRON
ap-7656	120	43	=	=	NOUN
ap-7656	120	44	tr(ρa†	tr(ρa†	NOUN
ap-7656	120	45	ij	ij	NOUN
ap-7656	120	46	⊗	⊗	PROPN
ap-7656	120	47	i2	i2	PROPN
ap-7656	120	48	⊗	⊗	PROPN
ap-7656	120	49	i3	i3	PROPN
ap-7656	120	50	)	)	PUNCT
ap-7656	120	51	,	,	PUNCT
ap-7656	120	52	vkl	vkl	NOUN
ap-7656	120	53	=	=	SYM
ap-7656	121	1	tr(ρi2	tr(ρi2	NUM
ap-7656	121	2	⊗a†	⊗a†	NUM
ap-7656	121	3	kl	kl	PROPN
ap-7656	121	4	⊗	⊗	PROPN
ap-7656	121	5	i3	i3	PROPN
ap-7656	121	6	)	)	PUNCT
ap-7656	121	7	,	,	PUNCT
ap-7656	121	8	wst	wst	PROPN
ap-7656	121	9	=	=	PROPN
ap-7656	121	10	tr(ρi2	tr(ρi2	PROPN
ap-7656	121	11	⊗	⊗	PROPN
ap-7656	121	12	i2	i2	PROPN
ap-7656	121	13	⊗b†	⊗b†	PROPN
ap-7656	121	14	st	st	PROPN
ap-7656	121	15	)	)	PUNCT
ap-7656	121	16	,	,	PUNCT
ap-7656	121	17	xij	xij	PRON
ap-7656	121	18	,	,	PUNCT
ap-7656	121	19	kl	kl	NOUN
ap-7656	121	20	=	=	SYM
ap-7656	122	1	tr(ρa†	tr(ρa†	NOUN
ap-7656	122	2	ij	ij	INTJ
ap-7656	122	3	⊗a†	⊗a†	NUM
ap-7656	122	4	kl⊗i3	kl⊗i3	PROPN
ap-7656	122	5	)	)	PUNCT
ap-7656	122	6	,	,	PUNCT
ap-7656	122	7	yij	yij	PROPN
ap-7656	122	8	,	,	PUNCT
ap-7656	122	9	st	st	PROPN
ap-7656	122	10	=	=	NOUN
ap-7656	122	11	tr(ρa†	tr(ρa†	NOUN
ap-7656	122	12	ij	ij	NOUN
ap-7656	122	13	⊗i2⊗b†	⊗i2⊗b†	PROPN
ap-7656	122	14	st	st	PROPN
ap-7656	122	15	)	)	PUNCT
ap-7656	122	16	,	,	PUNCT
ap-7656	122	17	zkl	zkl	NOUN
ap-7656	122	18	,	,	PUNCT
ap-7656	123	1	st	st	PROPN
ap-7656	123	2	=	=	SYM
ap-7656	123	3	tr(ρi2	tr(ρi2	NUM
ap-7656	123	4	⊗a†	⊗a†	NUM
ap-7656	123	5	kl	kl	PROPN
ap-7656	123	6	⊗b†	⊗b†	PROPN
ap-7656	123	7	st	st	PROPN
ap-7656	123	8	)	)	PUNCT
ap-7656	123	9	and	and	CCONJ
ap-7656	123	10	rij	rij	ADJ
ap-7656	123	11	,	,	PUNCT
ap-7656	123	12	kl	kl	PROPN
ap-7656	123	13	,	,	PUNCT
ap-7656	123	14	st	st	PROPN
ap-7656	124	1	=	=	SYM
ap-7656	124	2	tr(ρa†	tr(ρa†	PROPN
ap-7656	124	3	ij	ij	NOUN
ap-7656	124	4	⊗a†	⊗a†	X
ap-7656	124	5	kl	kl	PROPN
ap-7656	124	6	⊗b†	⊗b†	PROPN
ap-7656	124	7	st	st	PROPN
ap-7656	124	8	)	)	PUNCT
ap-7656	124	9	.	.	PUNCT
ap-7656	125	1	denote	denote	PROPN
ap-7656	125	2	t	t	PROPN
ap-7656	125	3	1|23	1|23	NUM
ap-7656	125	4	1	1	NUM
ap-7656	125	5	,	,	PUNCT
ap-7656	125	6	t	t	PROPN
ap-7656	125	7	1|23	1|23	NUM
ap-7656	125	8	2	2	NUM
ap-7656	125	9	,	,	PUNCT
ap-7656	125	10	t	t	PROPN
ap-7656	125	11	2|13	2|13	VERB
ap-7656	125	12	1	1	NUM
ap-7656	125	13	,	,	PUNCT
ap-7656	125	14	t	t	NOUN
ap-7656	125	15	2|13	2|13	VERB
ap-7656	125	16	2	2	NUM
ap-7656	125	17	,	,	PUNCT
ap-7656	125	18	t	t	NOUN
ap-7656	125	19	3|12	3|12	NUM
ap-7656	125	20	1	1	NUM
ap-7656	126	1	and	and	CCONJ
ap-7656	126	2	t	t	NOUN
ap-7656	126	3	3|12	3|12	NUM
ap-7656	126	4	2	2	NUM
ap-7656	126	5	the	the	DET
ap-7656	126	6	matrices	matrix	NOUN
ap-7656	126	7	with	with	ADP
ap-7656	126	8	entries	entry	NOUN
ap-7656	126	9	given	give	VERB
ap-7656	126	10	by	by	ADP
ap-7656	126	11	r01,kl	r01,kl	PROPN
ap-7656	126	12	,	,	PUNCT
ap-7656	126	13	st	st	PROPN
ap-7656	126	14	,	,	PUNCT
ap-7656	126	15	r11,kl	r11,kl	PROPN
ap-7656	126	16	,	,	PUNCT
ap-7656	126	17	st	st	NOUN
ap-7656	126	18	,	,	PUNCT
ap-7656	126	19	rij,01,st	rij,01,st	PROPN
ap-7656	126	20	,	,	PUNCT
ap-7656	126	21	rij,11,st	rij,11,st	NOUN
ap-7656	126	22	,	,	PUNCT
ap-7656	126	23	rij	rij	ADJ
ap-7656	126	24	,	,	PUNCT
ap-7656	126	25	kl,10	kl,10	X
ap-7656	126	26	and	and	CCONJ
ap-7656	126	27	rij	rij	ADJ
ap-7656	126	28	,	,	PUNCT
ap-7656	126	29	kl,20	kl,20	PROPN
ap-7656	126	30	(	(	PUNCT
ap-7656	126	31	i	i	PROPN
ap-7656	126	32	,	,	PUNCT
ap-7656	126	33	j	j	PROPN
ap-7656	126	34	,	,	PUNCT
ap-7656	126	35	k	k	PROPN
ap-7656	126	36	,	,	PUNCT
ap-7656	126	37	l	l	PROPN
ap-7656	126	38	∈	∈	PROPN
ap-7656	126	39	z2	z2	PROPN
ap-7656	126	40	,	,	PUNCT
ap-7656	126	41	s	s	PROPN
ap-7656	126	42	,	,	PUNCT
ap-7656	126	43	t	t	PROPN
ap-7656	126	44	∈	∈	PROPN
ap-7656	126	45	z3	z3	PROPN
ap-7656	126	46	)	)	PUNCT
ap-7656	126	47	,	,	PUNCT
ap-7656	126	48	respectively	respectively	ADV
ap-7656	126	49	.	.	PUNCT
ap-7656	127	1	let	let	VERB
ap-7656	127	2	∥a∥tr	∥a∥tr	NOUN
ap-7656	127	3	=	=	NOUN
ap-7656	127	4	∑	∑	PUNCT
ap-7656	127	5	σi	σi	NOUN
ap-7656	127	6	=	=	PUNCT
ap-7656	127	7	tr	tr	VERB
ap-7656	127	8	√	√	NUM
ap-7656	127	9	aa†	aa†	PROPN
ap-7656	127	10	be	be	AUX
ap-7656	127	11	the	the	DET
ap-7656	127	12	trace	trace	NOUN
ap-7656	127	13	norm	norm	NOUN
ap-7656	127	14	of	of	ADP
ap-7656	127	15	a	a	DET
ap-7656	127	16	matrix	matrix	NOUN
ap-7656	127	17	a	a	DET
ap-7656	127	18	∈	∈	PROPN
ap-7656	127	19	rm×n	rm×n	NOUN
ap-7656	127	20	,	,	PUNCT
ap-7656	127	21	where	where	SCONJ
ap-7656	127	22	σi	σi	PRON
ap-7656	127	23	are	be	AUX
ap-7656	127	24	the	the	DET
ap-7656	127	25	singular	singular	ADJ
ap-7656	127	26	values	value	NOUN
ap-7656	127	27	of	of	ADP
ap-7656	127	28	the	the	DET
ap-7656	127	29	matrix	matrix	NOUN
ap-7656	127	30	a.	a.	NOUN
ap-7656	128	1	first	first	ADV
ap-7656	128	2	we	we	PRON
ap-7656	128	3	note	note	VERB
ap-7656	128	4	that	that	SCONJ
ap-7656	128	5	∥t	∥t	PROPN
ap-7656	128	6	1|23	1|23	NUM
ap-7656	128	7	1	1	NUM
ap-7656	128	8	−	−	PROPN
ap-7656	128	9	t	t	NOUN
ap-7656	128	10	1|23	1|23	NUM
ap-7656	128	11	2	2	NUM
ap-7656	128	12	∥tr	∥tr	PROPN
ap-7656	128	13	is	be	AUX
ap-7656	128	14	invariant	invariant	ADJ
ap-7656	128	15	under	under	ADP
ap-7656	128	16	local	local	ADJ
ap-7656	128	17	unitary	unitary	ADJ
ap-7656	128	18	transformations	transformation	NOUN
ap-7656	128	19	.	.	PUNCT
ap-7656	129	1	denote	denote	VERB
ap-7656	129	2	uau†	uau†	PROPN
ap-7656	129	3	by	by	ADP
ap-7656	129	4	au	au	PROPN
ap-7656	129	5	.	.	PUNCT
ap-7656	130	1	suppose	suppose	VERB
ap-7656	130	2	ρ′	ρ′	PUNCT
ap-7656	130	3	=	=	SYM
ap-7656	130	4	ρ(i⊗u2⊗u3	ρ(i⊗u2⊗u3	NOUN
ap-7656	130	5	)	)	PUNCT
ap-7656	130	6	with	with	ADP
ap-7656	130	7	u2	u2	PROPN
ap-7656	130	8	∈	∈	PROPN
ap-7656	130	9	u(2	u(2	PROPN
ap-7656	130	10	)	)	PUNCT
ap-7656	130	11	and	and	CCONJ
ap-7656	130	12	u3	u3	PROPN
ap-7656	130	13	∈	∈	PROPN
ap-7656	130	14	u(3	u(3	PROPN
ap-7656	130	15	)	)	PUNCT
ap-7656	130	16	,	,	PUNCT
ap-7656	130	17	au2	au2	NOUN
ap-7656	130	18	ij	ij	NOUN
ap-7656	130	19	=	=	PUNCT
ap-7656	130	20	∑	∑	PROPN
ap-7656	130	21	(	(	PUNCT
ap-7656	130	22	i′,j′	i′,j′	NOUN
ap-7656	130	23	)	)	PUNCT
ap-7656	130	24	̸=(0,0	̸=(0,0	NOUN
ap-7656	130	25	)	)	PUNCT
ap-7656	130	26	mij	mij	NOUN
ap-7656	130	27	,	,	PUNCT
ap-7656	130	28	i′j′ai′j′	i′j′ai′j′	NOUN
ap-7656	130	29	and	and	CCONJ
ap-7656	130	30	bu3	bu3	NOUN
ap-7656	130	31	ij	ij	NOUN
ap-7656	130	32	=	=	NOUN
ap-7656	130	33	∑	∑	PROPN
ap-7656	130	34	(	(	PUNCT
ap-7656	130	35	i′,j′	i′,j′	PROPN
ap-7656	130	36	)	)	PUNCT
ap-7656	130	37	̸=(0,0	̸=(0,0	NOUN
ap-7656	130	38	)	)	PUNCT
ap-7656	130	39	nij	nij	NOUN
ap-7656	130	40	,	,	PUNCT
ap-7656	130	41	i′j′bi′j′	i′j′bi′j′	NOUN
ap-7656	130	42	for	for	ADP
ap-7656	130	43	some	some	DET
ap-7656	130	44	coefficients	coefficient	NOUN
ap-7656	130	45	mij	mij	NOUN
ap-7656	130	46	,	,	PUNCT
ap-7656	130	47	i′j′	i′j′	NOUN
ap-7656	130	48	and	and	CCONJ
ap-7656	130	49	nij	nij	NOUN
ap-7656	130	50	,	,	PUNCT
ap-7656	130	51	i′j′	i′j′	PROPN
ap-7656	130	52	.	.	PUNCT
ap-7656	131	1	the	the	DET
ap-7656	131	2	orthogonality	orthogonality	NOUN
ap-7656	131	3	of	of	ADP
ap-7656	131	4	{	{	PUNCT
ap-7656	131	5	au2	au2	NOUN
ap-7656	131	6	ij	ij	PROPN
ap-7656	131	7	}	}	PUNCT
ap-7656	131	8	and	and	CCONJ
ap-7656	131	9	{	{	PUNCT
ap-7656	131	10	bu3	bu3	NOUN
ap-7656	131	11	ij	ij	NOUN
ap-7656	131	12	}	}	PUNCT
ap-7656	131	13	requires	require	VERB
ap-7656	131	14	that	that	SCONJ
ap-7656	131	15	tr(au2	tr(au2	NOUN
ap-7656	131	16	ij	ij	INTJ
ap-7656	131	17	a	a	DET
ap-7656	131	18	u2	u2	PROPN
ap-7656	131	19	kl	kl	NOUN
ap-7656	131	20	)	)	PUNCT
ap-7656	132	1	=	=	PUNCT
ap-7656	132	2	tr(u2aija	tr(u2aija	NOUN
ap-7656	132	3	†	†	PROPN
ap-7656	132	4	klu	klu	PROPN
ap-7656	132	5	†	†	PROPN
ap-7656	132	6	2	2	NUM
ap-7656	132	7	)	)	PUNCT
ap-7656	132	8	=	=	X
ap-7656	132	9	tr(aija	tr(aija	PROPN
ap-7656	132	10	†	†	X
ap-7656	132	11	kl	kl	PROPN
ap-7656	132	12	)	)	PUNCT
ap-7656	132	13	=	=	SYM
ap-7656	132	14	2δikδjl	2δikδjl	NUM
ap-7656	132	15	;	;	PUNCT
ap-7656	132	16	tr(bu3	tr(bu3	NUM
ap-7656	132	17	ij	ij	NOUN
ap-7656	132	18	b	b	PROPN
ap-7656	132	19	u3	u3	X
ap-7656	132	20	kl	kl	X
ap-7656	132	21	)	)	PUNCT
ap-7656	133	1	=	=	SYM
ap-7656	133	2	tr(u3bijb	tr(u3bijb	NOUN
ap-7656	133	3	†	†	PROPN
ap-7656	133	4	klu	klu	PROPN
ap-7656	133	5	†	†	PROPN
ap-7656	133	6	3	3	NUM
ap-7656	133	7	)	)	PUNCT
ap-7656	133	8	=	=	PROPN
ap-7656	133	9	tr(bijb	tr(bijb	NOUN
ap-7656	133	10	†	†	X
ap-7656	133	11	kl	kl	PROPN
ap-7656	133	12	)	)	PUNCT
ap-7656	133	13	=	=	SYM
ap-7656	133	14	3δikδjl	3δikδjl	NUM
ap-7656	133	15	.	.	PUNCT
ap-7656	134	1	hence	hence	ADV
ap-7656	134	2	,	,	PUNCT
ap-7656	134	3	we	we	PRON
ap-7656	134	4	have	have	VERB
ap-7656	134	5	m	m	VERB
ap-7656	134	6	=	=	SYM
ap-7656	134	7	(	(	PUNCT
ap-7656	134	8	mij	mij	NOUN
ap-7656	134	9	,	,	PUNCT
ap-7656	134	10	i′j′	i′j′	NOUN
ap-7656	134	11	)	)	PUNCT
ap-7656	134	12	∈	∈	PROPN
ap-7656	134	13	su(3	su(3	PROPN
ap-7656	134	14	)	)	PUNCT
ap-7656	134	15	and	and	CCONJ
ap-7656	134	16	n	n	NOUN
ap-7656	134	17	=	=	SYM
ap-7656	134	18	(	(	PUNCT
ap-7656	134	19	nij	nij	PROPN
ap-7656	134	20	,	,	PUNCT
ap-7656	134	21	i′j′	i′j′	NOUN
ap-7656	134	22	)	)	PUNCT
ap-7656	134	23	∈	∈	PROPN
ap-7656	134	24	su(8	su(8	PROPN
ap-7656	134	25	)	)	PUNCT
ap-7656	134	26	since	since	SCONJ
ap-7656	134	27	any	any	DET
ap-7656	134	28	two	two	NUM
ap-7656	134	29	orthogonal	orthogonal	ADJ
ap-7656	134	30	bases	basis	NOUN
ap-7656	134	31	are	be	AUX
ap-7656	134	32	transformed	transform	VERB
ap-7656	134	33	by	by	ADP
ap-7656	134	34	an	an	DET
ap-7656	134	35	unitary	unitary	ADJ
ap-7656	134	36	matrix	matrix	NOUN
ap-7656	134	37	.	.	PUNCT
ap-7656	135	1	one	one	NUM
ap-7656	135	2	sees	see	VERB
ap-7656	135	3	that∑	that∑	NOUN
ap-7656	135	4	(	(	PUNCT
ap-7656	135	5	i	i	PRON
ap-7656	135	6	,	,	PUNCT
ap-7656	135	7	j),(k	j),(k	PROPN
ap-7656	135	8	,	,	PUNCT
ap-7656	135	9	l	l	NOUN
ap-7656	135	10	)	)	PUNCT
ap-7656	135	11	,	,	PUNCT
ap-7656	135	12	(	(	PUNCT
ap-7656	135	13	s	s	X
ap-7656	135	14	,	,	PUNCT
ap-7656	135	15	t)̸=(0,0	t)̸=(0,0	NOUN
ap-7656	135	16	)	)	PUNCT
ap-7656	135	17	rij	rij	PROPN
ap-7656	135	18	,	,	PUNCT
ap-7656	135	19	kl	kl	PROPN
ap-7656	135	20	,	,	PUNCT
ap-7656	135	21	staij	staij	PROPN
ap-7656	135	22	⊗	⊗	PROPN
ap-7656	135	23	au2	au2	PROPN
ap-7656	135	24	kl	kl	PROPN
ap-7656	136	1	⊗	⊗	PROPN
ap-7656	136	2	bu3	bu3	PROPN
ap-7656	136	3	st	st	PROPN
ap-7656	136	4	=	=	SYM
ap-7656	136	5	∑	∑	PROPN
ap-7656	136	6	(	(	PUNCT
ap-7656	136	7	i	i	PROPN
ap-7656	136	8	,	,	PUNCT
ap-7656	136	9	j),(k	j),(k	PROPN
ap-7656	136	10	,	,	PUNCT
ap-7656	136	11	l	l	NOUN
ap-7656	136	12	)	)	PUNCT
ap-7656	136	13	,	,	PUNCT
ap-7656	136	14	(	(	PUNCT
ap-7656	136	15	s	s	X
ap-7656	136	16	,	,	PUNCT
ap-7656	136	17	t)̸=(0,0	t)̸=(0,0	NOUN
ap-7656	136	18	)	)	PUNCT
ap-7656	136	19	∑	∑	PROPN
ap-7656	136	20	(	(	PUNCT
ap-7656	136	21	k′,l′),(s′,t′	k′,l′),(s′,t′	PROPN
ap-7656	136	22	)	)	PUNCT
ap-7656	136	23	̸=(0,0	̸=(0,0	NOUN
ap-7656	136	24	)	)	PUNCT
ap-7656	136	25	rij	rij	ADJ
ap-7656	136	26	,	,	PUNCT
ap-7656	136	27	kl	kl	PROPN
ap-7656	136	28	,	,	PUNCT
ap-7656	136	29	stmkl	stmkl	ADV
ap-7656	136	30	,	,	PUNCT
ap-7656	136	31	k′l′	k′l′	PROPN
ap-7656	136	32	nst	nst	PROPN
ap-7656	136	33	,	,	PUNCT
ap-7656	136	34	s′t′	s′t′	PROPN
ap-7656	136	35	aij	aij	PROPN
ap-7656	136	36	⊗	⊗	PROPN
ap-7656	136	37	ak′l′	ak′l′	PROPN
ap-7656	136	38	⊗	⊗	PROPN
ap-7656	136	39	bs′t′	bs′t′	PROPN
ap-7656	136	40	=	=	PUNCT
ap-7656	136	41	∑	∑	PROPN
ap-7656	136	42	(	(	PUNCT
ap-7656	136	43	i	i	PROPN
ap-7656	136	44	,	,	PUNCT
ap-7656	136	45	j),(k	j),(k	PROPN
ap-7656	136	46	,	,	PUNCT
ap-7656	136	47	l	l	NOUN
ap-7656	136	48	)	)	PUNCT
ap-7656	136	49	,	,	PUNCT
ap-7656	136	50	(	(	PUNCT
ap-7656	136	51	s	s	X
ap-7656	136	52	,	,	PUNCT
ap-7656	136	53	t)̸=(0,0	t)̸=(0,0	NOUN
ap-7656	136	54	)	)	PUNCT
ap-7656	136	55	(	(	PUNCT
ap-7656	136	56	∑	∑	PROPN
ap-7656	136	57	(	(	PUNCT
ap-7656	136	58	k′,l′),(s′,t′	k′,l′),(s′,t′	PROPN
ap-7656	136	59	)	)	PUNCT
ap-7656	136	60	̸=(0,0	̸=(0,0	NOUN
ap-7656	136	61	)	)	PUNCT
ap-7656	136	62	mk′l′,klrij	mk′l′,klrij	NOUN
ap-7656	136	63	,	,	PUNCT
ap-7656	136	64	k′l′,s′t′	k′l′,s′t′	PROPN
ap-7656	136	65	ns′t′,st)aij	ns′t′,st)aij	PROPN
ap-7656	136	66	⊗	⊗	PROPN
ap-7656	136	67	akl	akl	PROPN
ap-7656	136	68	⊗	⊗	PROPN
ap-7656	136	69	bst	bst	PROPN
ap-7656	136	70	.	.	PUNCT
ap-7656	137	1	we	we	PRON
ap-7656	137	2	have	have	VERB
ap-7656	137	3	t	t	PROPN
ap-7656	137	4	1|23	1|23	NUM
ap-7656	137	5	1	1	NUM
ap-7656	137	6	(	(	PUNCT
ap-7656	137	7	ρ′	ρ′	NUM
ap-7656	137	8	)	)	PUNCT
ap-7656	137	9	=	=	SYM
ap-7656	138	1	m	m	VERB
ap-7656	138	2	tt	tt	PROPN
ap-7656	138	3	1|23	1|23	NUM
ap-7656	138	4	1	1	NUM
ap-7656	138	5	(	(	PUNCT
ap-7656	138	6	ρ)n	ρ)n	X
ap-7656	138	7	and	and	CCONJ
ap-7656	138	8	t	t	PROPN
ap-7656	138	9	1|23	1|23	NUM
ap-7656	138	10	2	2	NUM
ap-7656	138	11	(	(	PUNCT
ap-7656	138	12	ρ′	ρ′	NUM
ap-7656	138	13	)	)	PUNCT
ap-7656	138	14	=	=	SYM
ap-7656	139	1	m	m	VERB
ap-7656	139	2	tt	tt	PROPN
ap-7656	139	3	1|23	1|23	NUM
ap-7656	139	4	2	2	NUM
ap-7656	139	5	(	(	PUNCT
ap-7656	139	6	ρ)n	ρ)n	NOUN
ap-7656	139	7	.	.	PUNCT
ap-7656	140	1	therefore	therefore	ADV
ap-7656	140	2	,	,	PUNCT
ap-7656	140	3	∥t	∥t	PROPN
ap-7656	140	4	1|23	1|23	NUM
ap-7656	140	5	1	1	NUM
ap-7656	140	6	(	(	PUNCT
ap-7656	140	7	ρ′	ρ′	NUM
ap-7656	140	8	)	)	PUNCT
ap-7656	140	9	−	−	PROPN
ap-7656	140	10	t	t	NOUN
ap-7656	140	11	1|23	1|23	NUM
ap-7656	140	12	2	2	NUM
ap-7656	140	13	(	(	PUNCT
ap-7656	140	14	ρ′)∥tr	ρ′)∥tr	NOUN
ap-7656	140	15	=	=	SYM
ap-7656	140	16	∥t	∥t	NOUN
ap-7656	140	17	1|23	1|23	NUM
ap-7656	140	18	1	1	NUM
ap-7656	140	19	(	(	PUNCT
ap-7656	140	20	ρ	ρ	NOUN
ap-7656	140	21	)	)	PUNCT
ap-7656	141	1	−	−	PROPN
ap-7656	142	1	t	t	NOUN
ap-7656	142	2	1|23	1|23	NUM
ap-7656	142	3	2	2	NUM
ap-7656	142	4	(	(	PUNCT
ap-7656	142	5	ρ)∥tr	ρ)∥tr	PROPN
ap-7656	142	6	,	,	PUNCT
ap-7656	142	7	(	(	PUNCT
ap-7656	142	8	9	9	NUM
ap-7656	142	9	)	)	PUNCT
ap-7656	142	10	due	due	ADP
ap-7656	142	11	to	to	ADP
ap-7656	142	12	that	that	SCONJ
ap-7656	142	13	the	the	DET
ap-7656	142	14	singular	singular	ADJ
ap-7656	142	15	values	value	NOUN
ap-7656	142	16	of	of	ADP
ap-7656	142	17	a	a	DET
ap-7656	142	18	matrix	matrix	NOUN
ap-7656	142	19	are	be	AUX
ap-7656	142	20	the	the	DET
ap-7656	142	21	same	same	ADJ
ap-7656	142	22	as	as	ADP
ap-7656	142	23	those	those	PRON
ap-7656	142	24	of	of	ADP
ap-7656	142	25	m	m	PROPN
ap-7656	142	26	ttn	ttn	PROPN
ap-7656	142	27	when	when	SCONJ
ap-7656	142	28	m	m	PROPN
ap-7656	142	29	and	and	CCONJ
ap-7656	142	30	n	n	PRON
ap-7656	142	31	are	be	AUX
ap-7656	142	32	unitary	unitary	ADJ
ap-7656	142	33	matrices	matrix	NOUN
ap-7656	142	34	.	.	PUNCT
ap-7656	143	1	theorem	theorem	VERB
ap-7656	143	2	4	4	NUM
ap-7656	143	3	.	.	PUNCT
ap-7656	144	1	if	if	SCONJ
ap-7656	144	2	a	a	DET
ap-7656	144	3	mixed	mixed	ADJ
ap-7656	144	4	state	state	NOUN
ap-7656	144	5	ρ	ρ	NOUN
ap-7656	144	6	is	be	AUX
ap-7656	144	7	fully	fully	ADV
ap-7656	144	8	separable	separable	ADJ
ap-7656	144	9	,	,	PUNCT
ap-7656	144	10	then	then	ADV
ap-7656	144	11	∥t	∥t	PROPN
ap-7656	144	12	1|23	1|23	NUM
ap-7656	144	13	1	1	NUM
ap-7656	144	14	−	−	PROPN
ap-7656	144	15	t	t	NOUN
ap-7656	144	16	1|23	1|23	NUM
ap-7656	144	17	2	2	NUM
ap-7656	144	18	∥tr	∥tr	PROPN
ap-7656	144	19	≤	≤	NOUN
ap-7656	144	20	√	√	NUM
ap-7656	144	21	3	3	NUM
ap-7656	144	22	.	.	PUNCT
ap-7656	144	23	proof	proof	NOUN
ap-7656	144	24	if	if	SCONJ
ap-7656	144	25	ρ	ρ	PROPN
ap-7656	144	26	=	=	SYM
ap-7656	144	27	|φ⟩⟨φ|	|φ⟩⟨φ|	NOUN
ap-7656	144	28	is	be	AUX
ap-7656	144	29	fully	fully	ADV
ap-7656	144	30	separable	separable	ADJ
ap-7656	144	31	,	,	PUNCT
ap-7656	144	32	we	we	PRON
ap-7656	144	33	have	have	VERB
ap-7656	144	34	|φ1|2|3⟩	|φ1|2|3⟩	NOUN
ap-7656	144	35	=	=	SYM
ap-7656	144	36	|φ1⟩	|φ1⟩	NUM
ap-7656	144	37	⊗	⊗	NOUN
ap-7656	144	38	|φ23⟩	|φ23⟩	PROPN
ap-7656	144	39	∈	∈	PROPN
ap-7656	144	40	h2	h2	NOUN
ap-7656	144	41	1	1	NUM
ap-7656	144	42	⊗	⊗	PROPN
ap-7656	144	43	h6	h6	PROPN
ap-7656	144	44	23	23	NUM
ap-7656	144	45	,	,	PUNCT
ap-7656	144	46	where	where	SCONJ
ap-7656	144	47	|φ23⟩	|φ23⟩	PROPN
ap-7656	144	48	=	=	SYM
ap-7656	144	49	|φ2⟩	|φ2⟩	PROPN
ap-7656	145	1	⊗	⊗	NUM
ap-7656	145	2	|φ3⟩	|φ3⟩	PROPN
ap-7656	145	3	∈	∈	PROPN
ap-7656	145	4	h2	h2	NOUN
ap-7656	145	5	2	2	NUM
ap-7656	145	6	⊗	⊗	PROPN
ap-7656	145	7	h3	h3	NOUN
ap-7656	145	8	3	3	NUM
ap-7656	145	9	.	.	PUNCT
ap-7656	146	1	then	then	ADV
ap-7656	146	2	by	by	ADP
ap-7656	146	3	schmidt	schmidt	ADJ
ap-7656	146	4	decomposition	decomposition	NOUN
ap-7656	146	5	,	,	PUNCT
ap-7656	146	6	|φ1|2|3⟩	|φ1|2|3⟩	X
ap-7656	146	7	=	=	SYM
ap-7656	146	8	t0|0α⟩	t0|0α⟩	NOUN
ap-7656	146	9	+	+	CCONJ
ap-7656	146	10	t1|1β⟩	t1|1β⟩	NOUN
ap-7656	146	11	,	,	PUNCT
ap-7656	147	1	where	where	SCONJ
ap-7656	147	2	t20	t20	VERB
ap-7656	147	3	+	+	CCONJ
ap-7656	147	4	t21	t21	NOUN
ap-7656	147	5	=	=	SYM
ap-7656	147	6	1	1	X
ap-7656	147	7	.	.	X
ap-7656	147	8	taking	take	VERB
ap-7656	147	9	into	into	ADP
ap-7656	147	10	account	account	NOUN
ap-7656	147	11	the	the	DET
ap-7656	147	12	local	local	ADJ
ap-7656	147	13	unitary	unitary	ADJ
ap-7656	147	14	equivalence	equivalence	NOUN
ap-7656	147	15	in	in	ADP
ap-7656	147	16	h2	h2	NOUN
ap-7656	147	17	2	2	NUM
ap-7656	147	18	⊗	⊗	PROPN
ap-7656	147	19	h3	h3	NOUN
ap-7656	147	20	3	3	NUM
ap-7656	147	21	and	and	CCONJ
ap-7656	147	22	using	use	VERB
ap-7656	147	23	(	(	PUNCT
ap-7656	147	24	9	9	NUM
ap-7656	147	25	)	)	PUNCT
ap-7656	147	26	,	,	PUNCT
ap-7656	147	27	we	we	PRON
ap-7656	147	28	only	only	ADV
ap-7656	147	29	need	need	VERB
ap-7656	147	30	to	to	PART
ap-7656	147	31	consider	consider	VERB
ap-7656	147	32	that	that	PRON
ap-7656	147	33	{	{	PUNCT
ap-7656	147	34	|α⟩	|α⟩	ADV
ap-7656	147	35	,	,	PUNCT
ap-7656	147	36	|β⟩	|β⟩	PROPN
ap-7656	147	37	}	}	PUNCT
ap-7656	147	38	=	=	SYM
ap-7656	147	39	{	{	PUNCT
ap-7656	147	40	|00⟩	|00⟩	NOUN
ap-7656	147	41	,	,	PUNCT
ap-7656	147	42	|01⟩	|01⟩	ADJ
ap-7656	147	43	}	}	PUNCT
ap-7656	147	44	.	.	PUNCT
ap-7656	148	1	then	then	ADV
ap-7656	148	2	224	224	NUM
ap-7656	148	3	vol	vol	NOUN
ap-7656	148	4	.	.	PUNCT
ap-7656	149	1	62	62	NUM
ap-7656	149	2	no	no	INTJ
ap-7656	149	3	.	.	PUNCT
ap-7656	150	1	1/2022	1/2022	NUM
ap-7656	150	2	a	a	DET
ap-7656	150	3	note	note	NOUN
ap-7656	150	4	on	on	ADP
ap-7656	150	5	entanglement	entanglement	NOUN
ap-7656	150	6	classification	classification	NOUN
ap-7656	150	7	for	for	ADP
ap-7656	150	8	tripartite	tripartite	ADJ
ap-7656	150	9	.	.	PUNCT
ap-7656	150	10	.	.	PUNCT
ap-7656	150	11	.	.	PUNCT
ap-7656	151	1	|φ1|2|3⟩	|φ1|2|3⟩	X
ap-7656	151	2	=	=	PUNCT
ap-7656	151	3	t0|000⟩	t0|000⟩	NOUN
ap-7656	151	4	+	+	X
ap-7656	151	5	t1|101⟩.	t1|101⟩.	NUM
ap-7656	151	6	t	t	NOUN
ap-7656	151	7	1|23	1|23	NUM
ap-7656	151	8	1	1	NUM
ap-7656	151	9	and	and	CCONJ
ap-7656	151	10	t	t	NOUN
ap-7656	151	11	1|23	1|23	NUM
ap-7656	151	12	2	2	NUM
ap-7656	151	13	are	be	AUX
ap-7656	151	14	given	give	VERB
ap-7656	151	15	by	by	ADP
ap-7656	151	16	t	t	NOUN
ap-7656	151	17	1|23	1|23	NUM
ap-7656	151	18	1	1	NUM
ap-7656	151	19	=	=	SYM
ap-7656	151	20			NOUN
ap-7656	151	21	0	0	PUNCT
ap-7656	151	22	t0t1	t0t1	NOUN
ap-7656	151	23	0	0	NUM
ap-7656	151	24	0	0	NUM
ap-7656	151	25	t0t1	t0t1	X
ap-7656	151	26	0	0	NUM
ap-7656	151	27	0	0	NUM
ap-7656	151	28	0	0	NUM
ap-7656	151	29	0	0	NUM
ap-7656	151	30	0	0	NUM
ap-7656	151	31	t0t1	t0t1	X
ap-7656	151	32	0	0	NUM
ap-7656	151	33	0	0	NUM
ap-7656	151	34	t0t1ω	t0t1ω	NUM
ap-7656	151	35	2	2	NUM
ap-7656	151	36	0	0	NUM
ap-7656	151	37	0	0	NUM
ap-7656	151	38	0	0	NUM
ap-7656	151	39	0	0	NUM
ap-7656	151	40	0	0	NUM
ap-7656	152	1	t0t1	t0t1	X
ap-7656	152	2	0	0	NUM
ap-7656	152	3	0	0	NUM
ap-7656	152	4	t0t1ω	t0t1ω	SYM
ap-7656	152	5	0	0	NUM
ap-7656	152	6			PROPN
ap-7656	152	7	t	t	NOUN
ap-7656	152	8	,	,	PUNCT
ap-7656	152	9	(	(	PUNCT
ap-7656	152	10	10	10	NUM
ap-7656	152	11	)	)	PUNCT
ap-7656	152	12	t	t	NOUN
ap-7656	152	13	1|23	1|23	NUM
ap-7656	152	14	2	2	NUM
ap-7656	152	15	=	=	SYM
ap-7656	152	16			NOUN
ap-7656	152	17	0	0	PUNCT
ap-7656	153	1	t0t1	t0t1	NOUN
ap-7656	153	2	0	0	NUM
ap-7656	153	3	0	0	NUM
ap-7656	154	1	−t0t1	−t0t1	PROPN
ap-7656	154	2	0	0	NUM
ap-7656	154	3	0	0	NUM
ap-7656	154	4	0	0	NUM
ap-7656	154	5	0	0	NUM
ap-7656	154	6	0	0	NUM
ap-7656	154	7	t0t1	t0t1	X
ap-7656	154	8	0	0	NUM
ap-7656	154	9	0	0	NUM
ap-7656	155	1	−t0t1ω2	−t0t1ω2	CCONJ
ap-7656	155	2	0	0	NUM
ap-7656	155	3	0	0	NUM
ap-7656	155	4	0	0	NUM
ap-7656	155	5	0	0	NUM
ap-7656	155	6	0	0	NUM
ap-7656	155	7	t0t1	t0t1	X
ap-7656	155	8	0	0	SYM
ap-7656	155	9	0	0	NUM
ap-7656	155	10	−t0t1ω	−t0t1ω	NOUN
ap-7656	155	11	0	0	NUM
ap-7656	155	12			NUM
ap-7656	155	13	t	t	NOUN
ap-7656	155	14	.	.	PUNCT
ap-7656	156	1	(	(	PUNCT
ap-7656	156	2	11	11	NUM
ap-7656	156	3	)	)	PUNCT
ap-7656	156	4	with	with	ADP
ap-7656	156	5	ω3	ω3	NOUN
ap-7656	156	6	=	=	SYM
ap-7656	157	1	1	1	X
ap-7656	157	2	.	.	PUNCT
ap-7656	158	1	therefore	therefore	ADV
ap-7656	158	2	,	,	PUNCT
ap-7656	158	3	we	we	PRON
ap-7656	158	4	have	have	VERB
ap-7656	158	5	∥t	∥t	ADJ
ap-7656	158	6	1|23	1|23	NUM
ap-7656	158	7	1	1	NUM
ap-7656	158	8	−	−	PROPN
ap-7656	158	9	t	t	NOUN
ap-7656	158	10	1|23	1|23	NUM
ap-7656	158	11	2	2	NUM
ap-7656	158	12	∥tr	∥tr	NOUN
ap-7656	158	13	=	=	PRON
ap-7656	158	14	tr	tr	NOUN
ap-7656	158	15	√	√	PROPN
ap-7656	158	16	(	(	PUNCT
ap-7656	158	17	t	t	PROPN
ap-7656	158	18	1|23	1|23	NUM
ap-7656	158	19	1	1	NUM
ap-7656	158	20	−	−	PROPN
ap-7656	158	21	t	t	NOUN
ap-7656	158	22	1|23	1|23	NUM
ap-7656	158	23	2	2	NUM
ap-7656	158	24	)	)	PUNCT
ap-7656	158	25	(	(	PUNCT
ap-7656	158	26	t	t	NOUN
ap-7656	158	27	1|23	1|23	NUM
ap-7656	158	28	1	1	NUM
ap-7656	158	29	−	−	PROPN
ap-7656	158	30	t	t	NOUN
ap-7656	158	31	1|23	1|23	NUM
ap-7656	158	32	2	2	NUM
ap-7656	158	33	)	)	PUNCT
ap-7656	158	34	†	†	NOUN
ap-7656	158	35	=	=	PUNCT
ap-7656	158	36	√	√	PROPN
ap-7656	158	37	12t20t21	12t20t21	NUM
ap-7656	158	38	≤	≤	NUM
ap-7656	158	39	√	√	ADP
ap-7656	158	40	3	3	NUM
ap-7656	158	41	.	.	PUNCT
ap-7656	159	1	for	for	ADP
ap-7656	159	2	a	a	DET
ap-7656	159	3	fully	fully	ADV
ap-7656	159	4	separable	separable	ADJ
ap-7656	159	5	mixed	mixed	ADJ
ap-7656	159	6	state	state	NOUN
ap-7656	159	7	ρ	ρ	PROPN
ap-7656	159	8	=	=	SYM
ap-7656	159	9	∑	∑	PUNCT
ap-7656	159	10	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	159	11	,	,	PUNCT
ap-7656	159	12	we	we	PRON
ap-7656	159	13	get	get	VERB
ap-7656	159	14	∥t	∥t	ADJ
ap-7656	159	15	1|23	1|23	NUM
ap-7656	159	16	1	1	NUM
ap-7656	159	17	(	(	PUNCT
ap-7656	159	18	ρ	ρ	NOUN
ap-7656	159	19	)	)	PUNCT
ap-7656	159	20	−	−	PROPN
ap-7656	159	21	t	t	NOUN
ap-7656	159	22	1|23	1|23	NUM
ap-7656	159	23	2	2	NUM
ap-7656	159	24	(	(	PUNCT
ap-7656	159	25	ρ)∥tr	ρ)∥tr	NOUN
ap-7656	159	26	=	=	NOUN
ap-7656	159	27	∥t	∥t	ADJ
ap-7656	159	28	1|23	1|23	NUM
ap-7656	159	29	1	1	NUM
ap-7656	159	30	(	(	PUNCT
ap-7656	159	31	∑	∑	ADV
ap-7656	159	32	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	159	33	)	)	PUNCT
ap-7656	159	34	−	−	PROPN
ap-7656	160	1	t	t	NOUN
ap-7656	160	2	1|23	1|23	NUM
ap-7656	160	3	2	2	NUM
ap-7656	160	4	(	(	PUNCT
ap-7656	160	5	∑	∑	PUNCT
ap-7656	160	6	pi|φi⟩⟨φi|)∥tr	pi|φi⟩⟨φi|)∥tr	PROPN
ap-7656	160	7	≤	≤	NOUN
ap-7656	160	8	∑	∑	PUNCT
ap-7656	160	9	pi∥t	pi∥t	PROPN
ap-7656	160	10	1|23	1|23	NUM
ap-7656	160	11	1	1	NUM
ap-7656	160	12	(	(	PUNCT
ap-7656	160	13	|φi⟩⟨φi|	|φi⟩⟨φi|	NOUN
ap-7656	160	14	)	)	PUNCT
ap-7656	160	15	−	−	PROPN
ap-7656	160	16	t	t	NOUN
ap-7656	160	17	1|23	1|23	NUM
ap-7656	160	18	2	2	NUM
ap-7656	160	19	(	(	PUNCT
ap-7656	160	20	|φi⟩⟨φi|)∥tr	|φi⟩⟨φi|)∥tr	X
ap-7656	160	21	≤	≤	NOUN
ap-7656	160	22	√	√	NUM
ap-7656	160	23	3	3	NUM
ap-7656	160	24	,	,	PUNCT
ap-7656	160	25	which	which	PRON
ap-7656	160	26	proves	prove	VERB
ap-7656	160	27	the	the	DET
ap-7656	160	28	theorem	theorem	NOUN
ap-7656	160	29	.	.	PUNCT
ap-7656	161	1	□	□	PUNCT
ap-7656	161	2	theorem	theorem	ADJ
ap-7656	161	3	5	5	NUM
ap-7656	161	4	.	.	X
ap-7656	161	5	for	for	ADP
ap-7656	161	6	any	any	DET
ap-7656	161	7	mixed	mixed	ADJ
ap-7656	161	8	state	state	NOUN
ap-7656	161	9	ρ	ρ	PROPN
ap-7656	161	10	=	=	NOUN
ap-7656	161	11	∑	∑	PROPN
ap-7656	161	12	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	161	13	∈	∈	PROPN
ap-7656	161	14	h2	h2	NOUN
ap-7656	161	15	1	1	NUM
ap-7656	161	16	⊗h2	⊗h2	PROPN
ap-7656	161	17	2	2	NUM
ap-7656	161	18	⊗h3	⊗h3	NUM
ap-7656	161	19	3	3	NUM
ap-7656	161	20	,	,	PUNCT
ap-7656	161	21	∑	∑	ADP
ap-7656	161	22	pi	pi	NOUN
ap-7656	161	23	=	=	SYM
ap-7656	161	24	1	1	NUM
ap-7656	161	25	,	,	PUNCT
ap-7656	161	26	0	0	NUM
ap-7656	161	27	<	<	X
ap-7656	161	28	pi	pi	NOUN
ap-7656	161	29	≤	≤	NUM
ap-7656	161	30	1	1	NUM
ap-7656	161	31	,	,	PUNCT
ap-7656	161	32	we	we	PRON
ap-7656	161	33	have	have	VERB
ap-7656	161	34	:	:	PUNCT
ap-7656	161	35	(	(	PUNCT
ap-7656	161	36	1	1	X
ap-7656	161	37	)	)	PUNCT
ap-7656	161	38	if	if	SCONJ
ap-7656	161	39	ρ	ρ	PROPN
ap-7656	161	40	is	be	AUX
ap-7656	161	41	1|23	1|23	NUM
ap-7656	161	42	separable	separable	ADJ
ap-7656	161	43	,	,	PUNCT
ap-7656	161	44	then	then	ADV
ap-7656	161	45	∥t	∥t	PROPN
ap-7656	161	46	1|23	1|23	NUM
ap-7656	161	47	1	1	NUM
ap-7656	161	48	−t	−t	NOUN
ap-7656	161	49	1|23	1|23	NUM
ap-7656	161	50	2	2	NUM
ap-7656	161	51	∥tr	∥tr	NOUN
ap-7656	161	52	≤	≤	NOUN
ap-7656	162	1	√	√	ADP
ap-7656	162	2	6	6	NUM
ap-7656	162	3	;	;	PUNCT
ap-7656	162	4	(	(	PUNCT
ap-7656	162	5	2	2	X
ap-7656	162	6	)	)	PUNCT
ap-7656	162	7	if	if	SCONJ
ap-7656	162	8	ρ	ρ	PROPN
ap-7656	162	9	is	be	AUX
ap-7656	162	10	2|13	2|13	VERB
ap-7656	162	11	separable	separable	ADJ
ap-7656	162	12	,	,	PUNCT
ap-7656	162	13	then	then	ADV
ap-7656	162	14	∥t	∥t	PROPN
ap-7656	162	15	2|13	2|13	ADJ
ap-7656	162	16	1	1	NUM
ap-7656	162	17	−t	−t	NOUN
ap-7656	162	18	2|13	2|13	ADJ
ap-7656	162	19	2	2	NUM
ap-7656	162	20	∥tr	∥tr	NOUN
ap-7656	162	21	≤	≤	NOUN
ap-7656	162	22	√	√	ADP
ap-7656	162	23	6	6	NUM
ap-7656	162	24	;	;	PUNCT
ap-7656	162	25	(	(	PUNCT
ap-7656	162	26	3	3	X
ap-7656	162	27	)	)	PUNCT
ap-7656	162	28	if	if	SCONJ
ap-7656	162	29	ρ	ρ	PROPN
ap-7656	162	30	is	be	AUX
ap-7656	162	31	3|12	3|12	NUM
ap-7656	162	32	separable	separable	NOUN
ap-7656	162	33	,	,	PUNCT
ap-7656	162	34	then	then	ADV
ap-7656	162	35	∥t	∥t	PROPN
ap-7656	162	36	3|12	3|12	NUM
ap-7656	162	37	1	1	NUM
ap-7656	162	38	−t	−t	NOUN
ap-7656	162	39	3|12	3|12	NUM
ap-7656	162	40	2	2	NUM
ap-7656	162	41	∥tr	∥tr	NOUN
ap-7656	162	42	≤	≤	NOUN
ap-7656	162	43	√	√	NUM
ap-7656	162	44	3	3	NUM
ap-7656	162	45	.	.	PUNCT
ap-7656	163	1	proof	proof	NOUN
ap-7656	163	2	(	(	PUNCT
ap-7656	163	3	1	1	X
ap-7656	163	4	)	)	PUNCT
ap-7656	163	5	if	if	SCONJ
ap-7656	163	6	ρ	ρ	NUM
ap-7656	163	7	=	=	SYM
ap-7656	163	8	|φ⟩⟨φ|	|φ⟩⟨φ|	PROPN
ap-7656	163	9	is	be	AUX
ap-7656	163	10	1|23	1|23	NUM
ap-7656	163	11	separable	separable	ADJ
ap-7656	163	12	,	,	PUNCT
ap-7656	163	13	we	we	PRON
ap-7656	163	14	have	have	VERB
ap-7656	163	15	|φ1|23⟩	|φ1|23⟩	NOUN
ap-7656	163	16	=	=	SYM
ap-7656	163	17	|φ1⟩	|φ1⟩	NOUN
ap-7656	164	1	⊗	⊗	ADJ
ap-7656	164	2	|φ23⟩	|φ23⟩	PROPN
ap-7656	164	3	∈	∈	PROPN
ap-7656	164	4	h2	h2	NOUN
ap-7656	164	5	1	1	NUM
ap-7656	164	6	⊗	⊗	PROPN
ap-7656	164	7	h6	h6	PROPN
ap-7656	164	8	23	23	NUM
ap-7656	164	9	,	,	PUNCT
ap-7656	164	10	where	where	SCONJ
ap-7656	164	11	h6	h6	PROPN
ap-7656	164	12	23	23	NUM
ap-7656	164	13	=	=	SYM
ap-7656	164	14	h2	h2	NOUN
ap-7656	164	15	2	2	NUM
ap-7656	164	16	⊗h3	⊗h3	NUM
ap-7656	164	17	3	3	NUM
ap-7656	164	18	.	.	PUNCT
ap-7656	165	1	then	then	ADV
ap-7656	165	2	by	by	ADP
ap-7656	165	3	schmidt	schmidt	ADJ
ap-7656	165	4	decomposition	decomposition	NOUN
ap-7656	165	5	,	,	PUNCT
ap-7656	165	6	one	one	NUM
ap-7656	165	7	has	have	VERB
ap-7656	165	8	|φ1|23⟩	|φ1|23⟩	NOUN
ap-7656	165	9	=	=	SYM
ap-7656	165	10	t0|0α⟩	t0|0α⟩	NOUN
ap-7656	165	11	+	+	CCONJ
ap-7656	165	12	t1|1β⟩	t1|1β⟩	NOUN
ap-7656	165	13	,	,	PUNCT
ap-7656	166	1	where	where	SCONJ
ap-7656	166	2	t20	t20	VERB
ap-7656	166	3	+	+	CCONJ
ap-7656	166	4	t21	t21	NOUN
ap-7656	166	5	=	=	SYM
ap-7656	166	6	1	1	X
ap-7656	166	7	.	.	X
ap-7656	166	8	taking	take	VERB
ap-7656	166	9	into	into	ADP
ap-7656	166	10	account	account	NOUN
ap-7656	166	11	the	the	DET
ap-7656	166	12	local	local	ADJ
ap-7656	166	13	unitary	unitary	ADJ
ap-7656	166	14	equivalence	equivalence	NOUN
ap-7656	166	15	in	in	ADP
ap-7656	166	16	h2	h2	PROPN
ap-7656	166	17	2	2	NUM
ap-7656	166	18	⊗h3	⊗h3	NUM
ap-7656	166	19	3	3	NUM
ap-7656	166	20	and	and	CCONJ
ap-7656	166	21	using	use	VERB
ap-7656	166	22	(	(	PUNCT
ap-7656	166	23	9	9	NUM
ap-7656	166	24	)	)	PUNCT
ap-7656	166	25	,	,	PUNCT
ap-7656	166	26	we	we	PRON
ap-7656	166	27	only	only	ADV
ap-7656	166	28	need	need	VERB
ap-7656	166	29	to	to	PART
ap-7656	166	30	consider	consider	VERB
ap-7656	166	31	two	two	NUM
ap-7656	166	32	cases	case	NOUN
ap-7656	166	33	(	(	PUNCT
ap-7656	166	34	i	i	NOUN
ap-7656	166	35	)	)	PUNCT
ap-7656	166	36	{	{	PUNCT
ap-7656	166	37	|α⟩	|α⟩	NOUN
ap-7656	166	38	,	,	PUNCT
ap-7656	166	39	|β⟩	|β⟩	PROPN
ap-7656	166	40	}	}	PUNCT
ap-7656	166	41	=	=	SYM
ap-7656	166	42	{	{	PUNCT
ap-7656	166	43	|00⟩	|00⟩	NOUN
ap-7656	166	44	,	,	PUNCT
ap-7656	166	45	|01⟩	|01⟩	ADJ
ap-7656	166	46	}	}	PUNCT
ap-7656	166	47	and	and	CCONJ
ap-7656	166	48	(	(	PUNCT
ap-7656	166	49	ii	ii	NOUN
ap-7656	166	50	)	)	PUNCT
ap-7656	166	51	{	{	PUNCT
ap-7656	166	52	|00⟩	|00⟩	NOUN
ap-7656	166	53	,	,	PUNCT
ap-7656	166	54	|11⟩	|11⟩	NOUN
ap-7656	166	55	}	}	PUNCT
ap-7656	166	56	.	.	PUNCT
ap-7656	167	1	for	for	ADP
ap-7656	167	2	the	the	DET
ap-7656	167	3	first	first	ADJ
ap-7656	167	4	case	case	NOUN
ap-7656	167	5	we	we	PRON
ap-7656	167	6	have	have	VERB
ap-7656	167	7	∥t	∥t	ADJ
ap-7656	167	8	1|23	1|23	NUM
ap-7656	167	9	1	1	NUM
ap-7656	167	10	−	−	PROPN
ap-7656	167	11	t	t	NOUN
ap-7656	167	12	1|23	1|23	NUM
ap-7656	167	13	2	2	NUM
ap-7656	167	14	∥tr	∥tr	PROPN
ap-7656	167	15	≤	≤	NOUN
ap-7656	167	16	√	√	NUM
ap-7656	167	17	3	3	NUM
ap-7656	167	18	by	by	ADP
ap-7656	167	19	theorem	theorem	NOUN
ap-7656	167	20	4	4	NUM
ap-7656	167	21	.	.	X
ap-7656	168	1	for	for	ADP
ap-7656	168	2	the	the	DET
ap-7656	168	3	second	second	ADJ
ap-7656	168	4	case	case	NOUN
ap-7656	168	5	,	,	PUNCT
ap-7656	168	6	we	we	PRON
ap-7656	168	7	have	have	VERB
ap-7656	168	8	|φ1|23⟩	|φ1|23⟩	NOUN
ap-7656	168	9	=	=	SYM
ap-7656	168	10	t0|000⟩	t0|000⟩	NOUN
ap-7656	168	11	+	+	CCONJ
ap-7656	168	12	t1|111⟩	t1|111⟩	NOUN
ap-7656	168	13	,	,	PUNCT
ap-7656	168	14	where	where	SCONJ
ap-7656	168	15	t	t	NOUN
ap-7656	168	16	1|23	1|23	NUM
ap-7656	168	17	1	1	NUM
ap-7656	168	18	and	and	CCONJ
ap-7656	168	19	t	t	NOUN
ap-7656	168	20	1|23	1|23	NUM
ap-7656	168	21	2	2	NUM
ap-7656	168	22	are	be	AUX
ap-7656	168	23	given	give	VERB
ap-7656	168	24	by	by	ADP
ap-7656	168	25	t	t	NOUN
ap-7656	168	26	1|23	1|23	NUM
ap-7656	168	27	1	1	NUM
ap-7656	168	28	=	=	NUM
ap-7656	168	29			NOUN
ap-7656	168	30	t0t1	t0t1	X
ap-7656	168	31	0	0	NUM
ap-7656	168	32	t0t1	t0t1	PROPN
ap-7656	168	33	t0t1	t0t1	X
ap-7656	168	34	0	0	PUNCT
ap-7656	168	35	−t0t1	−t0t1	PROPN
ap-7656	168	36	0	0	NUM
ap-7656	168	37	0	0	SYM
ap-7656	168	38	0	0	NUM
ap-7656	168	39	t0t1	t0t1	X
ap-7656	168	40	0	0	NUM
ap-7656	168	41	t0t1	t0t1	X
ap-7656	168	42	t0t1ω	t0t1ω	NUM
ap-7656	168	43	2	2	NUM
ap-7656	168	44	0	0	NUM
ap-7656	168	45	−t0t1ω2	−t0t1ω2	CCONJ
ap-7656	168	46	0	0	NUM
ap-7656	168	47	0	0	NUM
ap-7656	168	48	0	0	NUM
ap-7656	168	49	t0t1	t0t1	X
ap-7656	168	50	0	0	NUM
ap-7656	168	51	t0t1	t0t1	X
ap-7656	168	52	t0t1ω	t0t1ω	X
ap-7656	168	53	0	0	NUM
ap-7656	169	1	−t0t1ω	−t0t1ω	NOUN
ap-7656	169	2			PROPN
ap-7656	169	3	t	t	NOUN
ap-7656	169	4	,	,	PUNCT
ap-7656	169	5	(	(	PUNCT
ap-7656	169	6	12	12	NUM
ap-7656	169	7	)	)	PUNCT
ap-7656	169	8	t	t	NOUN
ap-7656	169	9	1|23	1|23	NUM
ap-7656	169	10	2	2	NUM
ap-7656	169	11	=	=	SYM
ap-7656	169	12			NOUN
ap-7656	169	13	t0t1	t0t1	X
ap-7656	169	14	0	0	X
ap-7656	169	15	t0t1	t0t1	X
ap-7656	169	16	−t0t1	−t0t1	PROPN
ap-7656	169	17	0	0	NUM
ap-7656	169	18	t0t1	t0t1	NOUN
ap-7656	169	19	0	0	NUM
ap-7656	169	20	0	0	SYM
ap-7656	169	21	0	0	NUM
ap-7656	170	1	t0t1	t0t1	X
ap-7656	170	2	0	0	PUNCT
ap-7656	170	3	t0t1	t0t1	X
ap-7656	170	4	−t0t1ω2	−t0t1ω2	X
ap-7656	170	5	0	0	PUNCT
ap-7656	170	6	t0t1ω	t0t1ω	NUM
ap-7656	170	7	2	2	NUM
ap-7656	170	8	0	0	NUM
ap-7656	170	9	0	0	NUM
ap-7656	170	10	0	0	NUM
ap-7656	170	11	t0t1	t0t1	X
ap-7656	170	12	0	0	PUNCT
ap-7656	170	13	t0t1	t0t1	X
ap-7656	170	14	−t0t1ω	−t0t1ω	VERB
ap-7656	170	15	0	0	PUNCT
ap-7656	170	16	t0t1ω	t0t1ω	NUM
ap-7656	170	17			PROPN
ap-7656	170	18	t	t	NOUN
ap-7656	170	19	.	.	PUNCT
ap-7656	171	1	(	(	PUNCT
ap-7656	171	2	13	13	NUM
ap-7656	171	3	)	)	PUNCT
ap-7656	171	4	then	then	ADV
ap-7656	171	5	we	we	PRON
ap-7656	171	6	have	have	VERB
ap-7656	171	7	∥t	∥t	ADJ
ap-7656	171	8	1|23	1|23	NUM
ap-7656	171	9	1	1	NUM
ap-7656	171	10	−	−	PROPN
ap-7656	171	11	t	t	NOUN
ap-7656	171	12	1|23	1|23	NUM
ap-7656	171	13	2	2	NUM
ap-7656	171	14	∥tr	∥tr	NOUN
ap-7656	171	15	=	=	PRON
ap-7656	171	16	tr	tr	NOUN
ap-7656	171	17	√	√	PROPN
ap-7656	171	18	(	(	PUNCT
ap-7656	171	19	t	t	PROPN
ap-7656	171	20	1|23	1|23	NUM
ap-7656	171	21	1	1	NUM
ap-7656	171	22	−	−	PROPN
ap-7656	171	23	t	t	NOUN
ap-7656	171	24	1|23	1|23	NUM
ap-7656	171	25	2	2	NUM
ap-7656	171	26	)	)	PUNCT
ap-7656	171	27	(	(	PUNCT
ap-7656	171	28	t	t	NOUN
ap-7656	171	29	1|23	1|23	NUM
ap-7656	171	30	1	1	NUM
ap-7656	171	31	−	−	PROPN
ap-7656	171	32	t	t	NOUN
ap-7656	171	33	1|23	1|23	NUM
ap-7656	171	34	2	2	NUM
ap-7656	171	35	)	)	PUNCT
ap-7656	171	36	†	†	NOUN
ap-7656	172	1	=	=	PUNCT
ap-7656	172	2	√	√	PROPN
ap-7656	172	3	24t20t21	24t20t21	NUM
ap-7656	172	4	≤	≤	NUM
ap-7656	172	5	√	√	ADP
ap-7656	172	6	6	6	NUM
ap-7656	172	7	.	.	PUNCT
ap-7656	172	8	now	now	ADV
ap-7656	172	9	consider	consider	VERB
ap-7656	172	10	mixed	mixed	ADJ
ap-7656	172	11	state	state	NOUN
ap-7656	172	12	ρ	ρ	PROPN
ap-7656	172	13	=	=	SYM
ap-7656	172	14	∑	∑	PUNCT
ap-7656	172	15	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	172	16	.	.	PUNCT
ap-7656	173	1	we	we	PRON
ap-7656	173	2	obtain	obtain	VERB
ap-7656	173	3	∥t	∥t	ADJ
ap-7656	173	4	1|23	1|23	NUM
ap-7656	173	5	1	1	NUM
ap-7656	173	6	(	(	PUNCT
ap-7656	173	7	ρ	ρ	NOUN
ap-7656	173	8	)	)	PUNCT
ap-7656	173	9	−	−	PROPN
ap-7656	173	10	t	t	NOUN
ap-7656	173	11	1|23	1|23	NUM
ap-7656	173	12	2	2	NUM
ap-7656	173	13	(	(	PUNCT
ap-7656	173	14	ρ)∥tr	ρ)∥tr	NOUN
ap-7656	173	15	=	=	NOUN
ap-7656	173	16	∥t	∥t	ADJ
ap-7656	173	17	1|23	1|23	NUM
ap-7656	173	18	1	1	NUM
ap-7656	173	19	(	(	PUNCT
ap-7656	173	20	∑	∑	ADV
ap-7656	173	21	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	173	22	)	)	PUNCT
ap-7656	174	1	−	−	PROPN
ap-7656	175	1	t	t	NOUN
ap-7656	175	2	1|23	1|23	NUM
ap-7656	175	3	2	2	NUM
ap-7656	175	4	(	(	PUNCT
ap-7656	175	5	∑	∑	PUNCT
ap-7656	175	6	pi|φi⟩⟨φi|)∥tr	pi|φi⟩⟨φi|)∥tr	PROPN
ap-7656	175	7	≤	≤	NOUN
ap-7656	175	8	∑	∑	PUNCT
ap-7656	175	9	pi∥t	pi∥t	PROPN
ap-7656	175	10	1|23	1|23	NUM
ap-7656	175	11	1	1	NUM
ap-7656	175	12	(	(	PUNCT
ap-7656	175	13	|φi⟩⟨φi|	|φi⟩⟨φi|	NOUN
ap-7656	175	14	)	)	PUNCT
ap-7656	175	15	−	−	PROPN
ap-7656	175	16	t	t	NOUN
ap-7656	175	17	1|23	1|23	NUM
ap-7656	175	18	2	2	NUM
ap-7656	175	19	(	(	PUNCT
ap-7656	175	20	|φi⟩⟨φi|)∥tr	|φi⟩⟨φi|)∥tr	NUM
ap-7656	175	21	,	,	PUNCT
ap-7656	175	22	namely	namely	ADV
ap-7656	175	23	,	,	PUNCT
ap-7656	175	24	∥t	∥t	PROPN
ap-7656	175	25	1|23	1|23	NUM
ap-7656	175	26	1	1	NUM
ap-7656	175	27	(	(	PUNCT
ap-7656	175	28	ρ	ρ	NOUN
ap-7656	175	29	)	)	PUNCT
ap-7656	175	30	−	−	PROPN
ap-7656	176	1	t	t	NOUN
ap-7656	176	2	1|23	1|23	NUM
ap-7656	176	3	2	2	NUM
ap-7656	176	4	(	(	PUNCT
ap-7656	176	5	ρ)∥tr	ρ)∥tr	NOUN
ap-7656	176	6	≤	≤	NOUN
ap-7656	176	7	√	√	NUM
ap-7656	176	8	6	6	NUM
ap-7656	176	9	.	.	PUNCT
ap-7656	177	1	(	(	PUNCT
ap-7656	177	2	2	2	X
ap-7656	177	3	)	)	PUNCT
ap-7656	177	4	if	if	SCONJ
ap-7656	177	5	ρ	ρ	NUM
ap-7656	177	6	=	=	SYM
ap-7656	177	7	|φ⟩⟨φ|	|φ⟩⟨φ|	PROPN
ap-7656	177	8	is	be	AUX
ap-7656	177	9	2|13	2|13	VERB
ap-7656	177	10	separable	separable	ADJ
ap-7656	177	11	,	,	PUNCT
ap-7656	177	12	we	we	PRON
ap-7656	177	13	have	have	VERB
ap-7656	177	14	|φ2|13⟩	|φ2|13⟩	NUM
ap-7656	178	1	=	=	SYM
ap-7656	178	2	|φ2⟩	|φ2⟩	PROPN
ap-7656	178	3	⊗	⊗	PROPN
ap-7656	178	4	|φ13⟩	|φ13⟩	PROPN
ap-7656	178	5	∈	∈	PROPN
ap-7656	178	6	h2	h2	NOUN
ap-7656	178	7	2	2	NUM
ap-7656	178	8	⊗	⊗	PROPN
ap-7656	178	9	h6	h6	PROPN
ap-7656	178	10	13	13	NUM
ap-7656	178	11	,	,	PUNCT
ap-7656	178	12	where	where	SCONJ
ap-7656	178	13	h6	h6	PROPN
ap-7656	178	14	13	13	NUM
ap-7656	178	15	=	=	SYM
ap-7656	178	16	h2	h2	PROPN
ap-7656	178	17	1	1	NUM
ap-7656	178	18	⊗	⊗	PROPN
ap-7656	178	19	h3	h3	NOUN
ap-7656	178	20	3	3	NUM
ap-7656	178	21	.	.	PUNCT
ap-7656	179	1	then	then	ADV
ap-7656	179	2	by	by	ADP
ap-7656	179	3	schmidt	schmidt	ADJ
ap-7656	179	4	decomposition	decomposition	NOUN
ap-7656	179	5	,	,	PUNCT
ap-7656	179	6	one	one	PRON
ap-7656	179	7	has	have	VERB
ap-7656	179	8	|φ2|13⟩	|φ2|13⟩	NUM
ap-7656	179	9	=	=	SYM
ap-7656	179	10	t0|0α⟩+t1|1β⟩	t0|0α⟩+t1|1β⟩	PROPN
ap-7656	179	11	,	,	PUNCT
ap-7656	179	12	where	where	SCONJ
ap-7656	179	13	t20	t20	VERB
ap-7656	179	14	+	+	NOUN
ap-7656	179	15	t21	t21	NOUN
ap-7656	179	16	=	=	SYM
ap-7656	179	17	1	1	X
ap-7656	179	18	.	.	X
ap-7656	179	19	taking	take	VERB
ap-7656	179	20	into	into	ADP
ap-7656	179	21	account	account	NOUN
ap-7656	179	22	the	the	DET
ap-7656	179	23	local	local	ADJ
ap-7656	179	24	unitary	unitary	ADJ
ap-7656	179	25	equivalence	equivalence	NOUN
ap-7656	179	26	in	in	ADP
ap-7656	179	27	h2	h2	PROPN
ap-7656	179	28	1	1	NUM
ap-7656	180	1	⊗h3	⊗h3	NUM
ap-7656	180	2	3	3	NUM
ap-7656	180	3	,	,	PUNCT
ap-7656	180	4	we	we	PRON
ap-7656	180	5	obtain	obtain	VERB
ap-7656	180	6	a	a	DET
ap-7656	180	7	similar	similar	ADJ
ap-7656	180	8	equation	equation	NOUN
ap-7656	180	9	of	of	ADP
ap-7656	180	10	(	(	PUNCT
ap-7656	180	11	9	9	NUM
ap-7656	180	12	)	)	PUNCT
ap-7656	180	13	.	.	PUNCT
ap-7656	181	1	thus	thus	ADV
ap-7656	181	2	we	we	PRON
ap-7656	181	3	only	only	ADV
ap-7656	181	4	need	need	VERB
ap-7656	181	5	to	to	PART
ap-7656	181	6	consider	consider	VERB
ap-7656	181	7	again	again	ADV
ap-7656	181	8	the	the	DET
ap-7656	181	9	two	two	NUM
ap-7656	181	10	cases	case	NOUN
ap-7656	181	11	(	(	PUNCT
ap-7656	181	12	i	i	NOUN
ap-7656	181	13	)	)	PUNCT
ap-7656	181	14	{	{	PUNCT
ap-7656	181	15	|α⟩	|α⟩	NOUN
ap-7656	181	16	,	,	PUNCT
ap-7656	181	17	|β⟩	|β⟩	PROPN
ap-7656	181	18	}	}	PUNCT
ap-7656	181	19	=	=	SYM
ap-7656	181	20	{	{	PUNCT
ap-7656	181	21	|00⟩	|00⟩	NOUN
ap-7656	181	22	,	,	PUNCT
ap-7656	181	23	|01⟩	|01⟩	ADJ
ap-7656	181	24	}	}	PUNCT
ap-7656	181	25	and	and	CCONJ
ap-7656	181	26	(	(	PUNCT
ap-7656	181	27	ii	ii	NOUN
ap-7656	181	28	)	)	PUNCT
ap-7656	181	29	{	{	PUNCT
ap-7656	181	30	|00⟩	|00⟩	NOUN
ap-7656	181	31	,	,	PUNCT
ap-7656	181	32	|11⟩	|11⟩	NOUN
ap-7656	181	33	}	}	PUNCT
ap-7656	181	34	.	.	PUNCT
ap-7656	182	1	in	in	ADP
ap-7656	182	2	the	the	DET
ap-7656	182	3	first	first	ADJ
ap-7656	182	4	case	case	NOUN
ap-7656	182	5	,	,	PUNCT
ap-7656	182	6	|φ2|13⟩	|φ2|13⟩	PROPN
ap-7656	182	7	=	=	SYM
ap-7656	182	8	t0|000⟩	t0|000⟩	NOUN
ap-7656	182	9	+	+	NOUN
ap-7656	182	10	t1|101⟩	t1|101⟩	NUM
ap-7656	182	11	,	,	PUNCT
ap-7656	182	12	and	and	CCONJ
ap-7656	182	13	t	t	PROPN
ap-7656	182	14	2|13	2|13	VERB
ap-7656	182	15	1	1	NUM
ap-7656	182	16	and	and	CCONJ
ap-7656	182	17	t	t	PROPN
ap-7656	182	18	2|13	2|13	ADJ
ap-7656	182	19	2	2	NUM
ap-7656	182	20	are	be	AUX
ap-7656	182	21	zero	zero	NUM
ap-7656	182	22	matrices	matrix	NOUN
ap-7656	182	23	.	.	PUNCT
ap-7656	183	1	in	in	ADP
ap-7656	183	2	the	the	DET
ap-7656	183	3	second	second	ADJ
ap-7656	183	4	case	case	NOUN
ap-7656	183	5	,	,	PUNCT
ap-7656	183	6	|φ2|13⟩	|φ2|13⟩	PROPN
ap-7656	183	7	=	=	SYM
ap-7656	183	8	t0|000⟩	t0|000⟩	NOUN
ap-7656	183	9	+	+	CCONJ
ap-7656	183	10	t1|111⟩	t1|111⟩	NOUN
ap-7656	183	11	,	,	PUNCT
ap-7656	183	12	with	with	ADP
ap-7656	183	13	t	t	NOUN
ap-7656	183	14	2|13	2|13	VERB
ap-7656	183	15	1	1	NUM
ap-7656	183	16	and	and	CCONJ
ap-7656	183	17	t	t	PROPN
ap-7656	183	18	2|13	2|13	VERB
ap-7656	183	19	2	2	NUM
ap-7656	183	20	given	give	VERB
ap-7656	183	21	by	by	ADP
ap-7656	183	22	t	t	NOUN
ap-7656	183	23	2|13	2|13	ADJ
ap-7656	183	24	1	1	NUM
ap-7656	183	25	=	=	NUM
ap-7656	183	26			NOUN
ap-7656	183	27	t0t1	t0t1	X
ap-7656	183	28	0	0	NUM
ap-7656	183	29	t0t1	t0t1	PROPN
ap-7656	183	30	t0t1	t0t1	X
ap-7656	183	31	0	0	PUNCT
ap-7656	183	32	−t0t1	−t0t1	PROPN
ap-7656	183	33	0	0	NUM
ap-7656	183	34	0	0	SYM
ap-7656	183	35	0	0	NUM
ap-7656	184	1	t0t1	t0t1	X
ap-7656	184	2	0	0	NUM
ap-7656	184	3	t0t1	t0t1	X
ap-7656	184	4	t0t1ω	t0t1ω	NUM
ap-7656	184	5	2	2	NUM
ap-7656	184	6	0	0	NUM
ap-7656	184	7	−t0t1ω2	−t0t1ω2	CCONJ
ap-7656	184	8	0	0	NUM
ap-7656	184	9	0	0	NUM
ap-7656	184	10	0	0	NUM
ap-7656	185	1	t0t1	t0t1	X
ap-7656	185	2	0	0	NUM
ap-7656	185	3	t0t1	t0t1	X
ap-7656	185	4	t0t1ω	t0t1ω	X
ap-7656	185	5	0	0	NUM
ap-7656	186	1	−t0t1ω	−t0t1ω	NOUN
ap-7656	186	2			PROPN
ap-7656	186	3	t	t	NOUN
ap-7656	186	4	,	,	PUNCT
ap-7656	186	5	(	(	PUNCT
ap-7656	186	6	14	14	NUM
ap-7656	186	7	)	)	PUNCT
ap-7656	186	8	225	225	NUM
ap-7656	186	9	h.	h.	PROPN
ap-7656	186	10	zhao	zhao	PROPN
ap-7656	186	11	,	,	PUNCT
ap-7656	186	12	y.-q	y.-q	PROPN
ap-7656	186	13	.	.	PUNCT
ap-7656	187	1	liu	liu	PROPN
ap-7656	187	2	,	,	PUNCT
ap-7656	187	3	z.-x	z.-x	PROPN
ap-7656	187	4	.	.	PUNCT
ap-7656	188	1	wang	wang	PROPN
ap-7656	188	2	,	,	PUNCT
ap-7656	188	3	s.-m	s.-m	PROPN
ap-7656	188	4	.	.	PUNCT
ap-7656	189	1	fei	fei	PROPN
ap-7656	189	2	acta	acta	PROPN
ap-7656	189	3	polytechnica	polytechnica	PROPN
ap-7656	189	4	t	t	PROPN
ap-7656	189	5	2|13	2|13	ADJ
ap-7656	189	6	2	2	NUM
ap-7656	189	7	=	=	NUM
ap-7656	189	8			NOUN
ap-7656	189	9	t0t1	t0t1	X
ap-7656	189	10	0	0	X
ap-7656	189	11	t0t1	t0t1	X
ap-7656	189	12	−t0t1	−t0t1	PROPN
ap-7656	189	13	0	0	NUM
ap-7656	189	14	t0t1	t0t1	NOUN
ap-7656	189	15	0	0	NUM
ap-7656	189	16	0	0	SYM
ap-7656	189	17	0	0	NUM
ap-7656	189	18	t0t1	t0t1	X
ap-7656	189	19	0	0	PUNCT
ap-7656	189	20	t0t1	t0t1	X
ap-7656	189	21	−t0t1ω2	−t0t1ω2	X
ap-7656	189	22	0	0	PUNCT
ap-7656	189	23	t0t1ω	t0t1ω	NUM
ap-7656	189	24	2	2	NUM
ap-7656	189	25	0	0	NUM
ap-7656	189	26	0	0	NUM
ap-7656	189	27	0	0	NUM
ap-7656	189	28	t0t1	t0t1	X
ap-7656	189	29	0	0	PUNCT
ap-7656	189	30	t0t1	t0t1	X
ap-7656	189	31	−t0t1ω	−t0t1ω	VERB
ap-7656	189	32	0	0	PUNCT
ap-7656	189	33	t0t1ω	t0t1ω	NUM
ap-7656	189	34			PROPN
ap-7656	189	35	t	t	NOUN
ap-7656	189	36	.	.	PUNCT
ap-7656	190	1	(	(	PUNCT
ap-7656	190	2	15	15	NUM
ap-7656	190	3	)	)	PUNCT
ap-7656	190	4	then	then	ADV
ap-7656	190	5	we	we	PRON
ap-7656	190	6	have	have	VERB
ap-7656	190	7	∥t	∥t	ADJ
ap-7656	190	8	2|13	2|13	ADJ
ap-7656	190	9	1	1	NUM
ap-7656	190	10	−	−	NOUN
ap-7656	190	11	t	t	NOUN
ap-7656	190	12	2|13	2|13	VERB
ap-7656	190	13	2	2	NUM
ap-7656	190	14	∥tr	∥tr	NOUN
ap-7656	190	15	=	=	PRON
ap-7656	190	16	tr	tr	VERB
ap-7656	190	17	√	√	PROPN
ap-7656	190	18	(	(	PUNCT
ap-7656	190	19	t	t	NOUN
ap-7656	190	20	2|13	2|13	VERB
ap-7656	190	21	1	1	NUM
ap-7656	190	22	−	−	NOUN
ap-7656	190	23	t	t	NOUN
ap-7656	190	24	2|13	2|13	VERB
ap-7656	190	25	2	2	NUM
ap-7656	190	26	)	)	PUNCT
ap-7656	190	27	(	(	PUNCT
ap-7656	190	28	t	t	NOUN
ap-7656	190	29	2|13	2|13	VERB
ap-7656	190	30	1	1	NUM
ap-7656	190	31	−	−	NOUN
ap-7656	190	32	t	t	NOUN
ap-7656	190	33	2|13	2|13	VERB
ap-7656	190	34	2	2	NUM
ap-7656	190	35	)	)	PUNCT
ap-7656	190	36	†	†	NOUN
ap-7656	190	37	=	=	PUNCT
ap-7656	190	38	√	√	PROPN
ap-7656	190	39	24t20t21	24t20t21	NUM
ap-7656	190	40	≤	≤	NUM
ap-7656	191	1	√	√	ADP
ap-7656	191	2	6	6	NUM
ap-7656	191	3	.	.	PUNCT
ap-7656	192	1	for	for	ADP
ap-7656	192	2	the	the	DET
ap-7656	192	3	mixed	mixed	ADJ
ap-7656	192	4	state	state	NOUN
ap-7656	192	5	ρ	ρ	PROPN
ap-7656	192	6	=	=	SYM
ap-7656	192	7	∑	∑	PUNCT
ap-7656	192	8	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	192	9	,	,	PUNCT
ap-7656	192	10	we	we	PRON
ap-7656	192	11	have	have	VERB
ap-7656	192	12	∥t	∥t	ADJ
ap-7656	192	13	2|13	2|13	ADJ
ap-7656	192	14	1	1	NUM
ap-7656	192	15	(	(	PUNCT
ap-7656	192	16	ρ	ρ	NOUN
ap-7656	192	17	)	)	PUNCT
ap-7656	192	18	−	−	PROPN
ap-7656	192	19	t	t	NOUN
ap-7656	192	20	2|13	2|13	ADJ
ap-7656	192	21	2	2	NUM
ap-7656	192	22	(	(	PUNCT
ap-7656	192	23	ρ)∥tr	ρ)∥tr	NOUN
ap-7656	192	24	=	=	SYM
ap-7656	192	25	∥t	∥t	PROPN
ap-7656	192	26	2|13	2|13	ADJ
ap-7656	192	27	1	1	NUM
ap-7656	192	28	(	(	PUNCT
ap-7656	192	29	∑	∑	ADV
ap-7656	192	30	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	192	31	)	)	PUNCT
ap-7656	192	32	−	−	PROPN
ap-7656	192	33	t	t	NOUN
ap-7656	192	34	2|13	2|13	ADJ
ap-7656	192	35	2	2	NUM
ap-7656	192	36	(	(	PUNCT
ap-7656	192	37	∑	∑	PUNCT
ap-7656	192	38	pi|φi⟩⟨φi|)∥tr	pi|φi⟩⟨φi|)∥tr	PROPN
ap-7656	192	39	≤	≤	NOUN
ap-7656	192	40	∑	∑	PUNCT
ap-7656	192	41	pi∥t	pi∥t	NOUN
ap-7656	192	42	2|13	2|13	VERB
ap-7656	192	43	1	1	NUM
ap-7656	192	44	(	(	PUNCT
ap-7656	192	45	|φi⟩⟨φi|	|φi⟩⟨φi|	NOUN
ap-7656	192	46	)	)	PUNCT
ap-7656	192	47	−	−	PROPN
ap-7656	192	48	t	t	NOUN
ap-7656	192	49	2|13	2|13	ADJ
ap-7656	192	50	2	2	NUM
ap-7656	192	51	(	(	PUNCT
ap-7656	192	52	|φi⟩⟨φi|)∥tr	|φi⟩⟨φi|)∥tr	X
ap-7656	192	53	≤	≤	NOUN
ap-7656	192	54	√	√	NUM
ap-7656	192	55	6	6	NUM
ap-7656	192	56	.	.	PUNCT
ap-7656	193	1	(	(	PUNCT
ap-7656	193	2	3	3	X
ap-7656	193	3	)	)	PUNCT
ap-7656	193	4	if	if	SCONJ
ap-7656	193	5	ρ	ρ	NUM
ap-7656	193	6	=	=	SYM
ap-7656	193	7	|φ⟩⟨φ|	|φ⟩⟨φ|	PROPN
ap-7656	193	8	is	be	AUX
ap-7656	193	9	3|12	3|12	NUM
ap-7656	193	10	separable	separable	NOUN
ap-7656	193	11	,	,	PUNCT
ap-7656	193	12	we	we	PRON
ap-7656	193	13	have	have	VERB
ap-7656	193	14	|φ3|12⟩	|φ3|12⟩	NOUN
ap-7656	193	15	=	=	SYM
ap-7656	193	16	|φ3⟩⊗|φ12⟩	|φ3⟩⊗|φ12⟩	ADP
ap-7656	193	17	∈	∈	PROPN
ap-7656	193	18	h3	h3	NOUN
ap-7656	193	19	3	3	NUM
ap-7656	193	20	⊗h4	⊗h4	PROPN
ap-7656	193	21	12	12	NUM
ap-7656	193	22	,	,	PUNCT
ap-7656	193	23	where	where	SCONJ
ap-7656	193	24	h4	h4	PROPN
ap-7656	193	25	12	12	NUM
ap-7656	193	26	=	=	SYM
ap-7656	193	27	h2	h2	NOUN
ap-7656	193	28	1	1	NUM
ap-7656	193	29	⊗h2	⊗h2	PROPN
ap-7656	193	30	2	2	NUM
ap-7656	193	31	.	.	PUNCT
ap-7656	194	1	then	then	ADV
ap-7656	194	2	by	by	ADP
ap-7656	194	3	schmidt	schmidt	ADJ
ap-7656	194	4	decomposition	decomposition	NOUN
ap-7656	194	5	,	,	PUNCT
ap-7656	194	6	we	we	PRON
ap-7656	194	7	have	have	VERB
ap-7656	194	8	|φ3|12⟩	|φ3|12⟩	NOUN
ap-7656	194	9	=	=	NOUN
ap-7656	194	10	t0|0α0⟩+	t0|0α0⟩+	NOUN
ap-7656	195	1	t1|1α1⟩	t1|1α1⟩	PROPN
ap-7656	195	2	+	+	CCONJ
ap-7656	195	3	t2|2α2⟩	t2|2α2⟩	PROPN
ap-7656	195	4	,	,	PUNCT
ap-7656	195	5	where	where	SCONJ
ap-7656	195	6	t20	t20	VERB
ap-7656	195	7	+	+	CCONJ
ap-7656	195	8	t21	t21	NOUN
ap-7656	195	9	+	+	CCONJ
ap-7656	195	10	t22	t22	X
ap-7656	195	11	=	=	SYM
ap-7656	195	12	1	1	X
ap-7656	195	13	.	.	X
ap-7656	196	1	taking	take	VERB
ap-7656	196	2	into	into	ADP
ap-7656	196	3	account	account	NOUN
ap-7656	196	4	the	the	DET
ap-7656	196	5	local	local	ADJ
ap-7656	196	6	unitary	unitary	ADJ
ap-7656	196	7	equivalence	equivalence	NOUN
ap-7656	196	8	in	in	ADP
ap-7656	196	9	h2	h2	PROPN
ap-7656	196	10	1	1	NUM
ap-7656	196	11	⊗	⊗	PROPN
ap-7656	196	12	h2	h2	PROPN
ap-7656	196	13	2	2	NUM
ap-7656	196	14	,	,	PUNCT
ap-7656	196	15	we	we	PRON
ap-7656	196	16	obtain	obtain	VERB
ap-7656	196	17	similar	similar	ADJ
ap-7656	196	18	equation	equation	NOUN
ap-7656	196	19	of	of	ADP
ap-7656	196	20	(	(	PUNCT
ap-7656	196	21	9	9	NUM
ap-7656	196	22	)	)	PUNCT
ap-7656	196	23	.	.	PUNCT
ap-7656	197	1	we	we	PRON
ap-7656	197	2	only	only	ADV
ap-7656	197	3	need	need	VERB
ap-7656	197	4	to	to	PART
ap-7656	197	5	consider	consider	VERB
ap-7656	197	6	the	the	DET
ap-7656	197	7	case	case	NOUN
ap-7656	197	8	|φ3|12⟩	|φ3|12⟩	NOUN
ap-7656	197	9	=	=	NOUN
ap-7656	197	10	t0|000⟩	t0|000⟩	NOUN
ap-7656	197	11	+	+	NOUN
ap-7656	197	12	t1|101⟩	t1|101⟩	NUM
ap-7656	198	1	+	+	CCONJ
ap-7656	198	2	t2|210⟩.	t2|210⟩.	ADV
ap-7656	198	3	we	we	PRON
ap-7656	198	4	have	have	VERB
ap-7656	198	5	t	t	X
ap-7656	198	6	3|12	3|12	NUM
ap-7656	198	7	1	1	NUM
ap-7656	198	8	=	=	SYM
ap-7656	198	9			NOUN
ap-7656	198	10	0	0	NUM
ap-7656	198	11	0	0	NUM
ap-7656	198	12	0	0	NUM
ap-7656	198	13	0	0	NUM
ap-7656	198	14	t20	t20	NOUN
ap-7656	198	15	−	−	PROPN
ap-7656	198	16	ωt21	ωt21	PROPN
ap-7656	198	17	+	+	CCONJ
ap-7656	198	18	ω2t22	ω2t22	X
ap-7656	198	19	0	0	NUM
ap-7656	198	20	0	0	NUM
ap-7656	198	21	0	0	NUM
ap-7656	198	22	0	0	NUM
ap-7656	198	23			NOUN
ap-7656	198	24	,	,	PUNCT
ap-7656	198	25	t	t	NOUN
ap-7656	198	26	3|12	3|12	NUM
ap-7656	198	27	2	2	NUM
ap-7656	198	28	=	=	SYM
ap-7656	198	29			NOUN
ap-7656	198	30	0	0	NUM
ap-7656	198	31	0	0	NUM
ap-7656	198	32	0	0	NUM
ap-7656	198	33	0	0	NUM
ap-7656	198	34	t20	t20	NOUN
ap-7656	198	35	−	−	PROPN
ap-7656	198	36	ω2t21	ω2t21	NOUN
ap-7656	198	37	+	+	CCONJ
ap-7656	199	1	ωt22	ωt22	PROPN
ap-7656	199	2	0	0	NUM
ap-7656	199	3	0	0	NUM
ap-7656	199	4	0	0	NUM
ap-7656	199	5	0	0	NUM
ap-7656	199	6			NOUN
ap-7656	199	7	.	.	PUNCT
ap-7656	200	1	(	(	PUNCT
ap-7656	200	2	16	16	NUM
ap-7656	200	3	)	)	PUNCT
ap-7656	200	4	using	use	VERB
ap-7656	200	5	1	1	NUM
ap-7656	200	6	+	+	NUM
ap-7656	200	7	ω	ω	NUM
ap-7656	200	8	+	+	CCONJ
ap-7656	200	9	ω2	ω2	ADJ
ap-7656	200	10	=	=	SYM
ap-7656	200	11	0	0	NUM
ap-7656	200	12	,	,	PUNCT
ap-7656	200	13	we	we	PRON
ap-7656	200	14	have	have	VERB
ap-7656	200	15	∥t	∥t	NUM
ap-7656	200	16	3|12	3|12	NUM
ap-7656	200	17	1	1	NUM
ap-7656	200	18	−	−	PROPN
ap-7656	201	1	t	t	NOUN
ap-7656	202	1	3|12	3|12	NUM
ap-7656	202	2	2	2	NUM
ap-7656	202	3	∥tr	∥tr	NOUN
ap-7656	202	4	=	=	PRON
ap-7656	202	5	tr	tr	VERB
ap-7656	202	6	√	√	PROPN
ap-7656	202	7	(	(	PUNCT
ap-7656	202	8	t	t	NOUN
ap-7656	202	9	3|12	3|12	NUM
ap-7656	202	10	1	1	NUM
ap-7656	202	11	−	−	PROPN
ap-7656	202	12	t	t	NOUN
ap-7656	202	13	3|12	3|12	NUM
ap-7656	202	14	2	2	NUM
ap-7656	202	15	)	)	PUNCT
ap-7656	202	16	(	(	PUNCT
ap-7656	202	17	t	t	NOUN
ap-7656	202	18	3|12	3|12	NUM
ap-7656	202	19	1	1	NUM
ap-7656	202	20	−	−	PROPN
ap-7656	202	21	t	t	NOUN
ap-7656	202	22	3|12	3|12	NUM
ap-7656	202	23	2	2	NUM
ap-7656	202	24	)	)	PUNCT
ap-7656	202	25	†	†	X
ap-7656	202	26	=	=	PUNCT
ap-7656	203	1	√	√	NUM
ap-7656	203	2	3(t20	3(t20	NUM
ap-7656	203	3	+	+	CCONJ
ap-7656	203	4	t21)2	t21)2	ADJ
ap-7656	203	5	≤	≤	NOUN
ap-7656	203	6	√	√	ADP
ap-7656	203	7	3	3	NUM
ap-7656	203	8	.	.	PUNCT
ap-7656	204	1	for	for	ADP
ap-7656	204	2	the	the	DET
ap-7656	204	3	mixed	mixed	ADJ
ap-7656	204	4	state	state	NOUN
ap-7656	204	5	ρ	ρ	PROPN
ap-7656	204	6	=	=	SYM
ap-7656	204	7	∑	∑	PUNCT
ap-7656	204	8	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	204	9	,	,	PUNCT
ap-7656	204	10	we	we	PRON
ap-7656	204	11	get	get	VERB
ap-7656	204	12	∥t	∥t	ADJ
ap-7656	204	13	3|12	3|12	NUM
ap-7656	204	14	1	1	NUM
ap-7656	204	15	(	(	PUNCT
ap-7656	204	16	ρ	ρ	NOUN
ap-7656	204	17	)	)	PUNCT
ap-7656	204	18	−	−	PROPN
ap-7656	204	19	t	t	NOUN
ap-7656	204	20	3|12	3|12	NUM
ap-7656	204	21	2	2	NUM
ap-7656	204	22	(	(	PUNCT
ap-7656	204	23	ρ)∥tr	ρ)∥tr	NOUN
ap-7656	204	24	=	=	NOUN
ap-7656	204	25	∥t	∥t	PROPN
ap-7656	204	26	3|12	3|12	NUM
ap-7656	204	27	1	1	NUM
ap-7656	204	28	(	(	PUNCT
ap-7656	204	29	∑	∑	ADV
ap-7656	204	30	pi|φi⟩⟨φi|	pi|φi⟩⟨φi|	NOUN
ap-7656	204	31	)	)	PUNCT
ap-7656	205	1	−	−	PROPN
ap-7656	205	2	t	t	NOUN
ap-7656	205	3	3|12	3|12	NUM
ap-7656	205	4	2	2	NUM
ap-7656	205	5	(	(	PUNCT
ap-7656	205	6	∑	∑	PUNCT
ap-7656	205	7	pi|φi⟩⟨φi|)∥tr	pi|φi⟩⟨φi|)∥tr	PROPN
ap-7656	205	8	≤	≤	NOUN
ap-7656	205	9	∑	∑	PUNCT
ap-7656	205	10	pi∥t	pi∥t	NOUN
ap-7656	205	11	3|12	3|12	NUM
ap-7656	205	12	1	1	NUM
ap-7656	205	13	(	(	PUNCT
ap-7656	205	14	|φi⟩⟨φi|	|φi⟩⟨φi|	NOUN
ap-7656	205	15	)	)	PUNCT
ap-7656	205	16	−	−	PROPN
ap-7656	205	17	t	t	NOUN
ap-7656	205	18	3|12	3|12	NUM
ap-7656	205	19	2	2	NUM
ap-7656	205	20	(	(	PUNCT
ap-7656	205	21	|φi⟩⟨φi|)∥tr	|φi⟩⟨φi|)∥tr	X
ap-7656	205	22	≤	≤	NOUN
ap-7656	205	23	√	√	NUM
ap-7656	205	24	3	3	NUM
ap-7656	205	25	.	.	PUNCT
ap-7656	206	1	as	as	ADP
ap-7656	206	2	an	an	DET
ap-7656	206	3	example	example	NOUN
ap-7656	206	4	,	,	PUNCT
ap-7656	206	5	let	let	VERB
ap-7656	206	6	us	we	PRON
ap-7656	206	7	consider	consider	VERB
ap-7656	206	8	the	the	DET
ap-7656	206	9	2	2	NUM
ap-7656	206	10	⊗	⊗	NUM
ap-7656	206	11	2	2	NUM
ap-7656	206	12	⊗	⊗	PROPN
ap-7656	206	13	3	3	NUM
ap-7656	206	14	state	state	NOUN
ap-7656	206	15	,	,	PUNCT
ap-7656	206	16	ρ	ρ	PROPN
ap-7656	206	17	=	=	PUNCT
ap-7656	206	18	x|ghz	x|ghz	PROPN
ap-7656	206	19	′⟩⟨ghz	′⟩⟨ghz	VERB
ap-7656	206	20	′|	′|	NUM
ap-7656	206	21	+	+	CCONJ
ap-7656	206	22	(	(	PUNCT
ap-7656	206	23	1	1	NUM
ap-7656	206	24	−	−	PROPN
ap-7656	206	25	x)i12	x)i12	PROPN
ap-7656	206	26	,	,	PUNCT
ap-7656	206	27	0	0	NUM
ap-7656	206	28	≤	≤	NUM
ap-7656	206	29	x	x	SYM
ap-7656	206	30	≤	≤	NUM
ap-7656	206	31	1	1	NUM
ap-7656	206	32	,	,	PUNCT
ap-7656	206	33	where	where	SCONJ
ap-7656	206	34	|ghz	|ghz	VERB
ap-7656	206	35	′⟩	′⟩	NOUN
ap-7656	206	36	=	=	NOUN
ap-7656	206	37	1	1	NUM
ap-7656	206	38	2	2	NUM
ap-7656	206	39	(	(	PUNCT
ap-7656	206	40	|000⟩	|000⟩	NOUN
ap-7656	206	41	+	+	X
ap-7656	206	42	|101⟩	|101⟩	PRON
ap-7656	206	43	+	+	CCONJ
ap-7656	206	44	|011⟩	|011⟩	NOUN
ap-7656	206	45	+	+	CCONJ
ap-7656	206	46	|112⟩	|112⟩	NOUN
ap-7656	206	47	)	)	PUNCT
ap-7656	206	48	.	.	PUNCT
ap-7656	207	1	by	by	ADP
ap-7656	207	2	theorem	theorem	NOUN
ap-7656	207	3	4	4	NUM
ap-7656	207	4	,	,	PUNCT
ap-7656	207	5	we	we	PRON
ap-7656	207	6	have	have	VERB
ap-7656	207	7	that	that	PRON
ap-7656	207	8	when	when	SCONJ
ap-7656	207	9	∥t	∥t	PROPN
ap-7656	207	10	1|23	1|23	NUM
ap-7656	207	11	1	1	NUM
ap-7656	207	12	−	−	PROPN
ap-7656	207	13	t	t	NOUN
ap-7656	207	14	1|23	1|23	NUM
ap-7656	207	15	2	2	NUM
ap-7656	207	16	∥	∥	NUM
ap-7656	207	17	=	=	SYM
ap-7656	207	18	(	(	PUNCT
ap-7656	207	19	2	2	NUM
ap-7656	207	20	√	√	NUM
ap-7656	207	21	3	3	NUM
ap-7656	207	22	2	2	NUM
ap-7656	207	23	+	+	NUM
ap-7656	207	24	1)x	1)x	NUM
ap-7656	207	25	>	>	SYM
ap-7656	207	26	√	√	NUM
ap-7656	207	27	3	3	NUM
ap-7656	207	28	,	,	PUNCT
ap-7656	207	29	i.e.	i.e.	X
ap-7656	207	30	,	,	PUNCT
ap-7656	207	31	0.5021	0.5021	NUM
ap-7656	207	32	<	<	X
ap-7656	207	33	x	x	SYM
ap-7656	207	34	≤	≤	NUM
ap-7656	207	35	1	1	NUM
ap-7656	207	36	,	,	PUNCT
ap-7656	207	37	ρ	ρ	PROPN
ap-7656	207	38	is	be	AUX
ap-7656	207	39	not	not	PART
ap-7656	207	40	fully	fully	ADV
ap-7656	207	41	separable	separable	ADJ
ap-7656	207	42	.	.	PUNCT
ap-7656	208	1	by	by	ADP
ap-7656	208	2	theorem	theorem	NOUN
ap-7656	208	3	5	5	NUM
ap-7656	208	4	,	,	PUNCT
ap-7656	208	5	when	when	SCONJ
ap-7656	208	6	∥t	∥t	PROPN
ap-7656	208	7	1|23	1|23	NUM
ap-7656	208	8	1	1	NUM
ap-7656	208	9	−	−	PROPN
ap-7656	208	10	t	t	NOUN
ap-7656	208	11	1|23	1|23	NUM
ap-7656	208	12	2	2	NUM
ap-7656	208	13	∥	∥	NOUN
ap-7656	208	14	=	=	SYM
ap-7656	208	15	∥t	∥t	PROPN
ap-7656	208	16	2|13	2|13	ADJ
ap-7656	208	17	1	1	NUM
ap-7656	208	18	−	−	NOUN
ap-7656	208	19	t	t	NOUN
ap-7656	208	20	2|13	2|13	VERB
ap-7656	208	21	2	2	NUM
ap-7656	208	22	∥	∥	NUM
ap-7656	208	23	=	=	SYM
ap-7656	208	24	(	(	PUNCT
ap-7656	208	25	2	2	NUM
ap-7656	208	26	√	√	NUM
ap-7656	208	27	3	3	NUM
ap-7656	208	28	2	2	NUM
ap-7656	208	29	+	+	NUM
ap-7656	208	30	1)x	1)x	NUM
ap-7656	208	31	>	>	SYM
ap-7656	208	32	√	√	NUM
ap-7656	208	33	6	6	NUM
ap-7656	208	34	,	,	PUNCT
ap-7656	208	35	i.e.	i.e.	X
ap-7656	208	36	,	,	PUNCT
ap-7656	208	37	0.7101	0.7101	PRON
ap-7656	208	38	<	<	X
ap-7656	208	39	x	x	SYM
ap-7656	208	40	≤	≤	NUM
ap-7656	208	41	1	1	NUM
ap-7656	208	42	,	,	PUNCT
ap-7656	208	43	ρ	ρ	PROPN
ap-7656	208	44	is	be	AUX
ap-7656	208	45	not	not	PART
ap-7656	208	46	separable	separable	ADJ
ap-7656	208	47	under	under	ADP
ap-7656	208	48	bipartition	bipartition	NOUN
ap-7656	208	49	1|23	1|23	NUM
ap-7656	208	50	or	or	CCONJ
ap-7656	208	51	2|13	2|13	ADJ
ap-7656	208	52	.	.	PUNCT
ap-7656	209	1	when	when	SCONJ
ap-7656	209	2	∥t	∥t	ADJ
ap-7656	209	3	3|12	3|12	NUM
ap-7656	209	4	1	1	NUM
ap-7656	209	5	−	−	NOUN
ap-7656	209	6	t	t	NOUN
ap-7656	209	7	3|12	3|12	NUM
ap-7656	209	8	2	2	NUM
ap-7656	209	9	∥	∥	X
ap-7656	209	10	=	=	SYM
ap-7656	209	11	7	7	NUM
ap-7656	209	12	√	√	NUM
ap-7656	209	13	3	3	NUM
ap-7656	209	14	4	4	NUM
ap-7656	209	15	x	x	SYM
ap-7656	209	16	>	>	X
ap-7656	209	17	√	√	NUM
ap-7656	209	18	3	3	NUM
ap-7656	209	19	,	,	PUNCT
ap-7656	209	20	i.e.	i.e.	X
ap-7656	209	21	,	,	PUNCT
ap-7656	209	22	0.5714	0.5714	NUM
ap-7656	209	23	<	<	X
ap-7656	209	24	x	x	SYM
ap-7656	209	25	≤	≤	NUM
ap-7656	209	26	1	1	NUM
ap-7656	209	27	,	,	PUNCT
ap-7656	209	28	ρ	ρ	PROPN
ap-7656	209	29	is	be	AUX
ap-7656	209	30	not	not	PART
ap-7656	209	31	separable	separable	ADJ
ap-7656	209	32	under	under	ADP
ap-7656	209	33	bipartition	bipartition	NOUN
ap-7656	209	34	3|12	3|12	NUM
ap-7656	209	35	.	.	PUNCT
ap-7656	210	1	4	4	X
ap-7656	210	2	.	.	X
ap-7656	210	3	conclusions	conclusion	NOUN
ap-7656	210	4	we	we	PRON
ap-7656	210	5	have	have	AUX
ap-7656	210	6	presented	present	VERB
ap-7656	210	7	quantum	quantum	ADJ
ap-7656	210	8	upper	upper	ADJ
ap-7656	210	9	bounds	bound	NOUN
ap-7656	210	10	for	for	ADP
ap-7656	210	11	triqutrit	triqutrit	NOUN
ap-7656	210	12	mixed	mix	VERB
ap-7656	210	13	states	state	NOUN
ap-7656	210	14	by	by	ADP
ap-7656	210	15	using	use	VERB
ap-7656	210	16	the	the	DET
ap-7656	210	17	generalized	generalized	ADJ
ap-7656	210	18	bell	bell	NOUN
ap-7656	210	19	functions	function	NOUN
ap-7656	210	20	and	and	CCONJ
ap-7656	210	21	the	the	DET
ap-7656	210	22	generalized	generalized	ADJ
ap-7656	210	23	three	three	NUM
ap-7656	210	24	dimensional	dimensional	ADJ
ap-7656	210	25	pauli	pauli	PROPN
ap-7656	210	26	operators	operator	NOUN
ap-7656	210	27	,	,	PUNCT
ap-7656	210	28	from	from	ADP
ap-7656	210	29	which	which	PRON
ap-7656	210	30	the	the	DET
ap-7656	210	31	triqutrit	triqutrit	NOUN
ap-7656	210	32	entanglement	entanglement	NOUN
ap-7656	210	33	has	have	AUX
ap-7656	210	34	been	be	AUX
ap-7656	210	35	identified	identify	VERB
ap-7656	210	36	.	.	PUNCT
ap-7656	211	1	our	our	PRON
ap-7656	211	2	inequalities	inequality	NOUN
ap-7656	211	3	distinguish	distinguish	VERB
ap-7656	211	4	fully	fully	ADV
ap-7656	211	5	separable	separable	ADJ
ap-7656	211	6	states	state	NOUN
ap-7656	211	7	and	and	CCONJ
ap-7656	211	8	three	three	NUM
ap-7656	211	9	types	type	NOUN
ap-7656	211	10	of	of	ADP
ap-7656	211	11	bi	bi	ADJ
ap-7656	211	12	-	-	ADJ
ap-7656	211	13	separable	separable	ADJ
ap-7656	211	14	states	state	NOUN
ap-7656	211	15	for	for	ADP
ap-7656	211	16	triqutrit	triqutrit	NOUN
ap-7656	211	17	states	state	NOUN
ap-7656	211	18	.	.	PUNCT
ap-7656	212	1	moreover	moreover	ADV
ap-7656	212	2	,	,	PUNCT
ap-7656	212	3	any	any	DET
ap-7656	212	4	triqutrits	triqutrit	NOUN
ap-7656	212	5	states	state	NOUN
ap-7656	212	6	are	be	AUX
ap-7656	212	7	confined	confine	VERB
ap-7656	212	8	in	in	ADP
ap-7656	212	9	a	a	DET
ap-7656	212	10	cube	cube	NOUN
ap-7656	212	11	with	with	ADP
ap-7656	212	12	size	size	NOUN
ap-7656	212	13	5	5	NUM
ap-7656	212	14	4	4	NUM
ap-7656	212	15	×	×	NOUN
ap-7656	212	16	5	5	NUM
ap-7656	212	17	4	4	NUM
ap-7656	212	18	×	×	NOUN
ap-7656	212	19	5	5	NUM
ap-7656	212	20	4	4	NUM
ap-7656	212	21	and	and	CCONJ
ap-7656	212	22	the	the	DET
ap-7656	212	23	biseparable	biseparable	ADJ
ap-7656	212	24	states	state	NOUN
ap-7656	212	25	are	be	AUX
ap-7656	212	26	in	in	ADP
ap-7656	212	27	a	a	DET
ap-7656	212	28	cube	cube	NOUN
ap-7656	212	29	with	with	ADP
ap-7656	212	30	the	the	DET
ap-7656	212	31	size	size	NOUN
ap-7656	212	32	3	3	NUM
ap-7656	212	33	4	4	NUM
ap-7656	212	34	×	×	NOUN
ap-7656	212	35	3	3	NUM
ap-7656	212	36	4	4	NUM
ap-7656	212	37	×	×	NOUN
ap-7656	212	38	3	3	NUM
ap-7656	212	39	4	4	NUM
ap-7656	212	40	.	.	PUNCT
ap-7656	213	1	we	we	PRON
ap-7656	213	2	have	have	AUX
ap-7656	213	3	also	also	ADV
ap-7656	213	4	studied	study	VERB
ap-7656	213	5	the	the	DET
ap-7656	213	6	classification	classification	NOUN
ap-7656	213	7	of	of	ADP
ap-7656	213	8	quantum	quantum	ADJ
ap-7656	213	9	entanglement	entanglement	NOUN
ap-7656	213	10	for	for	ADP
ap-7656	213	11	2	2	NUM
ap-7656	213	12	⊗	⊗	PROPN
ap-7656	213	13	2	2	NUM
ap-7656	213	14	⊗	⊗	PROPN
ap-7656	213	15	3	3	NUM
ap-7656	213	16	systems	system	NOUN
ap-7656	213	17	by	by	ADP
ap-7656	213	18	using	use	VERB
ap-7656	213	19	the	the	DET
ap-7656	213	20	correlation	correlation	NOUN
ap-7656	213	21	tensors	tensor	NOUN
ap-7656	213	22	in	in	ADP
ap-7656	213	23	the	the	DET
ap-7656	213	24	principal	principal	ADJ
ap-7656	213	25	basis	basis	NOUN
ap-7656	213	26	representation	representation	NOUN
ap-7656	213	27	of	of	ADP
ap-7656	213	28	density	density	NOUN
ap-7656	213	29	matrices	matrix	NOUN
ap-7656	213	30	.	.	PUNCT
ap-7656	214	1	by	by	ADP
ap-7656	214	2	considering	consider	VERB
ap-7656	214	3	the	the	DET
ap-7656	214	4	upper	upper	ADJ
ap-7656	214	5	bounds	bound	NOUN
ap-7656	214	6	on	on	ADP
ap-7656	214	7	some	some	DET
ap-7656	214	8	the	the	DET
ap-7656	214	9	trace	trace	NOUN
ap-7656	214	10	norms	norm	NOUN
ap-7656	214	11	,	,	PUNCT
ap-7656	214	12	we	we	PRON
ap-7656	214	13	have	have	AUX
ap-7656	214	14	obtained	obtain	VERB
ap-7656	214	15	the	the	DET
ap-7656	214	16	criteria	criterion	NOUN
ap-7656	214	17	which	which	PRON
ap-7656	214	18	detect	detect	VERB
ap-7656	214	19	fully	fully	ADV
ap-7656	214	20	separable	separable	ADJ
ap-7656	214	21	and	and	CCONJ
ap-7656	214	22	bi	bi	ADJ
ap-7656	214	23	-	-	ADJ
ap-7656	214	24	separable	separable	ADJ
ap-7656	214	25	2	2	NUM
ap-7656	214	26	⊗	⊗	PROPN
ap-7656	214	27	2	2	NUM
ap-7656	214	28	⊗	⊗	NUM
ap-7656	214	29	3	3	NUM
ap-7656	214	30	quantum	quantum	NOUN
ap-7656	214	31	mixed	mix	VERB
ap-7656	214	32	states	state	NOUN
ap-7656	214	33	.	.	PUNCT
ap-7656	215	1	detailed	detailed	ADJ
ap-7656	215	2	example	example	NOUN
ap-7656	215	3	has	have	AUX
ap-7656	215	4	been	be	AUX
ap-7656	215	5	given	give	VERB
ap-7656	215	6	to	to	PART
ap-7656	215	7	show	show	VERB
ap-7656	215	8	the	the	DET
ap-7656	215	9	classification	classification	NOUN
ap-7656	215	10	of	of	ADP
ap-7656	215	11	tripartite	tripartite	ADJ
ap-7656	215	12	entanglement	entanglement	NOUN
ap-7656	215	13	by	by	ADP
ap-7656	215	14	using	use	VERB
ap-7656	215	15	our	our	PRON
ap-7656	215	16	criteria	criterion	NOUN
ap-7656	215	17	.	.	PUNCT
ap-7656	216	1	acknowledgements	acknowledgement	NOUN
ap-7656	216	2	this	this	DET
ap-7656	216	3	work	work	NOUN
ap-7656	216	4	is	be	AUX
ap-7656	216	5	supported	support	VERB
ap-7656	216	6	by	by	ADP
ap-7656	216	7	the	the	DET
ap-7656	216	8	national	national	ADJ
ap-7656	216	9	natural	natural	PROPN
ap-7656	216	10	science	science	PROPN
ap-7656	216	11	foundation	foundation	PROPN
ap-7656	216	12	of	of	ADP
ap-7656	216	13	china	china	PROPN
ap-7656	216	14	under	under	ADP
ap-7656	216	15	grant	grant	PROPN
ap-7656	216	16	nos	nos	PROPN
ap-7656	216	17	.	.	PROPN
ap-7656	216	18	11101017	11101017	NUM
ap-7656	216	19	,	,	PUNCT
ap-7656	216	20	11531004	11531004	NUM
ap-7656	216	21	,	,	PUNCT
ap-7656	216	22	11726016	11726016	NUM
ap-7656	216	23	,	,	PUNCT
ap-7656	216	24	12075159	12075159	NUM
ap-7656	216	25	and	and	CCONJ
ap-7656	216	26	12171044	12171044	NUM
ap-7656	216	27	,	,	PUNCT
ap-7656	216	28	simons	simons	PROPN
ap-7656	216	29	foundation	foundation	PROPN
ap-7656	216	30	under	under	ADP
ap-7656	216	31	grant	grant	NOUN
ap-7656	216	32	no	no	NOUN
ap-7656	216	33	.	.	PROPN
ap-7656	216	34	523868	523868	NUM
ap-7656	216	35	,	,	PUNCT
ap-7656	216	36	beijing	beijing	PROPN
ap-7656	216	37	natural	natural	PROPN
ap-7656	216	38	science	science	PROPN
ap-7656	216	39	foundation	foundation	NOUN
ap-7656	216	40	(	(	PUNCT
ap-7656	216	41	z190005	z190005	NOUN
ap-7656	216	42	)	)	PUNCT
ap-7656	216	43	,	,	PUNCT
ap-7656	216	44	academy	academy	NOUN
ap-7656	216	45	for	for	ADP
ap-7656	216	46	multidisciplinary	multidisciplinary	ADJ
ap-7656	216	47	studies	study	NOUN
ap-7656	216	48	,	,	PUNCT
ap-7656	216	49	capital	capital	NOUN
ap-7656	216	50	normal	normal	ADJ
ap-7656	216	51	university	university	NOUN
ap-7656	216	52	,	,	PUNCT
ap-7656	216	53	shenzhen	shenzhen	PROPN
ap-7656	216	54	institute	institute	PROPN
ap-7656	216	55	for	for	ADP
ap-7656	216	56	quantum	quantum	NOUN
ap-7656	216	57	science	science	NOUN
ap-7656	216	58	and	and	CCONJ
ap-7656	216	59	engineering	engineering	NOUN
ap-7656	216	60	,	,	PUNCT
ap-7656	216	61	southern	southern	ADJ
ap-7656	216	62	university	university	PROPN
ap-7656	216	63	of	of	ADP
ap-7656	216	64	science	science	NOUN
ap-7656	216	65	and	and	CCONJ
ap-7656	216	66	technology	technology	NOUN
ap-7656	216	67	(	(	PUNCT
ap-7656	216	68	siqse202001	siqse202001	PROPN
ap-7656	216	69	)	)	PUNCT
ap-7656	216	70	,	,	PUNCT
ap-7656	216	71	and	and	CCONJ
ap-7656	216	72	the	the	DET
ap-7656	216	73	academician	academician	ADJ
ap-7656	216	74	innovation	innovation	NOUN
ap-7656	216	75	platform	platform	NOUN
ap-7656	216	76	of	of	ADP
ap-7656	216	77	hainan	hainan	PROPN
ap-7656	216	78	province	province	PROPN
ap-7656	216	79	.	.	PUNCT
ap-7656	217	1	references	reference	NOUN
ap-7656	217	2	[	[	X
ap-7656	217	3	1	1	NUM
ap-7656	217	4	]	]	PUNCT
ap-7656	217	5	a.	a.	NOUN
ap-7656	217	6	einstein	einstein	PROPN
ap-7656	217	7	,	,	PUNCT
ap-7656	217	8	b.	b.	PROPN
ap-7656	217	9	podolsky	podolsky	PROPN
ap-7656	217	10	,	,	PUNCT
ap-7656	217	11	n.	n.	PROPN
ap-7656	217	12	rosen	rosen	PROPN
ap-7656	217	13	.	.	PUNCT
ap-7656	218	1	can	can	AUX
ap-7656	218	2	quantum	quantum	ADJ
ap-7656	218	3	-	-	ADJ
ap-7656	218	4	mechanical	mechanical	ADJ
ap-7656	218	5	description	description	NOUN
ap-7656	218	6	of	of	ADP
ap-7656	218	7	physical	physical	ADJ
ap-7656	218	8	reality	reality	NOUN
ap-7656	218	9	be	be	AUX
ap-7656	218	10	considered	consider	VERB
ap-7656	218	11	complete	complete	ADJ
ap-7656	218	12	?	?	PUNCT
ap-7656	219	1	physical	physical	ADJ
ap-7656	219	2	review	review	PROPN
ap-7656	219	3	47(10):777–780	47(10):777–780	PROPN
ap-7656	219	4	,	,	PUNCT
ap-7656	219	5	1935	1935	NUM
ap-7656	219	6	.	.	PUNCT
ap-7656	220	1	https://doi.org/10.1103/physrev.47.777	https://doi.org/10.1103/physrev.47.777	NOUN
ap-7656	220	2	.	.	PUNCT
ap-7656	221	1	[	[	X
ap-7656	221	2	2	2	X
ap-7656	221	3	]	]	PUNCT
ap-7656	221	4	j.	j.	PROPN
ap-7656	221	5	s.	s.	PROPN
ap-7656	221	6	bell	bell	PROPN
ap-7656	221	7	.	.	PUNCT
ap-7656	222	1	on	on	ADP
ap-7656	222	2	the	the	DET
ap-7656	222	3	einstein	einstein	PROPN
ap-7656	222	4	podolsky	podolsky	PROPN
ap-7656	222	5	rosen	rosen	PROPN
ap-7656	222	6	paradox	paradox	PROPN
ap-7656	222	7	.	.	PUNCT
ap-7656	223	1	physics	physics	NOUN
ap-7656	223	2	1(3):195–200	1(3):195–200	NUM
ap-7656	223	3	,	,	PUNCT
ap-7656	223	4	1964	1964	NUM
ap-7656	223	5	.	.	PUNCT
ap-7656	224	1	https	https	NOUN
ap-7656	224	2	:	:	PUNCT
ap-7656	224	3	//doi.org/10.1103	//doi.org/10.1103	X
ap-7656	224	4	/	/	SYM
ap-7656	224	5	physicsphysiquefizika.1.195	physicsphysiquefizika.1.195	NOUN
ap-7656	224	6	.	.	PUNCT
ap-7656	225	1	[	[	X
ap-7656	225	2	3	3	X
ap-7656	225	3	]	]	PUNCT
ap-7656	225	4	j.	j.	PROPN
ap-7656	225	5	f.	f.	PROPN
ap-7656	225	6	clauser	clauser	PROPN
ap-7656	225	7	,	,	PUNCT
ap-7656	225	8	m.	m.	NOUN
ap-7656	225	9	a.	a.	PROPN
ap-7656	225	10	horne	horne	PROPN
ap-7656	225	11	,	,	PUNCT
ap-7656	225	12	a.	a.	NOUN
ap-7656	225	13	shimony	shimony	PROPN
ap-7656	225	14	,	,	PUNCT
ap-7656	225	15	r.	r.	PROPN
ap-7656	225	16	a.	a.	PROPN
ap-7656	225	17	holt	holt	PROPN
ap-7656	225	18	.	.	PUNCT
ap-7656	226	1	proposed	propose	VERB
ap-7656	226	2	experiment	experiment	NOUN
ap-7656	226	3	to	to	PART
ap-7656	226	4	test	test	VERB
ap-7656	226	5	local	local	ADJ
ap-7656	226	6	hidden	hide	VERB
ap-7656	226	7	-	-	PUNCT
ap-7656	226	8	variable	variable	ADJ
ap-7656	226	9	theories	theory	NOUN
ap-7656	226	10	.	.	PUNCT
ap-7656	227	1	physical	physical	ADJ
ap-7656	227	2	review	review	NOUN
ap-7656	227	3	letters	letter	NOUN
ap-7656	227	4	23(15):880–884	23(15):880–884	NUM
ap-7656	227	5	,	,	PUNCT
ap-7656	227	6	1969	1969	NUM
ap-7656	227	7	.	.	PUNCT
ap-7656	228	1	https://doi.org/10.1103/physrevlett.23.880	https://doi.org/10.1103/physrevlett.23.880	ADJ
ap-7656	228	2	.	.	PUNCT
ap-7656	229	1	[	[	X
ap-7656	229	2	4	4	X
ap-7656	229	3	]	]	PUNCT
ap-7656	229	4	p.	p.	NOUN
ap-7656	229	5	y.	y.	PROPN
ap-7656	229	6	chang	chang	PROPN
ap-7656	229	7	,	,	PUNCT
ap-7656	229	8	s.	s.	PROPN
ap-7656	229	9	k.	k.	PROPN
ap-7656	229	10	chu	chu	PROPN
ap-7656	229	11	,	,	PUNCT
ap-7656	230	1	c.	c.	PROPN
ap-7656	230	2	t.	t.	PROPN
ap-7656	230	3	ma	ma	PROPN
ap-7656	230	4	.	.	PROPN
ap-7656	230	5	bell	bell	PROPN
ap-7656	230	6	’s	’s	PART
ap-7656	230	7	inequality	inequality	NOUN
ap-7656	230	8	and	and	CCONJ
ap-7656	230	9	entanglement	entanglement	NOUN
ap-7656	230	10	in	in	ADP
ap-7656	230	11	qubits	qubit	NOUN
ap-7656	230	12	.	.	PUNCT
ap-7656	231	1	journal	journal	NOUN
ap-7656	231	2	of	of	ADP
ap-7656	231	3	high	high	ADJ
ap-7656	231	4	energy	energy	NOUN
ap-7656	231	5	physics	physics	NOUN
ap-7656	231	6	volume	volume	NOUN
ap-7656	231	7	2017(9):100	2017(9):100	NUM
ap-7656	231	8	,	,	PUNCT
ap-7656	231	9	2017	2017	NUM
ap-7656	231	10	.	.	PUNCT
ap-7656	232	1	https://doi.org/10.1007/jhep09(2017)100	https://doi.org/10.1007/jhep09(2017)100	PROPN
ap-7656	232	2	.	.	PUNCT
ap-7656	233	1	226	226	NUM
ap-7656	233	2	https://doi.org/10.1103/physrev.47.777	https://doi.org/10.1103/physrev.47.777	NOUN
ap-7656	233	3	https://doi.org/10.1103/physicsphysiquefizika.1.195	https://doi.org/10.1103/physicsphysiquefizika.1.195	PROPN
ap-7656	233	4	https://doi.org/10.1103/physicsphysiquefizika.1.195	https://doi.org/10.1103/physicsphysiquefizika.1.195	PROPN
ap-7656	233	5	https://doi.org/10.1103/physrevlett.23.880	https://doi.org/10.1103/physrevlett.23.880	PROPN
ap-7656	233	6	https://doi.org/10.1007/jhep09(2017)100	https://doi.org/10.1007/jhep09(2017)100	PROPN
ap-7656	233	7	vol	vol	NOUN
ap-7656	233	8	.	.	PUNCT
ap-7656	234	1	62	62	NUM
ap-7656	234	2	no	no	INTJ
ap-7656	234	3	.	.	PUNCT
ap-7656	235	1	1/2022	1/2022	NUM
ap-7656	235	2	a	a	DET
ap-7656	235	3	note	note	NOUN
ap-7656	235	4	on	on	ADP
ap-7656	235	5	entanglement	entanglement	NOUN
ap-7656	235	6	classification	classification	NOUN
ap-7656	235	7	for	for	ADP
ap-7656	235	8	tripartite	tripartite	ADJ
ap-7656	235	9	.	.	PUNCT
ap-7656	235	10	.	.	PUNCT
ap-7656	235	11	.	.	PUNCT
ap-7656	236	1	[	[	X
ap-7656	236	2	5	5	NUM
ap-7656	236	3	]	]	PUNCT
ap-7656	236	4	m.	m.	NOUN
ap-7656	236	5	li	li	PROPN
ap-7656	236	6	,	,	PUNCT
ap-7656	236	7	s.	s.	PROPN
ap-7656	236	8	m.	m.	PROPN
ap-7656	236	9	fei	fei	PROPN
ap-7656	236	10	.	.	PUNCT
ap-7656	237	1	bell	bell	PROPN
ap-7656	237	2	inequalities	inequality	NOUN
ap-7656	237	3	for	for	ADP
ap-7656	237	4	multipartite	multipartite	ADJ
ap-7656	237	5	qubit	qubit	NOUN
ap-7656	237	6	quantum	quantum	NOUN
ap-7656	237	7	systems	system	NOUN
ap-7656	237	8	and	and	CCONJ
ap-7656	237	9	their	their	PRON
ap-7656	237	10	maximal	maximal	ADJ
ap-7656	237	11	violation	violation	NOUN
ap-7656	237	12	.	.	PUNCT
ap-7656	238	1	physical	physical	ADJ
ap-7656	238	2	review	review	NOUN
ap-7656	238	3	a	a	DET
ap-7656	238	4	86(5):052119	86(5):052119	NUM
ap-7656	238	5	,	,	PUNCT
ap-7656	238	6	2012	2012	NUM
ap-7656	238	7	.	.	PUNCT
ap-7656	239	1	https://doi.org/10.1103/physreva.86.052119	https://doi.org/10.1103/physreva.86.052119	X
ap-7656	239	2	.	.	PUNCT
ap-7656	240	1	[	[	X
ap-7656	240	2	6	6	NUM
ap-7656	240	3	]	]	X
ap-7656	240	4	d.	d.	PROPN
ap-7656	240	5	collins	collins	PROPN
ap-7656	240	6	,	,	PUNCT
ap-7656	240	7	n.	n.	PROPN
ap-7656	240	8	gisin	gisin	PROPN
ap-7656	240	9	,	,	PUNCT
ap-7656	240	10	s.	s.	PROPN
ap-7656	240	11	popescu	popescu	PROPN
ap-7656	240	12	,	,	PUNCT
ap-7656	240	13	et	et	PROPN
ap-7656	240	14	al	al	PROPN
ap-7656	240	15	.	.	PUNCT
ap-7656	240	16	bell	bell	NOUN
ap-7656	240	17	-	-	PUNCT
ap-7656	240	18	type	type	NOUN
ap-7656	240	19	inequalities	inequality	NOUN
ap-7656	240	20	to	to	PART
ap-7656	240	21	detect	detect	VERB
ap-7656	240	22	true	true	ADJ
ap-7656	240	23	n	n	CCONJ
ap-7656	240	24	-	-	PUNCT
ap-7656	240	25	body	body	NOUN
ap-7656	240	26	nonseparability	nonseparability	NOUN
ap-7656	240	27	.	.	PUNCT
ap-7656	241	1	physical	physical	PROPN
ap-7656	241	2	review	review	PROPN
ap-7656	241	3	letters	letter	NOUN
ap-7656	241	4	88(17):170405	88(17):170405	NUM
ap-7656	241	5	,	,	PUNCT
ap-7656	241	6	2002	2002	NUM
ap-7656	241	7	.	.	PUNCT
ap-7656	242	1	https://doi.org/10.1103/physrevlett.88.170405	https://doi.org/10.1103/physrevlett.88.170405	NOUN
ap-7656	242	2	.	.	PUNCT
ap-7656	243	1	[	[	X
ap-7656	243	2	7	7	X
ap-7656	243	3	]	]	PUNCT
ap-7656	243	4	s.	s.	PROPN
ap-7656	243	5	w.	w.	PROPN
ap-7656	243	6	ji	ji	PROPN
ap-7656	243	7	,	,	PUNCT
ap-7656	243	8	j.	j.	PROPN
ap-7656	243	9	lee	lee	PROPN
ap-7656	243	10	,	,	PUNCT
ap-7656	243	11	j.	j.	PROPN
ap-7656	243	12	lim	lim	PROPN
ap-7656	243	13	,	,	PUNCT
ap-7656	243	14	et	et	PROPN
ap-7656	243	15	al	al	PROPN
ap-7656	243	16	.	.	PUNCT
ap-7656	243	17	multi	multi	ADJ
ap-7656	243	18	-	-	ADJ
ap-7656	243	19	setting	set	VERB
ap-7656	243	20	bell	bell	NOUN
ap-7656	243	21	inequality	inequality	NOUN
ap-7656	243	22	for	for	ADP
ap-7656	243	23	qudits	qudit	NOUN
ap-7656	243	24	.	.	PUNCT
ap-7656	244	1	physical	physical	ADJ
ap-7656	244	2	review	review	NOUN
ap-7656	244	3	a	a	DET
ap-7656	244	4	78(5):052103	78(5):052103	NOUN
ap-7656	244	5	,	,	PUNCT
ap-7656	244	6	2008	2008	NUM
ap-7656	244	7	.	.	PUNCT
ap-7656	245	1	https://doi.org/10.1103/physreva.78.052103	https://doi.org/10.1103/physreva.78.052103	X
ap-7656	245	2	.	.	PUNCT
ap-7656	246	1	[	[	X
ap-7656	246	2	8	8	NUM
ap-7656	246	3	]	]	X
ap-7656	246	4	h.	h.	PROPN
ap-7656	246	5	zhao	zhao	PROPN
ap-7656	246	6	.	.	PUNCT
ap-7656	247	1	entanglement	entanglement	NOUN
ap-7656	247	2	of	of	ADP
ap-7656	247	3	bell	bell	NOUN
ap-7656	247	4	diagonal	diagonal	ADJ
ap-7656	247	5	mixed	mixed	ADJ
ap-7656	247	6	states	state	NOUN
ap-7656	247	7	.	.	PUNCT
ap-7656	248	1	physics	physics	NOUN
ap-7656	248	2	letters	letter	NOUN
ap-7656	248	3	a	a	DET
ap-7656	248	4	373(43):3924–3930	373(43):3924–3930	NUM
ap-7656	248	5	,	,	PUNCT
ap-7656	248	6	2009	2009	NUM
ap-7656	248	7	.	.	PUNCT
ap-7656	249	1	https://doi.org/10.1016/j.physleta.2009.08.048	https://doi.org/10.1016/j.physleta.2009.08.048	NOUN
ap-7656	249	2	.	.	PUNCT
ap-7656	250	1	[	[	X
ap-7656	250	2	9	9	NUM
ap-7656	250	3	]	]	X
ap-7656	250	4	d.	d.	PROPN
ap-7656	250	5	ding	ding	PROPN
ap-7656	250	6	,	,	PUNCT
ap-7656	250	7	y.	y.	PROPN
ap-7656	250	8	q.	q.	PROPN
ap-7656	251	1	he	he	PRON
ap-7656	251	2	,	,	PUNCT
ap-7656	251	3	f.	f.	PROPN
ap-7656	251	4	l.	l.	PROPN
ap-7656	251	5	yan	yan	PROPN
ap-7656	251	6	,	,	PUNCT
ap-7656	251	7	t.	t.	PROPN
ap-7656	251	8	gao	gao	PROPN
ap-7656	251	9	.	.	PUNCT
ap-7656	251	10	entanglement	entanglement	NOUN
ap-7656	251	11	measure	measure	NOUN
ap-7656	251	12	and	and	CCONJ
ap-7656	251	13	quantum	quantum	ADJ
ap-7656	251	14	violation	violation	NOUN
ap-7656	251	15	of	of	ADP
ap-7656	251	16	bell	bell	NOUN
ap-7656	251	17	-	-	PUNCT
ap-7656	251	18	type	type	NOUN
ap-7656	251	19	inequality	inequality	NOUN
ap-7656	251	20	.	.	PUNCT
ap-7656	252	1	international	international	ADJ
ap-7656	252	2	journal	journal	PROPN
ap-7656	252	3	of	of	ADP
ap-7656	252	4	theoretical	theoretical	ADJ
ap-7656	252	5	physics	physics	NOUN
ap-7656	252	6	55(10):4231–4237	55(10):4231–4237	NUM
ap-7656	252	7	,	,	PUNCT
ap-7656	252	8	2016	2016	NUM
ap-7656	252	9	.	.	PUNCT
ap-7656	253	1	https://doi.org/10.1007/s10773-016-3048-1	https://doi.org/10.1007/s10773-016-3048-1	NUM
ap-7656	253	2	.	.	PUNCT
ap-7656	254	1	[	[	X
ap-7656	254	2	10	10	NUM
ap-7656	254	3	]	]	PUNCT
ap-7656	254	4	x.	x.	PROPN
ap-7656	254	5	f.	f.	PROPN
ap-7656	254	6	huang	huang	PROPN
ap-7656	254	7	,	,	PUNCT
ap-7656	254	8	n.	n.	PROPN
ap-7656	254	9	h.	h.	PROPN
ap-7656	254	10	jing	jing	PROPN
ap-7656	254	11	,	,	PUNCT
ap-7656	254	12	t.	t.	PROPN
ap-7656	254	13	g.	g.	PROPN
ap-7656	254	14	zhang	zhang	PROPN
ap-7656	254	15	.	.	PUNCT
ap-7656	255	1	an	an	DET
ap-7656	255	2	upper	upper	ADJ
ap-7656	255	3	bound	bind	VERB
ap-7656	255	4	of	of	ADP
ap-7656	255	5	fully	fully	ADV
ap-7656	255	6	entangled	entangle	VERB
ap-7656	255	7	fraction	fraction	NOUN
ap-7656	255	8	of	of	ADP
ap-7656	255	9	mixed	mixed	ADJ
ap-7656	255	10	states	state	NOUN
ap-7656	255	11	.	.	PUNCT
ap-7656	256	1	communications	communication	NOUN
ap-7656	256	2	in	in	ADP
ap-7656	256	3	theoretical	theoretical	ADJ
ap-7656	256	4	physics	physics	NOUN
ap-7656	256	5	65(6):701–704	65(6):701–704	NOUN
ap-7656	256	6	,	,	PUNCT
ap-7656	256	7	2016	2016	NUM
ap-7656	256	8	.	.	PUNCT
ap-7656	257	1	https://doi.org/10.1088/0253-6102/65/6/701	https://doi.org/10.1088/0253-6102/65/6/701	PROPN
ap-7656	257	2	.	.	PUNCT
ap-7656	258	1	[	[	X
ap-7656	258	2	11	11	NUM
ap-7656	258	3	]	]	PUNCT
ap-7656	258	4	j.	j.	PROPN
ap-7656	258	5	i.	i.	PROPN
ap-7656	258	6	de	de	PROPN
ap-7656	258	7	vicente	vicente	PROPN
ap-7656	258	8	,	,	PUNCT
ap-7656	258	9	m.	m.	NOUN
ap-7656	258	10	huber	huber	PROPN
ap-7656	258	11	.	.	PROPN
ap-7656	258	12	multipartite	multipartite	PROPN
ap-7656	258	13	entanglement	entanglement	NOUN
ap-7656	258	14	detection	detection	NOUN
ap-7656	258	15	from	from	ADP
ap-7656	258	16	correlation	correlation	NOUN
ap-7656	258	17	tensors	tensor	NOUN
ap-7656	258	18	.	.	PUNCT
ap-7656	259	1	physical	physical	ADJ
ap-7656	259	2	review	review	NOUN
ap-7656	259	3	a	a	DET
ap-7656	259	4	84(6):242–245	84(6):242–245	PROPN
ap-7656	259	5	,	,	PUNCT
ap-7656	259	6	2011	2011	NUM
ap-7656	259	7	.	.	PUNCT
ap-7656	260	1	https://doi.org/10.1103/physreva.84.062306	https://doi.org/10.1103/physreva.84.062306	NOUN
ap-7656	260	2	.	.	PUNCT
ap-7656	261	1	[	[	X
ap-7656	261	2	12	12	NUM
ap-7656	261	3	]	]	PUNCT
ap-7656	261	4	m.	m.	NOUN
ap-7656	261	5	li	li	PROPN
ap-7656	261	6	,	,	PUNCT
ap-7656	261	7	j.	j.	PROPN
ap-7656	261	8	wang	wang	PROPN
ap-7656	261	9	,	,	PUNCT
ap-7656	261	10	s.	s.	PROPN
ap-7656	261	11	m.	m.	PROPN
ap-7656	261	12	fei	fei	PROPN
ap-7656	261	13	,	,	PUNCT
ap-7656	261	14	x.	x.	PROPN
ap-7656	261	15	li	li	PROPN
ap-7656	261	16	-	-	PUNCT
ap-7656	261	17	jost	jost	NOUN
ap-7656	261	18	.	.	PUNCT
ap-7656	262	1	quantum	quantum	PROPN
ap-7656	262	2	separability	separability	NOUN
ap-7656	262	3	criteria	criterion	NOUN
ap-7656	262	4	for	for	ADP
ap-7656	262	5	arbitrary	arbitrary	ADJ
ap-7656	262	6	dimensional	dimensional	ADJ
ap-7656	262	7	multipartite	multipartite	ADJ
ap-7656	262	8	states	state	NOUN
ap-7656	262	9	.	.	PUNCT
ap-7656	263	1	physical	physical	ADJ
ap-7656	263	2	review	review	NOUN
ap-7656	263	3	a	a	DET
ap-7656	263	4	89(2):767–771	89(2):767–771	NOUN
ap-7656	263	5	,	,	PUNCT
ap-7656	263	6	2014	2014	NUM
ap-7656	263	7	.	.	PUNCT
ap-7656	264	1	https://doi.org/10.1103/physreva.89.022325	https://doi.org/10.1103/physreva.89.022325	PROPN
ap-7656	264	2	.	.	PUNCT
ap-7656	265	1	[	[	X
ap-7656	265	2	13	13	NUM
ap-7656	265	3	]	]	X
ap-7656	265	4	w.	w.	PROPN
ap-7656	265	5	son	son	PROPN
ap-7656	265	6	,	,	PUNCT
ap-7656	265	7	j.	j.	PROPN
ap-7656	265	8	lee	lee	PROPN
ap-7656	265	9	,	,	PUNCT
ap-7656	265	10	m.	m.	PROPN
ap-7656	265	11	s.	s.	PROPN
ap-7656	265	12	kim	kim	PROPN
ap-7656	265	13	.	.	PUNCT
ap-7656	265	14	generic	generic	ADJ
ap-7656	265	15	bell	bell	PROPN
ap-7656	265	16	inequalities	inequality	NOUN
ap-7656	265	17	for	for	ADP
ap-7656	265	18	multipartite	multipartite	ADJ
ap-7656	265	19	arbitrary	arbitrary	ADJ
ap-7656	265	20	dimensional	dimensional	ADJ
ap-7656	265	21	systems	system	NOUN
ap-7656	265	22	.	.	PUNCT
ap-7656	266	1	physical	physical	ADJ
ap-7656	266	2	review	review	NOUN
ap-7656	266	3	letters	letter	NOUN
ap-7656	266	4	96(6):060406	96(6):060406	NUM
ap-7656	266	5	,	,	PUNCT
ap-7656	266	6	2006	2006	NUM
ap-7656	266	7	.	.	PUNCT
ap-7656	267	1	https://doi.org/10.1103/physrevlett.96.060406	https://doi.org/10.1103/physrevlett.96.060406	NOUN
ap-7656	267	2	.	.	PUNCT
ap-7656	268	1	[	[	X
ap-7656	268	2	14	14	NUM
ap-7656	268	3	]	]	X
ap-7656	268	4	d.	d.	PROPN
ap-7656	268	5	gottesman	gottesman	PROPN
ap-7656	268	6	.	.	PUNCT
ap-7656	269	1	fault	fault	NOUN
ap-7656	269	2	-	-	PUNCT
ap-7656	269	3	tolerant	tolerant	ADJ
ap-7656	269	4	quantum	quantum	ADJ
ap-7656	269	5	computation	computation	NOUN
ap-7656	269	6	with	with	ADP
ap-7656	269	7	higher	high	ADJ
ap-7656	269	8	-	-	PUNCT
ap-7656	269	9	dimensional	dimensional	ADJ
ap-7656	269	10	systems	system	NOUN
ap-7656	269	11	.	.	PUNCT
ap-7656	270	1	chaos	chaos	NOUN
ap-7656	270	2	,	,	PUNCT
ap-7656	270	3	solitons	soliton	NOUN
ap-7656	270	4	&	&	CCONJ
ap-7656	270	5	fractals	fractal	NOUN
ap-7656	270	6	10(10):1749–1758	10(10):1749–1758	NUM
ap-7656	270	7	,	,	PUNCT
ap-7656	270	8	1999	1999	NUM
ap-7656	270	9	.	.	PUNCT
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ap-7656	271	2	.	.	PUNCT
ap-7656	272	1	[	[	X
ap-7656	272	2	15	15	NUM
ap-7656	272	3	]	]	X
ap-7656	272	4	h.	h.	PROPN
ap-7656	272	5	a.	a.	PROPN
ap-7656	272	6	carteret	carteret	PROPN
ap-7656	272	7	,	,	PUNCT
ap-7656	272	8	a.	a.	PROPN
ap-7656	272	9	higuchi	higuchi	PROPN
ap-7656	272	10	,	,	PUNCT
ap-7656	272	11	a.	a.	NOUN
ap-7656	272	12	sudbery	sudbery	NOUN
ap-7656	272	13	.	.	PUNCT
ap-7656	273	1	multipartite	multipartite	ADJ
ap-7656	273	2	generalisation	generalisation	NOUN
ap-7656	273	3	of	of	ADP
ap-7656	273	4	the	the	DET
ap-7656	273	5	schmidt	schmidt	ADJ
ap-7656	273	6	decomposition	decomposition	NOUN
ap-7656	273	7	.	.	PUNCT
ap-7656	274	1	journal	journal	NOUN
ap-7656	274	2	of	of	ADP
ap-7656	274	3	mathematical	mathematical	ADJ
ap-7656	274	4	physics	physics	NOUN
ap-7656	274	5	41(12):7932–7939	41(12):7932–7939	NUM
ap-7656	274	6	,	,	PUNCT
ap-7656	274	7	2000	2000	NUM
ap-7656	274	8	.	.	PUNCT
ap-7656	275	1	https://doi.org/10.1063/1.1319516	https://doi.org/10.1063/1.1319516	PROPN
ap-7656	275	2	.	.	PUNCT
ap-7656	276	1	227	227	NUM
ap-7656	276	2	https://doi.org/10.1103/physreva.86.052119	https://doi.org/10.1103/physreva.86.052119	NOUN
ap-7656	276	3	https://doi.org/10.1103/physrevlett.88.170405	https://doi.org/10.1103/physrevlett.88.170405	NOUN
ap-7656	276	4	https://doi.org/10.1103/physreva.78.052103	https://doi.org/10.1103/physreva.78.052103	X
ap-7656	276	5	https://doi.org/10.1016/j.physleta.2009.08.048	https://doi.org/10.1016/j.physleta.2009.08.048	PROPN
ap-7656	276	6	https://doi.org/10.1007/s10773-016-3048-1	https://doi.org/10.1007/s10773-016-3048-1	NUM
ap-7656	276	7	https://doi.org/10.1088/0253-6102/65/6/701	https://doi.org/10.1088/0253-6102/65/6/701	PROPN
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ap-7656	276	9	https://doi.org/10.1103/physreva.89.022325	https://doi.org/10.1103/physreva.89.022325	AUX
ap-7656	276	10	https://doi.org/10.1103/physrevlett.96.060406	https://doi.org/10.1103/physrevlett.96.060406	PROPN
ap-7656	276	11	https://doi.org/10.1016/s0960-0779(98)00218-5	https://doi.org/10.1016/s0960-0779(98)00218-5	PROPN
ap-7656	276	12	https://doi.org/10.1063/1.1319516	https://doi.org/10.1063/1.1319516	PROPN
ap-7656	276	13	acta	acta	PROPN
ap-7656	276	14	polytechnica	polytechnica	PROPN
ap-7656	277	1	62(1):222–227	62(1):222–227	PROPN
ap-7656	277	2	,	,	PUNCT
ap-7656	277	3	2022	2022	NUM
ap-7656	277	4	1	1	NUM
ap-7656	277	5	introduction	introduction	NOUN
ap-7656	277	6	2	2	NUM
ap-7656	277	7	entanglement	entanglement	NOUN
ap-7656	277	8	identification	identification	NOUN
ap-7656	277	9	with	with	ADP
ap-7656	277	10	bell	bell	PROPN
ap-7656	277	11	inequalities	inequality	NOUN
ap-7656	277	12	3	3	NUM
ap-7656	277	13	entanglement	entanglement	NOUN
ap-7656	277	14	classification	classification	NOUN
ap-7656	277	15	under	under	ADP
ap-7656	277	16	principal	principal	ADJ
ap-7656	277	17	basis	basis	NOUN
ap-7656	277	18	4	4	NUM
ap-7656	277	19	conclusions	conclusion	NOUN
ap-7656	277	20	acknowledgements	acknowledgement	NOUN
ap-7656	277	21	references	reference	NOUN