id	sid	tid	token	lemma	pos
ap-766	1	1	ap05_5.vp	ap05_5.vp	NOUN
ap-766	1	2	1	1	NUM
ap-766	1	3	introduction	introduction	NOUN
ap-766	1	4	in	in	ADP
ap-766	1	5	recent	recent	ADJ
ap-766	1	6	years	year	NOUN
ap-766	1	7	much	much	ADJ
ap-766	1	8	effort	effort	NOUN
ap-766	1	9	has	have	AUX
ap-766	1	10	been	be	AUX
ap-766	1	11	invested	invest	VERB
ap-766	1	12	in	in	ADP
ap-766	1	13	an	an	DET
ap-766	1	14	investigation	investigation	NOUN
ap-766	1	15	of	of	ADP
ap-766	1	16	how	how	SCONJ
ap-766	1	17	to	to	PART
ap-766	1	18	employ	employ	VERB
ap-766	1	19	quantum	quantum	NOUN
ap-766	1	20	systems	system	NOUN
ap-766	1	21	as	as	ADP
ap-766	1	22	parts	part	NOUN
ap-766	1	23	of	of	ADP
ap-766	1	24	a	a	DET
ap-766	1	25	computer	computer	NOUN
ap-766	1	26	.	.	PUNCT
ap-766	2	1	it	it	PRON
ap-766	2	2	has	have	AUX
ap-766	2	3	been	be	AUX
ap-766	2	4	demonstrated	demonstrate	VERB
ap-766	2	5	that	that	SCONJ
ap-766	2	6	quantum	quantum	ADJ
ap-766	2	7	information	information	NOUN
ap-766	2	8	is	be	AUX
ap-766	2	9	different	different	ADJ
ap-766	2	10	from	from	ADP
ap-766	2	11	classical	classical	ADJ
ap-766	2	12	information	information	NOUN
ap-766	2	13	and	and	CCONJ
ap-766	2	14	that	that	SCONJ
ap-766	2	15	the	the	DET
ap-766	2	16	essence	essence	NOUN
ap-766	2	17	of	of	ADP
ap-766	2	18	this	this	DET
ap-766	2	19	difference	difference	NOUN
ap-766	2	20	lies	lie	VERB
ap-766	2	21	in	in	ADP
ap-766	2	22	the	the	DET
ap-766	2	23	entanglement	entanglement	NOUN
ap-766	2	24	of	of	ADP
ap-766	2	25	quantum	quantum	NOUN
ap-766	2	26	systems	system	NOUN
ap-766	2	27	.	.	PUNCT
ap-766	3	1	entanglement	entanglement	NOUN
ap-766	3	2	is	be	AUX
ap-766	3	3	a	a	DET
ap-766	3	4	simple	simple	ADJ
ap-766	3	5	consequence	consequence	NOUN
ap-766	3	6	of	of	ADP
ap-766	3	7	the	the	DET
ap-766	3	8	linearity	linearity	NOUN
ap-766	3	9	of	of	ADP
ap-766	3	10	quantum	quantum	ADJ
ap-766	3	11	mechanics	mechanic	NOUN
ap-766	3	12	,	,	PUNCT
ap-766	3	13	hence	hence	ADV
ap-766	3	14	it	it	PRON
ap-766	3	15	does	do	AUX
ap-766	3	16	not	not	PART
ap-766	3	17	have	have	VERB
ap-766	3	18	a	a	DET
ap-766	3	19	classical	classical	ADJ
ap-766	3	20	counterpart	counterpart	NOUN
ap-766	3	21	.	.	PUNCT
ap-766	4	1	this	this	DET
ap-766	4	2	effect	effect	NOUN
ap-766	4	3	equips	equip	VERB
ap-766	4	4	a	a	DET
ap-766	4	5	quantum	quantum	ADJ
ap-766	4	6	computer	computer	NOUN
ap-766	4	7	with	with	ADP
ap-766	4	8	massive	massive	ADJ
ap-766	4	9	parallelism	parallelism	NOUN
ap-766	4	10	and	and	CCONJ
ap-766	4	11	hence	hence	ADV
ap-766	4	12	could	could	AUX
ap-766	4	13	be	be	AUX
ap-766	4	14	used	use	VERB
ap-766	4	15	to	to	PART
ap-766	4	16	speed	speed	VERB
ap-766	4	17	up	up	ADP
ap-766	4	18	computation	computation	NOUN
ap-766	4	19	.	.	PUNCT
ap-766	5	1	therefore	therefore	ADV
ap-766	5	2	quantum	quantum	ADJ
ap-766	5	3	information	information	NOUN
ap-766	5	4	processing	processing	NOUN
ap-766	5	5	could	could	AUX
ap-766	5	6	be	be	AUX
ap-766	5	7	more	more	ADV
ap-766	5	8	efficient	efficient	ADJ
ap-766	5	9	than	than	ADP
ap-766	5	10	classical	classical	ADJ
ap-766	5	11	information	information	NOUN
ap-766	5	12	processing	processing	NOUN
ap-766	5	13	.	.	PUNCT
ap-766	6	1	on	on	ADP
ap-766	6	2	the	the	DET
ap-766	6	3	other	other	ADJ
ap-766	6	4	hand	hand	NOUN
ap-766	6	5	,	,	PUNCT
ap-766	6	6	it	it	PRON
ap-766	6	7	has	have	AUX
ap-766	6	8	become	become	VERB
ap-766	6	9	clear	clear	ADJ
ap-766	6	10	that	that	SCONJ
ap-766	6	11	the	the	DET
ap-766	6	12	linear	linear	ADJ
ap-766	6	13	character	character	NOUN
ap-766	6	14	of	of	ADP
ap-766	6	15	quantum	quantum	NOUN
ap-766	6	16	theory	theory	NOUN
ap-766	6	17	imposes	impose	VERB
ap-766	6	18	severe	severe	ADJ
ap-766	6	19	restrictions	restriction	NOUN
ap-766	6	20	on	on	ADP
ap-766	6	21	the	the	DET
ap-766	6	22	character	character	NOUN
ap-766	6	23	of	of	ADP
ap-766	6	24	elementary	elementary	ADJ
ap-766	6	25	tasks	task	NOUN
ap-766	6	26	of	of	ADP
ap-766	6	27	quantum	quantum	ADJ
ap-766	6	28	information	information	NOUN
ap-766	6	29	processing	processing	NOUN
ap-766	6	30	.	.	PUNCT
ap-766	7	1	for	for	ADP
ap-766	7	2	example	example	NOUN
ap-766	7	3	it	it	PRON
ap-766	7	4	is	be	AUX
ap-766	7	5	impossible	impossible	ADJ
ap-766	7	6	to	to	PART
ap-766	7	7	clone	clone	VERB
ap-766	7	8	an	an	DET
ap-766	7	9	arbitrary	arbitrary	ADJ
ap-766	7	10	quantum	quantum	ADJ
ap-766	7	11	state	state	NOUN
ap-766	7	12	perfectly	perfectly	ADV
ap-766	7	13	[	[	X
ap-766	7	14	1	1	NUM
ap-766	7	15	]	]	PUNCT
ap-766	7	16	.	.	PUNCT
ap-766	8	1	nevertheless	nevertheless	ADV
ap-766	8	2	,	,	PUNCT
ap-766	8	3	imperfect	imperfect	ADJ
ap-766	8	4	copies	copy	NOUN
ap-766	8	5	can	can	AUX
ap-766	8	6	be	be	AUX
ap-766	8	7	made	make	VERB
ap-766	8	8	[	[	X
ap-766	8	9	2	2	NUM
ap-766	8	10	,	,	PUNCT
ap-766	8	11	3	3	NUM
ap-766	8	12	]	]	PUNCT
ap-766	8	13	.	.	PUNCT
ap-766	9	1	this	this	DET
ap-766	9	2	particular	particular	ADJ
ap-766	9	3	process	process	NOUN
ap-766	9	4	of	of	ADP
ap-766	9	5	cloning	cloning	NOUN
ap-766	9	6	belongs	belong	VERB
ap-766	9	7	to	to	ADP
ap-766	9	8	the	the	DET
ap-766	9	9	class	class	NOUN
ap-766	9	10	of	of	ADP
ap-766	9	11	so	so	ADV
ap-766	9	12	called	call	VERB
ap-766	9	13	universal	universal	ADJ
ap-766	9	14	processes	process	NOUN
ap-766	9	15	.	.	PUNCT
ap-766	10	1	these	these	DET
ap-766	10	2	processes	process	NOUN
ap-766	10	3	act	act	VERB
ap-766	10	4	on	on	ADP
ap-766	10	5	all	all	DET
ap-766	10	6	input	input	NOUN
ap-766	10	7	states	state	NOUN
ap-766	10	8	of	of	ADP
ap-766	10	9	a	a	DET
ap-766	10	10	quantum	quantum	ADJ
ap-766	10	11	system	system	NOUN
ap-766	10	12	in	in	ADP
ap-766	10	13	a	a	DET
ap-766	10	14	‘	'	PUNCT
ap-766	10	15	similar	similar	ADJ
ap-766	10	16	’	'	PUNCT
ap-766	10	17	way	way	NOUN
ap-766	10	18	.	.	PUNCT
ap-766	11	1	for	for	ADP
ap-766	11	2	universal	universal	ADJ
ap-766	11	3	processes	process	NOUN
ap-766	11	4	working	work	VERB
ap-766	11	5	with	with	ADP
ap-766	11	6	one	one	NUM
ap-766	11	7	quantum	quantum	NOUN
ap-766	11	8	system	system	NOUN
ap-766	11	9	in	in	ADP
ap-766	11	10	a	a	DET
ap-766	11	11	pure	pure	ADJ
ap-766	11	12	state	state	NOUN
ap-766	11	13	and	and	CCONJ
ap-766	11	14	finishing	finish	VERB
ap-766	11	15	in	in	ADP
ap-766	11	16	an	an	DET
ap-766	11	17	n	n	CCONJ
ap-766	11	18	-	-	PUNCT
ap-766	11	19	particle	particle	NOUN
ap-766	11	20	state	state	NOUN
ap-766	11	21	this	this	DET
ap-766	11	22	property	property	NOUN
ap-766	11	23	is	be	AUX
ap-766	11	24	mathematically	mathematically	ADV
ap-766	11	25	described	describe	VERB
ap-766	11	26	by	by	ADP
ap-766	11	27	the	the	DET
ap-766	11	28	so	so	ADV
ap-766	11	29	called	call	VERB
ap-766	11	30	covariance	covariance	NOUN
ap-766	11	31	condition	condition	NOUN
ap-766	11	32	.	.	PUNCT
ap-766	12	1	two	two	NUM
ap-766	12	2	-	-	PUNCT
ap-766	12	3	particle	particle	NOUN
ap-766	12	4	processes	process	NOUN
ap-766	12	5	fulfilling	fulfil	VERB
ap-766	12	6	this	this	DET
ap-766	12	7	condition	condition	NOUN
ap-766	12	8	were	be	AUX
ap-766	12	9	analyzed	analyze	VERB
ap-766	12	10	in	in	ADP
ap-766	12	11	[	[	X
ap-766	12	12	4	4	NUM
ap-766	12	13	]	]	PUNCT
ap-766	12	14	.	.	PUNCT
ap-766	13	1	in	in	ADP
ap-766	13	2	this	this	DET
ap-766	13	3	paper	paper	NOUN
ap-766	13	4	a	a	DET
ap-766	13	5	theoretical	theoretical	ADJ
ap-766	13	6	framework	framework	NOUN
ap-766	13	7	was	be	AUX
ap-766	13	8	developed	develop	VERB
ap-766	13	9	within	within	ADP
ap-766	13	10	which	which	PRON
ap-766	13	11	all	all	DET
ap-766	13	12	possible	possible	ADJ
ap-766	13	13	two	two	NUM
ap-766	13	14	-	-	PUNCT
ap-766	13	15	particle	particle	NOUN
ap-766	13	16	universal	universal	ADJ
ap-766	13	17	processes	process	NOUN
ap-766	13	18	can	can	AUX
ap-766	13	19	be	be	AUX
ap-766	13	20	described	describe	VERB
ap-766	13	21	and	and	CCONJ
ap-766	13	22	those	those	PRON
ap-766	13	23	compatible	compatible	ADJ
ap-766	13	24	with	with	ADP
ap-766	13	25	the	the	DET
ap-766	13	26	linear	linear	ADJ
ap-766	13	27	character	character	NOUN
ap-766	13	28	of	of	ADP
ap-766	13	29	quantum	quantum	NOUN
ap-766	13	30	theory	theory	NOUN
ap-766	13	31	were	be	AUX
ap-766	13	32	determined	determine	VERB
ap-766	13	33	.	.	PUNCT
ap-766	14	1	of	of	ADP
ap-766	14	2	special	special	ADJ
ap-766	14	3	interest	interest	NOUN
ap-766	14	4	were	be	AUX
ap-766	14	5	universal	universal	ADJ
ap-766	14	6	processes	process	NOUN
ap-766	14	7	generating	generate	VERB
ap-766	14	8	entangled	entangle	VERB
ap-766	14	9	two	two	NUM
ap-766	14	10	-	-	PUNCT
ap-766	14	11	particle	particle	NOUN
ap-766	14	12	output	output	NOUN
ap-766	14	13	states	state	NOUN
ap-766	14	14	which	which	PRON
ap-766	14	15	do	do	AUX
ap-766	14	16	not	not	PART
ap-766	14	17	contain	contain	VERB
ap-766	14	18	any	any	DET
ap-766	14	19	separable	separable	ADJ
ap-766	14	20	components	component	NOUN
ap-766	14	21	.	.	PUNCT
ap-766	15	1	it	it	PRON
ap-766	15	2	has	have	AUX
ap-766	15	3	been	be	AUX
ap-766	15	4	shown	show	VERB
ap-766	15	5	that	that	SCONJ
ap-766	15	6	this	this	DET
ap-766	15	7	particular	particular	ADJ
ap-766	15	8	subclass	subclass	NOUN
ap-766	15	9	forms	form	VERB
ap-766	15	10	a	a	DET
ap-766	15	11	one	one	NUM
ap-766	15	12	-	-	PUNCT
ap-766	15	13	parameter	parameter	NOUN
ap-766	15	14	family	family	NOUN
ap-766	15	15	of	of	ADP
ap-766	15	16	totally	totally	ADV
ap-766	15	17	anti	anti	ADJ
ap-766	15	18	-	-	ADJ
ap-766	15	19	symmetric	symmetric	ADJ
ap-766	15	20	states	state	NOUN
ap-766	15	21	with	with	ADP
ap-766	15	22	respect	respect	NOUN
ap-766	15	23	to	to	ADP
ap-766	15	24	permutations	permutation	NOUN
ap-766	15	25	of	of	ADP
ap-766	15	26	the	the	DET
ap-766	15	27	two	two	NUM
ap-766	15	28	particles	particle	NOUN
ap-766	15	29	.	.	PUNCT
ap-766	16	1	the	the	DET
ap-766	16	2	aim	aim	NOUN
ap-766	16	3	of	of	ADP
ap-766	16	4	this	this	DET
ap-766	16	5	paper	paper	NOUN
ap-766	16	6	is	be	AUX
ap-766	16	7	to	to	PART
ap-766	16	8	generalize	generalize	VERB
ap-766	16	9	the	the	DET
ap-766	16	10	results	result	NOUN
ap-766	16	11	obtained	obtain	VERB
ap-766	16	12	for	for	ADP
ap-766	16	13	two	two	NUM
ap-766	16	14	-	-	PUNCT
ap-766	16	15	particle	particle	NOUN
ap-766	16	16	universal	universal	ADJ
ap-766	16	17	processes	process	NOUN
ap-766	16	18	to	to	ADP
ap-766	16	19	the	the	DET
ap-766	16	20	subclass	subclass	NOUN
ap-766	16	21	of	of	ADP
ap-766	16	22	multi	multi	ADJ
ap-766	16	23	-	-	ADJ
ap-766	16	24	particle	particle	ADJ
ap-766	16	25	universal	universal	ADJ
ap-766	16	26	processes	process	NOUN
ap-766	16	27	from	from	ADP
ap-766	16	28	one	one	NUM
ap-766	16	29	to	to	ADP
ap-766	16	30	n	n	NOUN
ap-766	16	31	particles	particle	NOUN
ap-766	16	32	.	.	PUNCT
ap-766	17	1	for	for	ADP
ap-766	17	2	this	this	DET
ap-766	17	3	purpose	purpose	NOUN
ap-766	17	4	we	we	PRON
ap-766	17	5	use	use	VERB
ap-766	17	6	theoretical	theoretical	ADJ
ap-766	17	7	framework	framework	NOUN
ap-766	17	8	developed	develop	VERB
ap-766	17	9	in	in	ADP
ap-766	17	10	[	[	X
ap-766	17	11	4	4	NUM
ap-766	17	12	]	]	PUNCT
ap-766	17	13	.	.	PUNCT
ap-766	18	1	we	we	PRON
ap-766	18	2	show	show	VERB
ap-766	18	3	how	how	SCONJ
ap-766	18	4	the	the	DET
ap-766	18	5	general	general	ADJ
ap-766	18	6	statement	statement	NOUN
ap-766	18	7	for	for	ADP
ap-766	18	8	a	a	DET
ap-766	18	9	multi	multi	ADJ
ap-766	18	10	-	-	ADJ
ap-766	18	11	particle	particle	ADJ
ap-766	18	12	universal	universal	ADJ
ap-766	18	13	process	process	NOUN
ap-766	18	14	can	can	AUX
ap-766	18	15	be	be	AUX
ap-766	18	16	constructed	construct	VERB
ap-766	18	17	.	.	PUNCT
ap-766	19	1	the	the	DET
ap-766	19	2	one	one	NUM
ap-766	19	3	-	-	PUNCT
ap-766	19	4	parameter	parameter	NOUN
ap-766	19	5	family	family	NOUN
ap-766	19	6	of	of	ADP
ap-766	19	7	processes	process	NOUN
ap-766	19	8	generating	generate	VERB
ap-766	19	9	totally	totally	ADV
ap-766	19	10	anti	anti	ADJ
ap-766	19	11	-	-	ADJ
ap-766	19	12	symmetric	symmetric	ADJ
ap-766	19	13	states	state	NOUN
ap-766	19	14	was	be	AUX
ap-766	19	15	generalized	generalize	VERB
ap-766	19	16	to	to	ADP
ap-766	19	17	a	a	DET
ap-766	19	18	multi	multi	ADJ
ap-766	19	19	-	-	ADJ
ap-766	19	20	particle	particle	ADJ
ap-766	19	21	regime	regime	NOUN
ap-766	19	22	and	and	CCONJ
ap-766	19	23	its	its	PRON
ap-766	19	24	properties	property	NOUN
ap-766	19	25	were	be	AUX
ap-766	19	26	studied	study	VERB
ap-766	19	27	,	,	PUNCT
ap-766	19	28	mainly	mainly	ADV
ap-766	19	29	bipartite	bipartite	PROPN
ap-766	19	30	entanglement	entanglement	NOUN
ap-766	19	31	.	.	PUNCT
ap-766	20	1	for	for	ADP
ap-766	20	2	this	this	DET
ap-766	20	3	purpose	purpose	NOUN
ap-766	20	4	we	we	PRON
ap-766	20	5	use	use	VERB
ap-766	20	6	the	the	DET
ap-766	20	7	concept	concept	NOUN
ap-766	20	8	of	of	ADP
ap-766	20	9	negativity	negativity	NOUN
ap-766	20	10	[	[	X
ap-766	20	11	5	5	NUM
ap-766	20	12	]	]	PUNCT
ap-766	20	13	.	.	PUNCT
ap-766	21	1	finally	finally	ADV
ap-766	21	2	we	we	PRON
ap-766	21	3	briefly	briefly	ADV
ap-766	21	4	review	review	VERB
ap-766	21	5	the	the	DET
ap-766	21	6	question	question	NOUN
ap-766	21	7	of	of	ADP
ap-766	21	8	the	the	DET
ap-766	21	9	complete	complete	ADJ
ap-766	21	10	positivity	positivity	NOUN
ap-766	21	11	of	of	ADP
ap-766	21	12	the	the	DET
ap-766	21	13	obtained	obtain	VERB
ap-766	21	14	universal	universal	ADJ
ap-766	21	15	processes	process	NOUN
ap-766	21	16	.	.	PUNCT
ap-766	22	1	2	2	NUM
ap-766	22	2	general	general	ADJ
ap-766	22	3	structure	structure	NOUN
ap-766	22	4	of	of	ADP
ap-766	22	5	a	a	DET
ap-766	22	6	universal	universal	ADJ
ap-766	22	7	process	process	NOUN
ap-766	22	8	we	we	PRON
ap-766	22	9	will	will	AUX
ap-766	22	10	now	now	ADV
ap-766	22	11	derive	derive	VERB
ap-766	22	12	the	the	DET
ap-766	22	13	general	general	ADJ
ap-766	22	14	structure	structure	NOUN
ap-766	22	15	of	of	ADP
ap-766	22	16	the	the	DET
ap-766	22	17	n	n	CCONJ
ap-766	22	18	-	-	PUNCT
ap-766	22	19	particle	particle	NOUN
ap-766	22	20	covariant	covariant	ADJ
ap-766	22	21	mapping	mapping	NOUN
ap-766	22	22	using	use	VERB
ap-766	22	23	the	the	DET
ap-766	22	24	statement	statement	NOUN
ap-766	22	25	for	for	ADP
ap-766	22	26	the	the	DET
ap-766	22	27	two	two	NUM
ap-766	22	28	-	-	PUNCT
ap-766	22	29	particle	particle	NOUN
ap-766	22	30	case	case	NOUN
ap-766	22	31	[	[	X
ap-766	22	32	4	4	NUM
ap-766	22	33	]	]	PUNCT
ap-766	22	34	.	.	PUNCT
ap-766	23	1	in	in	ADP
ap-766	23	2	the	the	DET
ap-766	23	3	following	following	NOUN
ap-766	23	4	we	we	PRON
ap-766	23	5	assume	assume	VERB
ap-766	23	6	that	that	SCONJ
ap-766	23	7	the	the	DET
ap-766	23	8	d	d	ADJ
ap-766	23	9	-	-	ADJ
ap-766	23	10	dimensional	dimensional	ADJ
ap-766	23	11	one	one	NUM
ap-766	23	12	-	-	PUNCT
ap-766	23	13	particle	particle	NOUN
ap-766	23	14	hilbert	hilbert	NOUN
ap-766	23	15	space	space	NOUN
ap-766	23	16	�	�	PROPN
ap-766	23	17	is	be	AUX
ap-766	23	18	the	the	DET
ap-766	23	19	same	same	ADJ
ap-766	23	20	for	for	ADP
ap-766	23	21	all	all	DET
ap-766	23	22	n	n	PRON
ap-766	23	23	particles	particle	NOUN
ap-766	23	24	.	.	PUNCT
ap-766	24	1	an	an	DET
ap-766	24	2	arbitrary	arbitrary	ADJ
ap-766	24	3	one	one	NUM
ap-766	24	4	-	-	PUNCT
ap-766	24	5	particle	particle	NOUN
ap-766	24	6	pure	pure	ADJ
ap-766	24	7	state	state	NOUN
ap-766	24	8	can	can	AUX
ap-766	24	9	be	be	AUX
ap-766	24	10	described	describe	VERB
ap-766	24	11	by	by	ADP
ap-766	24	12	d	d	ADJ
ap-766	24	13	-	-	ADJ
ap-766	24	14	dimensional	dimensional	ADJ
ap-766	24	15	generalized	generalized	ADJ
ap-766	24	16	bloch	bloch	NOUN
ap-766	24	17	vector	vector	NOUN
ap-766	24	18	p.	p.	NOUN
ap-766	24	19	such	such	DET
ap-766	24	20	a	a	DET
ap-766	24	21	state	state	NOUN
ap-766	24	22	will	will	AUX
ap-766	24	23	be	be	AUX
ap-766	24	24	simply	simply	ADV
ap-766	24	25	denoted	denote	VERB
ap-766	24	26	by|p	by|p	NOUN
ap-766	24	27	.	.	PUNCT
ap-766	25	1	consider	consider	VERB
ap-766	25	2	a	a	DET
ap-766	25	3	linear	linear	ADJ
ap-766	25	4	map	map	NOUN
ap-766	25	5	�	�	PROPN
ap-766	25	6	from	from	ADP
ap-766	25	7	1	1	NUM
ap-766	25	8	to	to	ADP
ap-766	25	9	n	n	PRON
ap-766	25	10	particles	particle	NOUN
ap-766	25	11	,	,	PUNCT
ap-766	25	12	i.	i.	PROPN
ap-766	25	13	e.	e.	PROPN
ap-766	25	14	�	�	PROPN
ap-766	25	15	�	�	PROPN
ap-766	25	16	�	�	PROPN
ap-766	25	17	�	�	PROPN
ap-766	25	18	�	�	PROPN
ap-766	25	19	:	:	PUNCT
ap-766	25	20	(	(	PUNCT
ap-766	25	21	)	)	PUNCT
ap-766	25	22	(	(	PUNCT
ap-766	25	23	)	)	PUNCT
ap-766	25	24	,	,	PUNCT
ap-766	25	25	(	(	PUNCT
ap-766	25	26	)	)	PUNCT
ap-766	25	27	(	(	PUNCT
ap-766	25	28	)	)	PUNCT
ap-766	25	29	,	,	PUNCT
ap-766	25	30	(	(	PUNCT
ap-766	25	31	)	)	PUNCT
ap-766	25	32	(	(	PUNCT
ap-766	25	33	)	)	PUNCT
ap-766	25	34	,	,	PUNCT
ap-766	25	35	�	�	PROPN
ap-766	25	36	�	�	PROPN
ap-766	25	37	�	�	PROPN
ap-766	25	38	�	�	PROPN
ap-766	25	39	in	in	ADP
ap-766	25	40	out	out	ADV
ap-766	25	41	in	in	ADP
ap-766	25	42	out	out	ADP
ap-766	25	43	np	np	INTJ
ap-766	25	44	p	p	NOUN
ap-766	25	45	p	p	X
ap-766	25	46	p	p	PROPN
ap-766	25	47	�	�	PROPN
ap-766	25	48	�	�	PROPN
ap-766	25	49	�	�	PROPN
ap-766	25	50	�	�	PROPN
ap-766	25	51	(	(	PUNCT
ap-766	25	52	1	1	NUM
ap-766	25	53	)	)	PUNCT
ap-766	25	54	where	where	SCONJ
ap-766	25	55	the	the	DET
ap-766	25	56	density	density	NOUN
ap-766	25	57	matrix	matrix	NOUN
ap-766	25	58	�	�	PROPN
ap-766	25	59	in	in	ADP
ap-766	25	60	(	(	PUNCT
ap-766	25	61	)	)	PUNCT
ap-766	25	62	p	p	NOUN
ap-766	25	63	has	have	VERB
ap-766	25	64	the	the	DET
ap-766	25	65	form	form	NOUN
ap-766	25	66	�	�	PROPN
ap-766	25	67	in	in	ADP
ap-766	25	68	n	n	CCONJ
ap-766	25	69	n	n	NOUN
ap-766	25	70	d	d	PROPN
ap-766	25	71	i	i	PROPN
ap-766	25	72	(	(	PUNCT
ap-766	25	73	)	)	PUNCT
ap-766	25	74	(	(	PUNCT
ap-766	25	75	)	)	PUNCT
ap-766	25	76	(	(	PUNCT
ap-766	25	77	)	)	PUNCT
ap-766	25	78	p	p	X
ap-766	25	79	p	p	X
ap-766	25	80	p	p	X
ap-766	25	81	�	�	PROPN
ap-766	25	82	�	�	PROPN
ap-766	25	83	�	�	PROPN
ap-766	25	84	�	�	PROPN
ap-766	25	85	�	�	PROPN
ap-766	25	86	1	1	NUM
ap-766	25	87	1	1	NUM
ap-766	25	88	1	1	NUM
ap-766	25	89	,	,	PUNCT
ap-766	25	90	(	(	PUNCT
ap-766	25	91	2	2	NUM
ap-766	25	92	)	)	PUNCT
ap-766	25	93	i.e.	i.e.	X
ap-766	25	94	the	the	DET
ap-766	25	95	first	first	ADJ
ap-766	25	96	particle	particle	NOUN
ap-766	25	97	is	be	AUX
ap-766	25	98	in	in	ADP
ap-766	25	99	the	the	DET
ap-766	25	100	pure	pure	ADJ
ap-766	25	101	state	state	NOUN
ap-766	25	102	p	p	NOUN
ap-766	25	103	,	,	PUNCT
ap-766	25	104	and	and	CCONJ
ap-766	25	105	all	all	DET
ap-766	25	106	others	other	NOUN
ap-766	25	107	are	be	AUX
ap-766	25	108	in	in	ADP
ap-766	25	109	the	the	DET
ap-766	25	110	state	state	NOUN
ap-766	25	111	of	of	ADP
ap-766	25	112	a	a	DET
ap-766	25	113	complete	complete	ADJ
ap-766	25	114	mixture	mixture	NOUN
ap-766	25	115	.	.	PUNCT
ap-766	26	1	we	we	PRON
ap-766	26	2	will	will	AUX
ap-766	26	3	call	call	VERB
ap-766	26	4	this	this	DET
ap-766	26	5	map	map	NOUN
ap-766	26	6	universal	universal	ADJ
ap-766	26	7	(	(	PUNCT
ap-766	26	8	or	or	CCONJ
ap-766	26	9	covariant	covariant	NOUN
ap-766	26	10	)	)	PUNCT
ap-766	26	11	,	,	PUNCT
ap-766	26	12	if	if	SCONJ
ap-766	26	13	it	it	PRON
ap-766	26	14	possesses	possess	VERB
ap-766	26	15	the	the	DET
ap-766	26	16	following	follow	VERB
ap-766	26	17	covariance	covariance	NOUN
ap-766	26	18	property	property	NOUN
ap-766	26	19	�	�	PROPN
ap-766	26	20	�	�	PROPN
ap-766	26	21	out	out	ADP
ap-766	26	22	n	n	CCONJ
ap-766	26	23	out	out	ADP
ap-766	26	24	nu	nu	PROPN
ap-766	26	25	u	u	PROPN
ap-766	26	26	(	(	PUNCT
ap-766	26	27	)	)	PUNCT
ap-766	26	28	(	(	PUNCT
ap-766	26	29	(	(	PUNCT
ap-766	26	30	)	)	PUNCT
ap-766	26	31	)	)	PUNCT
ap-766	27	1	(	(	PUNCT
ap-766	27	2	)	)	PUNCT
ap-766	27	3	(	(	PUNCT
ap-766	27	4	(	(	PUNCT
ap-766	27	5	)	)	PUNCT
ap-766	27	6	)	)	PUNCT
ap-766	27	7	†p	†p	X
ap-766	28	1	p	p	X
ap-766	28	2	p	p	PROPN
ap-766	28	3	p	p	PROPN
ap-766	28	4	�	�	PROPN
ap-766	28	5	�	�	PROPN
ap-766	28	6	�	�	PROPN
ap-766	28	7	0	0	NUM
ap-766	28	8	(	(	PUNCT
ap-766	28	9	3	3	NUM
ap-766	28	10	)	)	PUNCT
ap-766	28	11	where	where	SCONJ
ap-766	28	12	the	the	DET
ap-766	28	13	one	one	NUM
ap-766	28	14	-	-	PUNCT
ap-766	28	15	particle	particle	NOUN
ap-766	28	16	unitary	unitary	ADJ
ap-766	28	17	transformation	transformation	NOUN
ap-766	28	18	u(p	u(p	NOUN
ap-766	28	19	)	)	PUNCT
ap-766	28	20	maps	map	VERB
ap-766	28	21	the	the	DET
ap-766	28	22	state	state	NOUN
ap-766	28	23	p0	p0	NOUN
ap-766	28	24	to	to	ADP
ap-766	28	25	the	the	DET
ap-766	28	26	state	state	NOUN
ap-766	28	27	p	p	NOUN
ap-766	28	28	,	,	PUNCT
ap-766	28	29	i.	i.	PROPN
ap-766	28	30	e.	e.	PROPN
ap-766	29	1	p	p	PROPN
ap-766	29	2	p	p	PROPN
ap-766	29	3	p	p	X
ap-766	29	4	�	�	PROPN
ap-766	29	5	u	u	NOUN
ap-766	29	6	(	(	PUNCT
ap-766	29	7	)	)	PUNCT
ap-766	29	8	0	0	NUM
ap-766	29	9	.	.	PUNCT
ap-766	30	1	(	(	PUNCT
ap-766	30	2	4	4	NUM
ap-766	30	3	)	)	PUNCT
ap-766	30	4	to	to	PART
ap-766	30	5	construct	construct	VERB
ap-766	30	6	the	the	DET
ap-766	30	7	general	general	ADJ
ap-766	30	8	statement	statement	NOUN
ap-766	30	9	for	for	ADP
ap-766	30	10	covariant	covariant	ADJ
ap-766	30	11	mapping	mapping	NOUN
ap-766	30	12	with	with	ADP
ap-766	30	13	n	n	ADP
ap-766	30	14	particles	particle	NOUN
ap-766	30	15	we	we	PRON
ap-766	30	16	will	will	AUX
ap-766	30	17	use	use	VERB
ap-766	30	18	the	the	DET
ap-766	30	19	results	result	NOUN
ap-766	30	20	for	for	ADP
ap-766	30	21	the	the	DET
ap-766	30	22	two	two	NUM
ap-766	30	23	-	-	PUNCT
ap-766	30	24	particle	particle	NOUN
ap-766	30	25	[	[	X
ap-766	30	26	4	4	NUM
ap-766	30	27	]	]	PUNCT
ap-766	30	28	.	.	PUNCT
ap-766	31	1	we	we	PRON
ap-766	31	2	will	will	AUX
ap-766	31	3	now	now	ADV
ap-766	31	4	summarize	summarize	VERB
ap-766	31	5	the	the	DET
ap-766	31	6	main	main	ADJ
ap-766	31	7	results	result	NOUN
ap-766	31	8	.	.	PUNCT
ap-766	32	1	an	an	DET
ap-766	32	2	arbitrary	arbitrary	ADJ
ap-766	32	3	density	density	NOUN
ap-766	32	4	operator	operator	NOUN
ap-766	32	5	of	of	ADP
ap-766	32	6	a	a	DET
ap-766	32	7	d	d	PROPN
ap-766	32	8	dimensional	dimensional	ADJ
ap-766	32	9	quantum	quantum	NOUN
ap-766	32	10	system	system	NOUN
ap-766	32	11	can	can	AUX
ap-766	32	12	be	be	AUX
ap-766	32	13	represented	represent	VERB
ap-766	32	14	in	in	ADP
ap-766	32	15	terms	term	NOUN
ap-766	32	16	of	of	ADP
ap-766	32	17	some	some	DET
ap-766	32	18	basis	basis	NOUN
ap-766	32	19	of	of	ADP
ap-766	32	20	the	the	DET
ap-766	32	21	su(d	su(d	NOUN
ap-766	32	22	)	)	PUNCT
ap-766	32	23	algebra	algebra	NOUN
ap-766	32	24	.	.	PUNCT
ap-766	33	1	in	in	ADP
ap-766	33	2	order	order	NOUN
ap-766	33	3	to	to	PART
ap-766	33	4	implement	implement	VERB
ap-766	33	5	the	the	DET
ap-766	33	6	covariance	covariance	NOUN
ap-766	33	7	condition	condition	NOUN
ap-766	33	8	(	(	PUNCT
ap-766	33	9	3	3	X
ap-766	33	10	)	)	PUNCT
ap-766	33	11	we	we	PRON
ap-766	33	12	used	use	VERB
ap-766	33	13	the	the	DET
ap-766	33	14	basis	basis	NOUN
ap-766	33	15	{	{	PUNCT
ap-766	33	16	}	}	PUNCT
ap-766	33	17	a	a	DET
ap-766	33	18	ij	ij	NOUN
ap-766	33	19	,	,	PUNCT
ap-766	33	20	(	(	PUNCT
ap-766	33	21	,	,	PUNCT
ap-766	33	22	,	,	PUNCT
ap-766	33	23	,	,	PUNCT
ap-766	33	24	)	)	PUNCT
ap-766	33	25	i	i	PRON
ap-766	33	26	j	j	PROPN
ap-766	33	27	d	d	VERB
ap-766	33	28	�	�	PROPN
ap-766	33	29	1	1	NUM
ap-766	33	30	�	�	PROPN
ap-766	33	31	,	,	PUNCT
ap-766	33	32	which	which	PRON
ap-766	33	33	fulfills	fulfill	VERB
ap-766	33	34	the	the	DET
ap-766	33	35	following	follow	VERB
ap-766	33	36	commutation	commutation	NOUN
ap-766	33	37	relations	relation	NOUN
ap-766	33	38	[	[	PUNCT
ap-766	33	39	,	,	PUNCT
ap-766	33	40	]	]	X
ap-766	33	41	(	(	PUNCT
ap-766	33	42	)	)	PUNCT
ap-766	33	43	a	a	DET
ap-766	33	44	a	a	DET
ap-766	33	45	aij	aij	PROPN
ap-766	33	46	mn	mn	PROPN
ap-766	33	47	ab	ab	PROPN
ap-766	33	48	jm	jm	PROPN
ap-766	33	49	ai	ai	VERB
ap-766	33	50	bn	bn	PROPN
ap-766	33	51	in	in	ADP
ap-766	33	52	am	be	AUX
ap-766	33	53	bj	bj	ADP
ap-766	33	54	�	�	PROPN
ap-766	33	55	�	�	PROPN
ap-766	33	56	�	�	PROPN
ap-766	33	57	�	�	PROPN
ap-766	33	58	�	�	PROPN
ap-766	33	59	�	�	PROPN
ap-766	33	60	�	�	PROPN
ap-766	33	61	�	�	PROPN
ap-766	33	62	,	,	PUNCT
ap-766	33	63	(	(	PUNCT
ap-766	33	64	5	5	NUM
ap-766	33	65	)	)	PUNCT
ap-766	33	66	(	(	PUNCT
ap-766	33	67	we	we	PRON
ap-766	33	68	have	have	AUX
ap-766	33	69	used	use	VERB
ap-766	33	70	the	the	DET
ap-766	33	71	einstein	einstein	ADJ
ap-766	33	72	summation	summation	NOUN
ap-766	33	73	convention	convention	PROPN
ap-766	33	74	in	in	ADP
ap-766	33	75	which	which	PRON
ap-766	33	76	we	we	PRON
ap-766	33	77	have	have	VERB
ap-766	33	78	to	to	PART
ap-766	33	79	sum	sum	VERB
ap-766	33	80	over	over	ADP
ap-766	33	81	all	all	DET
ap-766	33	82	indices	index	NOUN
ap-766	33	83	which	which	PRON
ap-766	33	84	appear	appear	VERB
ap-766	33	85	in	in	ADP
ap-766	33	86	an	an	DET
ap-766	33	87	expression	expression	NOUN
ap-766	33	88	twice	twice	ADV
ap-766	33	89	from	from	ADP
ap-766	33	90	one	one	NUM
ap-766	33	91	to	to	ADP
ap-766	33	92	d	d	PROPN
ap-766	33	93	)	)	PUNCT
ap-766	33	94	.	.	PUNCT
ap-766	34	1	a	a	DET
ap-766	34	2	representation	representation	NOUN
ap-766	34	3	of	of	ADP
ap-766	34	4	these	these	DET
ap-766	34	5	generators	generator	NOUN
ap-766	34	6	is	be	AUX
ap-766	34	7	given	give	VERB
ap-766	34	8	by	by	ADP
ap-766	34	9	the	the	DET
ap-766	34	10	d×d	d×d	PROPN
ap-766	34	11	matrices	matrix	NOUN
ap-766	34	12	(	(	PUNCT
ap-766	34	13	)	)	PUNCT
ap-766	34	14	(	(	PUNCT
ap-766	34	15	)	)	PUNCT
ap-766	34	16	a	a	DET
ap-766	34	17	ij	ij	INTJ
ap-766	34	18	kl	kl	X
ap-766	34	19	ik	ik	PROPN
ap-766	34	20	jl	jl	PROPN
ap-766	34	21	ij	ij	PROPN
ap-766	34	22	kld	kld	PROPN
ap-766	34	23	�	�	PROPN
ap-766	34	24	�	�	PROPN
ap-766	34	25	�	�	PROPN
ap-766	34	26	�	�	PROPN
ap-766	34	27	�	�	PROPN
ap-766	34	28	�	�	PROPN
ap-766	34	29	1	1	NUM
ap-766	34	30	.	.	PUNCT
ap-766	35	1	(	(	PUNCT
ap-766	35	2	6	6	NUM
ap-766	35	3	)	)	PUNCT
ap-766	35	4	the	the	DET
ap-766	35	5	density	density	NOUN
ap-766	35	6	matrix	matrix	NOUN
ap-766	35	7	�	�	PROPN
ap-766	35	8	in	in	ADP
ap-766	35	9	(	(	PUNCT
ap-766	35	10	)	)	PUNCT
ap-766	35	11	p	p	NOUN
ap-766	35	12	can	can	AUX
ap-766	35	13	be	be	AUX
ap-766	35	14	written	write	VERB
ap-766	35	15	in	in	ADP
ap-766	35	16	the	the	DET
ap-766	35	17	form	form	NOUN
ap-766	35	18	�	�	PROPN
ap-766	35	19	in	in	ADP
ap-766	35	20	ij	ij	NOUN
ap-766	35	21	ijd	ijd	PROPN
ap-766	36	1	p	p	NOUN
ap-766	36	2	a	a	PROPN
ap-766	36	3	(	(	PUNCT
ap-766	36	4	)	)	PUNCT
ap-766	36	5	(	(	PUNCT
ap-766	36	6	)	)	PUNCT
ap-766	36	7	.p	.p	PROPN
ap-766	37	1	i	i	PRON
ap-766	37	2	�	�	PROPN
ap-766	37	3	�	�	PROPN
ap-766	37	4	1	1	NUM
ap-766	37	5	(	(	PUNCT
ap-766	37	6	7	7	NUM
ap-766	37	7	)	)	PUNCT
ap-766	37	8	in	in	ADP
ap-766	37	9	terms	term	NOUN
ap-766	37	10	of	of	ADP
ap-766	37	11	matrices	matrix	NOUN
ap-766	37	12	(	(	PUNCT
ap-766	37	13	6	6	NUM
ap-766	37	14	)	)	PUNCT
ap-766	37	15	the	the	DET
ap-766	37	16	most	most	ADV
ap-766	37	17	general	general	ADJ
ap-766	37	18	output	output	NOUN
ap-766	37	19	state	state	NOUN
ap-766	37	20	is	be	AUX
ap-766	37	21	represented	represent	VERB
ap-766	37	22	by	by	ADP
ap-766	37	23	the	the	DET
ap-766	37	24	density	density	NOUN
ap-766	37	25	matrix	matrix	NOUN
ap-766	37	26	34	34	NUM
ap-766	37	27	©	©	PROPN
ap-766	37	28	czech	czech	PROPN
ap-766	37	29	technical	technical	PROPN
ap-766	37	30	university	university	PROPN
ap-766	37	31	publishing	publishing	NOUN
ap-766	37	32	house	house	NOUN
ap-766	37	33	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-766	37	34	acta	acta	PROPN
ap-766	37	35	polytechnica	polytechnica	PROPN
ap-766	37	36	vol	vol	NOUN
ap-766	37	37	.	.	PROPN
ap-766	38	1	45	45	NUM
ap-766	38	2	no	no	NOUN
ap-766	38	3	.	.	PUNCT
ap-766	39	1	5/2005	5/2005	NUM
ap-766	39	2	czech	czech	PROPN
ap-766	39	3	technical	technical	PROPN
ap-766	39	4	university	university	PROPN
ap-766	39	5	in	in	ADP
ap-766	39	6	prague	prague	PROPN
ap-766	39	7	multi	multi	ADJ
ap-766	39	8	-	-	ADJ
ap-766	39	9	particle	particle	ADJ
ap-766	39	10	universal	universal	ADJ
ap-766	39	11	processes	process	NOUN
ap-766	39	12	j.	j.	PROPN
ap-766	39	13	novotný	novotný	PROPN
ap-766	39	14	,	,	PUNCT
ap-766	39	15	m.	m.	NOUN
ap-766	39	16	štefaňák	štefaňák	PROPN
ap-766	39	17	,	,	PUNCT
ap-766	39	18	v.	v.	CCONJ
ap-766	40	1	košt’ák	košt’ák	NOUN
ap-766	40	2	we	we	PRON
ap-766	40	3	generalize	generalize	VERB
ap-766	40	4	bipartite	bipartite	ADJ
ap-766	40	5	universal	universal	ADJ
ap-766	40	6	processes	process	NOUN
ap-766	40	7	to	to	ADP
ap-766	40	8	the	the	DET
ap-766	40	9	subclass	subclass	NOUN
ap-766	40	10	of	of	ADP
ap-766	40	11	multi	multi	ADJ
ap-766	40	12	-	-	ADJ
ap-766	40	13	particle	particle	ADJ
ap-766	40	14	universal	universal	ADJ
ap-766	40	15	processes	process	NOUN
ap-766	40	16	from	from	ADP
ap-766	40	17	one	one	NUM
ap-766	40	18	to	to	ADP
ap-766	40	19	n	n	NOUN
ap-766	40	20	particles	particle	NOUN
ap-766	40	21	.	.	PUNCT
ap-766	41	1	we	we	PRON
ap-766	41	2	show	show	VERB
ap-766	41	3	how	how	SCONJ
ap-766	41	4	the	the	DET
ap-766	41	5	general	general	ADJ
ap-766	41	6	statement	statement	NOUN
ap-766	41	7	for	for	ADP
ap-766	41	8	a	a	DET
ap-766	41	9	multi	multi	ADJ
ap-766	41	10	-	-	ADJ
ap-766	41	11	particle	particle	ADJ
ap-766	41	12	universal	universal	ADJ
ap-766	41	13	process	process	NOUN
ap-766	41	14	can	can	AUX
ap-766	41	15	be	be	AUX
ap-766	41	16	constructed	construct	VERB
ap-766	41	17	.	.	PUNCT
ap-766	42	1	the	the	DET
ap-766	42	2	one	one	NUM
ap-766	42	3	-	-	PUNCT
ap-766	42	4	parameter	parameter	NOUN
ap-766	42	5	family	family	NOUN
ap-766	42	6	of	of	ADP
ap-766	42	7	processes	process	NOUN
ap-766	42	8	generating	generate	VERB
ap-766	42	9	totally	totally	ADV
ap-766	42	10	anti	anti	ADJ
ap-766	42	11	-	-	ADJ
ap-766	42	12	symmetric	symmetric	ADJ
ap-766	42	13	states	state	NOUN
ap-766	42	14	has	have	AUX
ap-766	42	15	been	be	AUX
ap-766	42	16	generalized	generalize	VERB
ap-766	42	17	to	to	ADP
ap-766	42	18	a	a	DET
ap-766	42	19	multi	multi	ADJ
ap-766	42	20	-	-	ADJ
ap-766	42	21	particle	particle	ADJ
ap-766	42	22	regime	regime	NOUN
ap-766	42	23	and	and	CCONJ
ap-766	42	24	its	its	PRON
ap-766	42	25	entanglement	entanglement	NOUN
ap-766	42	26	properties	property	NOUN
ap-766	42	27	have	have	AUX
ap-766	42	28	been	be	AUX
ap-766	42	29	studied	study	VERB
ap-766	42	30	.	.	PUNCT
ap-766	43	1	a	a	DET
ap-766	43	2	view	view	NOUN
ap-766	43	3	is	be	AUX
ap-766	43	4	given	give	VERB
ap-766	43	5	on	on	ADP
ap-766	43	6	the	the	DET
ap-766	43	7	complete	complete	ADJ
ap-766	43	8	positivity	positivity	NOUN
ap-766	43	9	and	and	CCONJ
ap-766	43	10	the	the	DET
ap-766	43	11	possible	possible	ADJ
ap-766	43	12	physical	physical	ADJ
ap-766	43	13	realization	realization	NOUN
ap-766	43	14	of	of	ADP
ap-766	43	15	universal	universal	ADJ
ap-766	43	16	processes	process	NOUN
ap-766	43	17	.	.	PUNCT
ap-766	44	1	keywords	keyword	NOUN
ap-766	44	2	:	:	PUNCT
ap-766	44	3	universal	universal	ADJ
ap-766	44	4	processes	process	NOUN
ap-766	44	5	,	,	PUNCT
ap-766	44	6	quantum	quantum	ADJ
ap-766	44	7	entanglement	entanglement	NOUN
ap-766	44	8	,	,	PUNCT
ap-766	44	9	complete	complete	ADJ
ap-766	44	10	positivity	positivity	NOUN
ap-766	44	11	.	.	PUNCT
ap-766	45	1	�	�	PROPN
ap-766	45	2	�	�	PROPN
ap-766	45	3	�	�	PROPN
ap-766	45	4	�	�	PROPN
ap-766	45	5	out	out	ADP
ap-766	46	1	ij	ij	INTJ
ap-766	46	2	ij	ij	INTJ
ap-766	46	3	ij	ij	INTJ
ap-766	46	4	ij	ij	INTJ
ap-766	46	5	ijkl	ijkl	PROPN
ap-766	46	6	n	n	PROPN
ap-766	46	7	(	(	PUNCT
ap-766	46	8	)	)	PUNCT
ap-766	46	9	(	(	PUNCT
ap-766	46	10	)	)	PUNCT
ap-766	46	11	(	(	PUNCT
ap-766	46	12	)	)	PUNCT
ap-766	46	13	(	(	PUNCT
ap-766	46	14	)	)	PUNCT
ap-766	46	15	(	(	PUNCT
ap-766	46	16	)	)	PUNCT
ap-766	47	1	p	p	X
ap-766	47	2	i	i	PRON
ap-766	48	1	i	i	PRON
ap-766	48	2	p	p	VERB
ap-766	49	1	a	a	PRON
ap-766	50	1	i	i	PRON
ap-766	50	2	p	p	X
ap-766	51	1	i	i	PRON
ap-766	51	2	a	a	DET
ap-766	51	3	�	�	PROPN
ap-766	51	4	�	�	PROPN
ap-766	51	5	�	�	PROPN
ap-766	51	6	�	�	PROPN
ap-766	51	7	�	�	PROPN
ap-766	51	8	�	�	PROPN
ap-766	51	9	�	�	PROPN
ap-766	51	10	1	1	NUM
ap-766	51	11	2	2	NUM
ap-766	51	12	1	1	NUM
ap-766	51	13	2	2	NUM
ap-766	51	14	(	(	PUNCT
ap-766	51	15	)	)	PUNCT
ap-766	51	16	,	,	PUNCT
ap-766	51	17	p	p	X
ap-766	51	18	a	a	DET
ap-766	51	19	aij	aij	PROPN
ap-766	51	20	kl	kl	PROPN
ap-766	51	21	�	�	PROPN
ap-766	51	22	(	(	PUNCT
ap-766	51	23	8)	8)	NUM
ap-766	51	24	where	where	SCONJ
ap-766	51	25	the	the	DET
ap-766	51	26	linearity	linearity	NOUN
ap-766	51	27	requirement	requirement	NOUN
ap-766	51	28	of	of	ADP
ap-766	51	29	quantum	quantum	ADJ
ap-766	51	30	mechanics	mechanic	NOUN
ap-766	51	31	implies	imply	VERB
ap-766	51	32	that	that	SCONJ
ap-766	51	33	�	�	PROPN
ap-766	51	34	ij	ij	INTJ
ap-766	51	35	(	(	PUNCT
ap-766	51	36	)	)	PUNCT
ap-766	51	37	(	(	PUNCT
ap-766	51	38	)	)	PUNCT
ap-766	51	39	1	1	NUM
ap-766	51	40	p	p	NOUN
ap-766	51	41	,	,	PUNCT
ap-766	51	42	�	�	PROPN
ap-766	51	43	ij	ij	NOUN
ap-766	51	44	(	(	PUNCT
ap-766	51	45	)	)	PUNCT
ap-766	51	46	(	(	PUNCT
ap-766	51	47	)	)	PUNCT
ap-766	51	48	2	2	NUM
ap-766	51	49	p	p	NOUN
ap-766	51	50	and	and	CCONJ
ap-766	51	51	�	�	PROPN
ap-766	51	52	ijkl	ijkl	PROPN
ap-766	51	53	(	(	PUNCT
ap-766	51	54	)	)	PUNCT
ap-766	51	55	p	p	NOUN
ap-766	51	56	have	have	VERB
ap-766	51	57	to	to	PART
ap-766	51	58	be	be	AUX
ap-766	51	59	linear	linear	ADJ
ap-766	51	60	with	with	ADP
ap-766	51	61	respect	respect	NOUN
ap-766	51	62	to	to	ADP
ap-766	51	63	the	the	DET
ap-766	51	64	parameters	parameter	NOUN
ap-766	51	65	of	of	ADP
ap-766	51	66	the	the	DET
ap-766	51	67	bloch	bloch	PROPN
ap-766	51	68	vector	vector	PROPN
ap-766	51	69	p.	p.	PROPN
ap-766	51	70	to	to	PART
ap-766	51	71	fulfill	fulfill	VERB
ap-766	51	72	the	the	DET
ap-766	51	73	covariance	covariance	NOUN
ap-766	51	74	condition	condition	NOUN
ap-766	51	75	(	(	PUNCT
ap-766	51	76	3	3	X
ap-766	51	77	)	)	PUNCT
ap-766	51	78	the	the	DET
ap-766	51	79	matrix	matrix	NOUN
ap-766	51	80	(	(	PUNCT
ap-766	51	81	8)	8)	NUM
ap-766	51	82	has	have	VERB
ap-766	51	83	to	to	PART
ap-766	51	84	involve	involve	VERB
ap-766	51	85	only	only	ADV
ap-766	51	86	terms	term	NOUN
ap-766	51	87	invariant	invariant	ADJ
ap-766	51	88	under	under	ADP
ap-766	51	89	the	the	DET
ap-766	51	90	transformation	transformation	NOUN
ap-766	51	91	of	of	ADP
ap-766	51	92	the	the	DET
ap-766	51	93	form	form	NOUN
ap-766	51	94	u	u	NOUN
ap-766	51	95	�	�	PROPN
ap-766	51	96	u	u	NOUN
ap-766	51	97	,	,	PUNCT
ap-766	51	98	i.e.	i.e.	X
ap-766	51	99	the	the	DET
ap-766	51	100	scalar	scalar	ADJ
ap-766	51	101	part	part	NOUN
ap-766	51	102	,	,	PUNCT
ap-766	51	103	or	or	CCONJ
ap-766	51	104	terms	term	NOUN
ap-766	51	105	which	which	PRON
ap-766	51	106	transform	transform	VERB
ap-766	51	107	like	like	ADP
ap-766	51	108	the	the	DET
ap-766	51	109	generators	generator	NOUN
ap-766	51	110	of	of	ADP
ap-766	51	111	the	the	DET
ap-766	51	112	su(d	su(d	PROPN
ap-766	51	113	)	)	PUNCT
ap-766	51	114	group	group	NOUN
ap-766	51	115	a	a	DET
ap-766	51	116	ij	ij	NOUN
ap-766	51	117	,	,	PUNCT
ap-766	51	118	i.e.	i.e.	X
ap-766	51	119	the	the	DET
ap-766	51	120	vector	vector	NOUN
ap-766	51	121	part	part	NOUN
ap-766	51	122	.	.	PUNCT
ap-766	52	1	it	it	PRON
ap-766	52	2	was	be	AUX
ap-766	52	3	shown	show	VERB
ap-766	52	4	in	in	ADP
ap-766	52	5	[	[	X
ap-766	52	6	4	4	X
ap-766	52	7	]	]	PUNCT
ap-766	52	8	that	that	SCONJ
ap-766	52	9	the	the	DET
ap-766	52	10	nontrivial	nontrivial	NOUN
ap-766	52	11	scalar	scalar	NOUN
ap-766	52	12	is	be	AUX
ap-766	52	13	a	a	DET
ap-766	52	14	aij	aij	PROPN
ap-766	52	15	ji	ji	PROPN
ap-766	52	16	�	�	PROPN
ap-766	52	17	and	and	CCONJ
ap-766	52	18	the	the	DET
ap-766	52	19	nontrivial	nontrivial	ADJ
ap-766	52	20	vectors	vector	NOUN
ap-766	52	21	have	have	VERB
ap-766	52	22	the	the	DET
ap-766	52	23	form	form	NOUN
ap-766	52	24	a	a	DET
ap-766	52	25	aki	aki	PROPN
ap-766	52	26	kj	kj	PROPN
ap-766	52	27	�	�	PROPN
ap-766	52	28	,	,	PUNCT
ap-766	52	29	a	a	DET
ap-766	52	30	aik	aik	NOUN
ap-766	52	31	kj	kj	PROPN
ap-766	52	32	�	�	PROPN
ap-766	52	33	.	.	PUNCT
ap-766	53	1	from	from	ADP
ap-766	53	2	these	these	DET
ap-766	53	3	facts	fact	NOUN
ap-766	53	4	,	,	PUNCT
ap-766	53	5	the	the	DET
ap-766	53	6	most	most	ADV
ap-766	53	7	general	general	ADJ
ap-766	53	8	output	output	NOUN
ap-766	53	9	matrix	matrix	NOUN
ap-766	53	10	that	that	PRON
ap-766	53	11	fulfills	fulfill	VERB
ap-766	53	12	the	the	DET
ap-766	53	13	covariance	covariance	NOUN
ap-766	53	14	condition	condition	NOUN
ap-766	53	15	(	(	PUNCT
ap-766	53	16	3	3	NUM
ap-766	53	17	)	)	PUNCT
ap-766	53	18	and	and	CCONJ
ap-766	53	19	depends	depend	VERB
ap-766	53	20	linearly	linearly	ADV
ap-766	53	21	on	on	ADP
ap-766	53	22	the	the	DET
ap-766	53	23	input	input	NOUN
ap-766	53	24	must	must	AUX
ap-766	53	25	have	have	VERB
ap-766	53	26	the	the	DET
ap-766	53	27	form	form	NOUN
ap-766	53	28	�	�	PROPN
ap-766	53	29	�	�	PROPN
ap-766	53	30	�	�	PROPN
ap-766	53	31	out	out	ADP
ap-766	53	32	ij	ij	NUM
ap-766	53	33	ij	ij	INTJ
ap-766	53	34	ij	ij	INTJ
ap-766	53	35	ij	ij	INTJ
ap-766	53	36	ij	ij	INTJ
ap-766	53	37	ji	ji	PROPN
ap-766	54	1	n	n	PRON
ap-766	54	2	p	p	X
ap-766	54	3	p	p	X
ap-766	54	4	c	c	PROPN
ap-766	54	5	(	(	PUNCT
ap-766	54	6	)	)	PUNCT
ap-766	54	7	(	(	PUNCT
ap-766	54	8	)	)	PUNCT
ap-766	54	9	(	(	PUNCT
ap-766	54	10	)	)	PUNCT
ap-766	54	11	p	p	X
ap-766	55	1	i	i	PRON
ap-766	55	2	i	i	PRON
ap-766	55	3	a	a	INTJ
ap-766	56	1	i	i	PRON
ap-766	56	2	i	i	PRON
ap-766	56	3	a	a	DET
ap-766	56	4	a	a	DET
ap-766	56	5	a	a	DET
ap-766	56	6	�	�	PROPN
ap-766	56	7	�	�	PROPN
ap-766	56	8	�	�	PROPN
ap-766	56	9	�	�	PROPN
ap-766	56	10	�	�	PROPN
ap-766	56	11	�	�	PROPN
ap-766	56	12	�	�	PROPN
ap-766	56	13	�	�	PROPN
ap-766	56	14	�	�	PROPN
ap-766	56	15	1	1	NUM
ap-766	56	16	2	2	NUM
ap-766	56	17	1	1	NUM
ap-766	56	18	2	2	NUM
ap-766	56	19	�	�	PROPN
ap-766	56	20	�	�	PROPN
ap-766	56	21	�	�	PROPN
ap-766	56	22	p	p	NOUN
ap-766	56	23	pij	pij	VERB
ap-766	56	24	ik	ik	PROPN
ap-766	57	1	kj	kj	PROPN
ap-766	57	2	ji	ji	PROPN
ap-766	57	3	ki	ki	PROPN
ap-766	57	4	jka	jka	PROPN
ap-766	57	5	a	a	DET
ap-766	57	6	a	a	DET
ap-766	57	7	a	a	DET
ap-766	57	8	�	�	PROPN
ap-766	57	9	�	�	PROPN
ap-766	57	10	�	�	PROPN
ap-766	57	11	.	.	PUNCT
ap-766	58	1	(	(	PUNCT
ap-766	58	2	9	9	X
ap-766	58	3	)	)	PUNCT
ap-766	58	4	where	where	SCONJ
ap-766	58	5	�	�	PROPN
ap-766	58	6	(	(	PUNCT
ap-766	58	7	,	,	PUNCT
ap-766	58	8	)	)	PUNCT
ap-766	58	9	12	12	NUM
ap-766	58	10	and	and	CCONJ
ap-766	58	11	c	c	NOUN
ap-766	58	12	are	be	AUX
ap-766	58	13	real	real	ADJ
ap-766	58	14	parameters	parameter	NOUN
ap-766	58	15	and	and	CCONJ
ap-766	58	16	�	�	PROPN
ap-766	58	17	is	be	AUX
ap-766	58	18	complex	complex	ADJ
ap-766	58	19	.	.	PUNCT
ap-766	59	1	the	the	DET
ap-766	59	2	ranges	range	NOUN
ap-766	59	3	of	of	ADP
ap-766	59	4	these	these	DET
ap-766	59	5	parameters	parameter	NOUN
ap-766	59	6	are	be	AUX
ap-766	59	7	restricted	restrict	VERB
ap-766	59	8	by	by	ADP
ap-766	59	9	the	the	DET
ap-766	59	10	fact	fact	NOUN
ap-766	59	11	that	that	SCONJ
ap-766	59	12	�	�	VERB
ap-766	59	13	out	out	ADP
ap-766	59	14	(	(	PUNCT
ap-766	59	15	)	)	PUNCT
ap-766	59	16	p	p	NOUN
ap-766	59	17	must	must	AUX
ap-766	59	18	be	be	AUX
ap-766	59	19	a	a	DET
ap-766	59	20	density	density	NOUN
ap-766	59	21	matrix	matrix	NOUN
ap-766	59	22	,	,	PUNCT
ap-766	59	23	i.	i.	PROPN
ap-766	59	24	e.	e.	PROPN
ap-766	60	1	a	a	DET
ap-766	60	2	positive	positive	ADJ
ap-766	60	3	operator	operator	NOUN
ap-766	60	4	with	with	ADP
ap-766	60	5	a	a	DET
ap-766	60	6	unit	unit	NOUN
ap-766	60	7	trace	trace	NOUN
ap-766	60	8	.	.	PUNCT
ap-766	61	1	this	this	DET
ap-766	61	2	statement	statement	NOUN
ap-766	61	3	can	can	AUX
ap-766	61	4	be	be	AUX
ap-766	61	5	easily	easily	ADV
ap-766	61	6	generalized	generalize	VERB
ap-766	61	7	to	to	ADP
ap-766	61	8	the	the	DET
ap-766	61	9	n	n	CCONJ
ap-766	61	10	-	-	PUNCT
ap-766	61	11	particle	particle	NOUN
ap-766	61	12	case	case	NOUN
ap-766	61	13	.	.	PUNCT
ap-766	62	1	the	the	DET
ap-766	62	2	output	output	NOUN
ap-766	62	3	density	density	NOUN
ap-766	62	4	matrix	matrix	NOUN
ap-766	62	5	has	have	VERB
ap-766	62	6	to	to	PART
ap-766	62	7	involve	involve	VERB
ap-766	62	8	only	only	ADV
ap-766	62	9	the	the	DET
ap-766	62	10	scalar	scalar	ADJ
ap-766	62	11	terms	term	NOUN
ap-766	62	12	(	(	PUNCT
ap-766	62	13	multiplied	multiply	VERB
ap-766	62	14	by	by	ADP
ap-766	62	15	an	an	DET
ap-766	62	16	arbitrary	arbitrary	ADJ
ap-766	62	17	constant	constant	NOUN
ap-766	62	18	)	)	PUNCT
ap-766	62	19	and	and	CCONJ
ap-766	62	20	the	the	DET
ap-766	62	21	vector	vector	NOUN
ap-766	62	22	terms	term	NOUN
ap-766	62	23	(	(	PUNCT
ap-766	62	24	multiplied	multiply	VERB
ap-766	62	25	by	by	ADP
ap-766	62	26	a	a	DET
ap-766	62	27	constant	constant	ADJ
ap-766	62	28	with	with	ADP
ap-766	62	29	the	the	DET
ap-766	62	30	parameters	parameter	NOUN
ap-766	62	31	of	of	ADP
ap-766	62	32	the	the	DET
ap-766	62	33	initial	initial	ADJ
ap-766	62	34	state	state	NOUN
ap-766	62	35	pij	pij	NOUN
ap-766	62	36	)	)	PUNCT
ap-766	62	37	.	.	PUNCT
ap-766	63	1	these	these	DET
ap-766	63	2	terms	term	NOUN
ap-766	63	3	can	can	AUX
ap-766	63	4	be	be	AUX
ap-766	63	5	constructed	construct	VERB
ap-766	63	6	by	by	ADP
ap-766	63	7	the	the	DET
ap-766	63	8	tensor	tensor	NOUN
ap-766	63	9	product	product	NOUN
ap-766	63	10	of	of	ADP
ap-766	63	11	the	the	DET
ap-766	63	12	one	one	NUM
ap-766	63	13	-	-	PUNCT
ap-766	63	14	particle	particle	NOUN
ap-766	63	15	scalar	scalar	NOUN
ap-766	63	16	i	i	PROPN
ap-766	63	17	and	and	CCONJ
ap-766	63	18	vector	vector	NOUN
ap-766	63	19	a	a	DET
ap-766	63	20	ij	ij	NOUN
ap-766	63	21	,	,	PUNCT
ap-766	63	22	and	and	CCONJ
ap-766	63	23	the	the	DET
ap-766	63	24	two	two	NUM
ap-766	63	25	particle	particle	NOUN
ap-766	63	26	scalar	scalar	ADJ
ap-766	63	27	and	and	CCONJ
ap-766	63	28	vector	vector	NOUN
ap-766	63	29	terms	term	NOUN
ap-766	63	30	.	.	PUNCT
ap-766	64	1	to	to	PART
ap-766	64	2	obtain	obtain	VERB
ap-766	64	3	a	a	DET
ap-766	64	4	scalar	scalar	ADJ
ap-766	64	5	term	term	NOUN
ap-766	64	6	we	we	PRON
ap-766	64	7	have	have	VERB
ap-766	64	8	to	to	PART
ap-766	64	9	sum	sum	VERB
ap-766	64	10	over	over	ADP
ap-766	64	11	all	all	DET
ap-766	64	12	free	free	ADJ
ap-766	64	13	indices	index	NOUN
ap-766	64	14	,	,	PUNCT
ap-766	64	15	and	and	CCONJ
ap-766	64	16	for	for	ADP
ap-766	64	17	a	a	DET
ap-766	64	18	vector	vector	NOUN
ap-766	64	19	term	term	NOUN
ap-766	64	20	two	two	NUM
ap-766	64	21	indices	index	NOUN
ap-766	64	22	must	must	AUX
ap-766	64	23	remain	remain	VERB
ap-766	64	24	free	free	ADJ
ap-766	64	25	(	(	PUNCT
ap-766	64	26	these	these	PRON
ap-766	64	27	are	be	AUX
ap-766	64	28	later	later	ADV
ap-766	64	29	summed	sum	VERB
ap-766	64	30	with	with	ADP
ap-766	64	31	the	the	DET
ap-766	64	32	parameters	parameter	NOUN
ap-766	64	33	pij	pij	VERB
ap-766	64	34	)	)	PUNCT
ap-766	64	35	.	.	PUNCT
ap-766	65	1	the	the	DET
ap-766	65	2	summation	summation	NOUN
ap-766	65	3	is	be	AUX
ap-766	65	4	done	do	VERB
ap-766	65	5	in	in	ADP
ap-766	65	6	such	such	DET
ap-766	65	7	a	a	DET
ap-766	65	8	way	way	NOUN
ap-766	65	9	that	that	PRON
ap-766	65	10	one	one	NUM
ap-766	65	11	summation	summation	NOUN
ap-766	65	12	index	index	NOUN
ap-766	65	13	is	be	AUX
ap-766	65	14	in	in	ADP
ap-766	65	15	the	the	DET
ap-766	65	16	first	first	ADJ
ap-766	65	17	position	position	NOUN
ap-766	65	18	while	while	SCONJ
ap-766	65	19	the	the	DET
ap-766	65	20	second	second	NOUN
ap-766	65	21	is	be	AUX
ap-766	65	22	in	in	ADP
ap-766	65	23	the	the	DET
ap-766	65	24	second	second	ADJ
ap-766	65	25	position	position	NOUN
ap-766	65	26	of	of	ADP
ap-766	65	27	the	the	DET
ap-766	65	28	generators	generator	NOUN
ap-766	65	29	(	(	PUNCT
ap-766	65	30	6	6	NUM
ap-766	65	31	)	)	PUNCT
ap-766	65	32	.	.	PUNCT
ap-766	66	1	for	for	ADP
ap-766	66	2	example	example	NOUN
ap-766	66	3	we	we	PRON
ap-766	66	4	will	will	AUX
ap-766	66	5	show	show	VERB
ap-766	66	6	the	the	DET
ap-766	66	7	explicit	explicit	ADJ
ap-766	66	8	form	form	NOUN
ap-766	66	9	of	of	ADP
ap-766	66	10	the	the	DET
ap-766	66	11	scalar	scalar	ADJ
ap-766	66	12	and	and	CCONJ
ap-766	66	13	vector	vector	NOUN
ap-766	66	14	terms	term	NOUN
ap-766	66	15	for	for	ADP
ap-766	66	16	the	the	DET
ap-766	66	17	case	case	NOUN
ap-766	66	18	n	n	X
ap-766	66	19	�	�	PROPN
ap-766	66	20	3	3	NUM
ap-766	66	21	(	(	PUNCT
ap-766	66	22	for	for	ADP
ap-766	66	23	more	more	ADJ
ap-766	66	24	information	information	NOUN
ap-766	66	25	on	on	ADP
ap-766	66	26	three	three	NUM
ap-766	66	27	-	-	PUNCT
ap-766	66	28	particle	particle	NOUN
ap-766	66	29	universal	universal	ADJ
ap-766	66	30	processes	process	NOUN
ap-766	66	31	see	see	VERB
ap-766	66	32	[	[	X
ap-766	66	33	6	6	NUM
ap-766	66	34	]	]	PUNCT
ap-766	66	35	):	):	PUNCT
ap-766	66	36	�	�	PROPN
ap-766	66	37	scalar	scalar	ADJ
ap-766	66	38	terms	term	NOUN
ap-766	66	39	–	–	PUNCT
ap-766	66	40	a	a	DET
ap-766	66	41	a	a	DET
ap-766	66	42	iij	iij	NOUN
ap-766	66	43	ji	ji	PROPN
ap-766	66	44	�	�	PROPN
ap-766	66	45	�	�	PROPN
ap-766	66	46	,	,	PUNCT
ap-766	66	47	a	a	DET
ap-766	66	48	i	i	PROPN
ap-766	66	49	aij	aij	PROPN
ap-766	66	50	ji	ji	PROPN
ap-766	66	51	�	�	PROPN
ap-766	66	52	�	�	PROPN
ap-766	66	53	,	,	PUNCT
ap-766	66	54	i	i	PRON
ap-766	66	55	a	a	DET
ap-766	66	56	a	a	DET
ap-766	66	57	�	�	PROPN
ap-766	66	58	�	�	PROPN
ap-766	66	59	ij	ij	NOUN
ap-766	66	60	ji	ji	PROPN
ap-766	66	61	,	,	PUNCT
ap-766	66	62	–	–	PUNCT
ap-766	66	63	a	a	DET
ap-766	66	64	a	a	DET
ap-766	66	65	aij	aij	PROPN
ap-766	66	66	jk	jk	PROPN
ap-766	66	67	ki	ki	PROPN
ap-766	66	68	�	�	PROPN
ap-766	66	69	�	�	PROPN
ap-766	66	70	�	�	PROPN
ap-766	66	71	hermitian	hermitian	PROPN
ap-766	66	72	conjugate	conjugate	ADJ
ap-766	66	73	�	�	PROPN
ap-766	66	74	vector	vector	NOUN
ap-766	66	75	terms	term	NOUN
ap-766	66	76	–	–	PUNCT
ap-766	66	77	a	a	DET
ap-766	66	78	i	i	PRON
ap-766	66	79	iij	iij	PROPN
ap-766	66	80	�	�	PROPN
ap-766	66	81	�	�	PROPN
ap-766	66	82	,	,	PUNCT
ap-766	66	83	i	i	PRON
ap-766	66	84	a	a	PRON
ap-766	66	85	i	i	PROPN
ap-766	66	86	�	�	PROPN
ap-766	66	87	�	�	PROPN
ap-766	67	1	ij	ij	NOUN
ap-766	67	2	,	,	PUNCT
ap-766	68	1	i	i	PRON
ap-766	68	2	i	i	PROPN
ap-766	68	3	a	a	DET
ap-766	68	4	�	�	PROPN
ap-766	68	5	�	�	PROPN
ap-766	68	6	ij	ij	NOUN
ap-766	68	7	,	,	PUNCT
ap-766	68	8	–	–	PUNCT
ap-766	68	9	a	a	DET
ap-766	68	10	a	a	DET
ap-766	68	11	iik	iik	PROPN
ap-766	68	12	kj	kj	PROPN
ap-766	68	13	�	�	PROPN
ap-766	68	14	�	�	PROPN
ap-766	68	15	,	,	PUNCT
ap-766	68	16	a	a	DET
ap-766	68	17	i	i	PRON
ap-766	68	18	aik	aik	NOUN
ap-766	68	19	kj	kj	PROPN
ap-766	68	20	�	�	PROPN
ap-766	68	21	�	�	PROPN
ap-766	68	22	,	,	PUNCT
ap-766	68	23	i	i	PRON
ap-766	68	24	a	a	DET
ap-766	68	25	a	a	DET
ap-766	68	26	�	�	PROPN
ap-766	68	27	�	�	PROPN
ap-766	68	28	ik	ik	PROPN
ap-766	68	29	kj	kj	PROPN
ap-766	68	30	+	+	PROPN
ap-766	68	31	hermitian	hermitian	ADJ
ap-766	68	32	conjugate	conjugate	ADJ
ap-766	68	33	–	–	PUNCT
ap-766	68	34	a	a	DET
ap-766	68	35	a	a	DET
ap-766	68	36	aij	aij	PROPN
ap-766	68	37	kl	kl	PROPN
ap-766	68	38	lk	lk	PROPN
ap-766	68	39	�	�	PROPN
ap-766	68	40	�	�	PROPN
ap-766	68	41	,	,	PUNCT
ap-766	68	42	a	a	DET
ap-766	68	43	a	a	DET
ap-766	68	44	akl	akl	PROPN
ap-766	68	45	ij	ij	NOUN
ap-766	68	46	lk	lk	PROPN
ap-766	68	47	�	�	PROPN
ap-766	68	48	�	�	PROPN
ap-766	68	49	,	,	PUNCT
ap-766	68	50	a	a	DET
ap-766	68	51	a	a	DET
ap-766	68	52	akl	akl	PROPN
ap-766	68	53	lk	lk	PROPN
ap-766	68	54	ij	ij	PROPN
ap-766	68	55	�	�	PROPN
ap-766	68	56	�	�	PROPN
ap-766	68	57	,	,	PUNCT
ap-766	68	58	–	–	PUNCT
ap-766	68	59	a	a	DET
ap-766	68	60	a	a	DET
ap-766	68	61	aik	aik	NOUN
ap-766	68	62	kl	kl	PROPN
ap-766	68	63	lj	lj	PROPN
ap-766	68	64	�	�	PROPN
ap-766	68	65	�	�	PROPN
ap-766	68	66	,	,	PUNCT
ap-766	68	67	a	a	DET
ap-766	68	68	a	a	DET
ap-766	68	69	akl	akl	PROPN
ap-766	68	70	ik	ik	PROPN
ap-766	68	71	lj	lj	PROPN
ap-766	68	72	�	�	PROPN
ap-766	68	73	�	�	PROPN
ap-766	68	74	,	,	PUNCT
ap-766	68	75	a	a	DET
ap-766	68	76	a	a	DET
ap-766	68	77	aik	aik	NOUN
ap-766	68	78	lj	lj	PROPN
ap-766	68	79	kl	kl	PROPN
ap-766	68	80	�	�	PROPN
ap-766	68	81	�	�	PROPN
ap-766	68	82	+	+	PROPN
ap-766	68	83	hermitian	hermitian	ADJ
ap-766	68	84	conjugate	conjugate	VERB
ap-766	68	85	in	in	ADP
ap-766	68	86	this	this	DET
ap-766	68	87	case	case	NOUN
ap-766	68	88	the	the	DET
ap-766	68	89	output	output	NOUN
ap-766	68	90	density	density	NOUN
ap-766	68	91	matrix	matrix	NOUN
ap-766	68	92	�	�	NOUN
ap-766	68	93	out	out	ADP
ap-766	68	94	(	(	PUNCT
ap-766	68	95	)	)	PUNCT
ap-766	68	96	p	p	NOUN
ap-766	68	97	depends	depend	VERB
ap-766	68	98	on	on	ADP
ap-766	68	99	23	23	NUM
ap-766	68	100	real	real	ADJ
ap-766	68	101	parameters	parameter	NOUN
ap-766	68	102	,	,	PUNCT
ap-766	68	103	which	which	PRON
ap-766	68	104	are	be	AUX
ap-766	68	105	restricted	restrict	VERB
ap-766	68	106	by	by	ADP
ap-766	68	107	the	the	DET
ap-766	68	108	positivity	positivity	NOUN
ap-766	68	109	of	of	ADP
ap-766	68	110	this	this	DET
ap-766	68	111	operator	operator	NOUN
ap-766	68	112	.	.	PUNCT
ap-766	69	1	compared	compare	VERB
ap-766	69	2	with	with	ADP
ap-766	69	3	just	just	ADV
ap-766	69	4	five	five	NUM
ap-766	69	5	real	real	ADJ
ap-766	69	6	parameters	parameter	NOUN
ap-766	69	7	in	in	ADP
ap-766	69	8	the	the	DET
ap-766	69	9	two	two	NUM
ap-766	69	10	-	-	PUNCT
ap-766	69	11	particle	particle	NOUN
ap-766	69	12	case	case	NOUN
ap-766	69	13	,	,	PUNCT
ap-766	69	14	we	we	PRON
ap-766	69	15	see	see	VERB
ap-766	69	16	that	that	SCONJ
ap-766	69	17	the	the	DET
ap-766	69	18	complexity	complexity	NOUN
ap-766	69	19	of	of	ADP
ap-766	69	20	the	the	DET
ap-766	69	21	n	n	CCONJ
ap-766	69	22	-	-	PUNCT
ap-766	69	23	particle	particle	NOUN
ap-766	69	24	covariant	covariant	NOUN
ap-766	69	25	mapping	mapping	NOUN
ap-766	69	26	grows	grow	VERB
ap-766	69	27	rapidly	rapidly	ADV
ap-766	69	28	with	with	ADP
ap-766	69	29	the	the	DET
ap-766	69	30	number	number	NOUN
ap-766	69	31	of	of	ADP
ap-766	69	32	particles	particle	NOUN
ap-766	69	33	n.	n.	NOUN
ap-766	69	34	if	if	SCONJ
ap-766	69	35	we	we	PRON
ap-766	69	36	want	want	VERB
ap-766	69	37	to	to	PART
ap-766	69	38	study	study	VERB
ap-766	69	39	the	the	DET
ap-766	69	40	properties	property	NOUN
ap-766	69	41	the	the	DET
ap-766	69	42	covariant	covariant	ADJ
ap-766	69	43	mappings	mapping	NOUN
ap-766	69	44	in	in	ADP
ap-766	69	45	more	more	ADJ
ap-766	69	46	detail	detail	NOUN
ap-766	69	47	,	,	PUNCT
ap-766	69	48	we	we	PRON
ap-766	69	49	can	can	AUX
ap-766	69	50	simply	simply	ADV
ap-766	69	51	study	study	VERB
ap-766	69	52	the	the	DET
ap-766	69	53	resulting	result	VERB
ap-766	69	54	density	density	NOUN
ap-766	69	55	matrix	matrix	NOUN
ap-766	69	56	for	for	ADP
ap-766	69	57	an	an	DET
ap-766	69	58	arbitrary	arbitrary	ADJ
ap-766	69	59	input	input	NOUN
ap-766	69	60	state	state	NOUN
ap-766	69	61	.	.	PUNCT
ap-766	70	1	due	due	ADP
ap-766	70	2	to	to	ADP
ap-766	70	3	the	the	DET
ap-766	70	4	covariance	covariance	NOUN
ap-766	70	5	(	(	PUNCT
ap-766	70	6	3	3	NUM
ap-766	70	7	)	)	PUNCT
ap-766	70	8	,	,	PUNCT
ap-766	70	9	functions	function	NOUN
ap-766	70	10	like	like	ADP
ap-766	70	11	the	the	DET
ap-766	70	12	entropy	entropy	NOUN
ap-766	70	13	or	or	CCONJ
ap-766	70	14	the	the	DET
ap-766	70	15	entanglement	entanglement	NOUN
ap-766	70	16	measures	measure	NOUN
ap-766	70	17	of	of	ADP
ap-766	70	18	the	the	DET
ap-766	70	19	particular	particular	ADJ
ap-766	70	20	universal	universal	ADJ
ap-766	70	21	process	process	NOUN
ap-766	70	22	will	will	AUX
ap-766	70	23	have	have	VERB
ap-766	70	24	the	the	DET
ap-766	70	25	same	same	ADJ
ap-766	70	26	value	value	NOUN
ap-766	70	27	for	for	ADP
ap-766	70	28	all	all	DET
ap-766	70	29	possible	possible	ADJ
ap-766	70	30	input	input	NOUN
ap-766	70	31	states	state	NOUN
ap-766	70	32	,	,	PUNCT
ap-766	70	33	because	because	SCONJ
ap-766	70	34	these	these	DET
ap-766	70	35	functions	function	NOUN
ap-766	70	36	are	be	AUX
ap-766	70	37	invariant	invariant	ADJ
ap-766	70	38	under	under	ADP
ap-766	70	39	local	local	ADJ
ap-766	70	40	transformations	transformation	NOUN
ap-766	70	41	.	.	PUNCT
ap-766	71	1	the	the	DET
ap-766	71	2	universal	universal	ADJ
ap-766	71	3	processes	process	NOUN
ap-766	71	4	generating	generate	VERB
ap-766	71	5	entangled	entangle	VERB
ap-766	71	6	two	two	NUM
ap-766	71	7	-	-	PUNCT
ap-766	71	8	particle	particle	NOUN
ap-766	71	9	output	output	NOUN
ap-766	71	10	states	state	NOUN
ap-766	71	11	which	which	PRON
ap-766	71	12	do	do	AUX
ap-766	71	13	not	not	PART
ap-766	71	14	contain	contain	VERB
ap-766	71	15	any	any	DET
ap-766	71	16	separable	separable	ADJ
ap-766	71	17	components	component	NOUN
ap-766	71	18	were	be	AUX
ap-766	71	19	studied	study	VERB
ap-766	71	20	in	in	ADP
ap-766	71	21	[	[	X
ap-766	71	22	4	4	NUM
ap-766	71	23	]	]	PUNCT
ap-766	71	24	.	.	PUNCT
ap-766	72	1	it	it	PRON
ap-766	72	2	has	have	AUX
ap-766	72	3	been	be	AUX
ap-766	72	4	shown	show	VERB
ap-766	72	5	that	that	SCONJ
ap-766	72	6	this	this	DET
ap-766	72	7	particular	particular	ADJ
ap-766	72	8	subclass	subclass	NOUN
ap-766	72	9	forms	form	VERB
ap-766	72	10	a	a	DET
ap-766	72	11	one	one	NUM
ap-766	72	12	-	-	PUNCT
ap-766	72	13	parameter	parameter	NOUN
ap-766	72	14	family	family	NOUN
ap-766	72	15	of	of	ADP
ap-766	72	16	totally	totally	ADV
ap-766	72	17	anti	anti	ADJ
ap-766	72	18	-	-	ADJ
ap-766	72	19	symmetric	symmetric	ADJ
ap-766	72	20	states	state	NOUN
ap-766	72	21	with	with	ADP
ap-766	72	22	respect	respect	NOUN
ap-766	72	23	to	to	ADP
ap-766	72	24	permutations	permutation	NOUN
ap-766	72	25	of	of	ADP
ap-766	72	26	the	the	DET
ap-766	72	27	two	two	NUM
ap-766	72	28	particles	particle	NOUN
ap-766	72	29	.	.	PUNCT
ap-766	73	1	we	we	PRON
ap-766	73	2	will	will	AUX
ap-766	73	3	now	now	ADV
ap-766	73	4	give	give	VERB
ap-766	73	5	a	a	DET
ap-766	73	6	generalization	generalization	NOUN
ap-766	73	7	of	of	ADP
ap-766	73	8	this	this	DET
ap-766	73	9	class	class	NOUN
ap-766	73	10	for	for	ADP
ap-766	73	11	the	the	DET
ap-766	73	12	case	case	NOUN
ap-766	73	13	of	of	ADP
ap-766	73	14	n	n	CCONJ
ap-766	73	15	-	-	PUNCT
ap-766	73	16	particle	particle	NOUN
ap-766	73	17	processes	process	NOUN
ap-766	73	18	.	.	PUNCT
ap-766	74	1	3	3	NUM
ap-766	74	2	generalization	generalization	NOUN
ap-766	74	3	of	of	ADP
ap-766	74	4	the	the	DET
ap-766	74	5	universal	universal	ADJ
ap-766	74	6	process	process	NOUN
ap-766	74	7	generating	generate	VERB
ap-766	74	8	anti	anti	ADJ
ap-766	74	9	-	-	ADJ
ap-766	74	10	symmetric	symmetric	ADJ
ap-766	74	11	states	state	NOUN
ap-766	74	12	to	to	ADP
ap-766	74	13	n	n	NOUN
ap-766	74	14	particles	particle	NOUN
ap-766	74	15	in	in	ADP
ap-766	74	16	this	this	DET
ap-766	74	17	section	section	NOUN
ap-766	74	18	we	we	PRON
ap-766	74	19	propose	propose	VERB
ap-766	74	20	a	a	DET
ap-766	74	21	generalization	generalization	NOUN
ap-766	74	22	of	of	ADP
ap-766	74	23	the	the	DET
ap-766	74	24	two	two	NUM
ap-766	74	25	-	-	PUNCT
ap-766	74	26	particle	particle	NOUN
ap-766	74	27	universal	universal	ADJ
ap-766	74	28	process	process	NOUN
ap-766	74	29	generating	generate	VERB
ap-766	74	30	totally	totally	ADV
ap-766	74	31	anti	anti	ADJ
ap-766	74	32	-	-	ADJ
ap-766	74	33	symmetric	symmetric	ADJ
ap-766	74	34	states	state	NOUN
ap-766	74	35	to	to	ADP
ap-766	74	36	an	an	DET
ap-766	74	37	arbitrary	arbitrary	ADJ
ap-766	74	38	number	number	NOUN
ap-766	74	39	of	of	ADP
ap-766	74	40	particles	particle	NOUN
ap-766	74	41	.	.	PUNCT
ap-766	75	1	the	the	DET
ap-766	75	2	initial	initial	ADJ
ap-766	75	3	state	state	NOUN
ap-766	75	4	of	of	ADP
ap-766	75	5	the	the	DET
ap-766	75	6	first	first	ADJ
ap-766	75	7	qudit	qudit	NOUN
ap-766	75	8	is	be	AUX
ap-766	75	9	assumed	assume	VERB
ap-766	75	10	to	to	PART
ap-766	75	11	be	be	AUX
ap-766	75	12	1	1	NUM
ap-766	75	13	without	without	ADP
ap-766	75	14	loss	loss	NOUN
ap-766	75	15	of	of	ADP
ap-766	75	16	generality	generality	NOUN
ap-766	75	17	,	,	PUNCT
ap-766	75	18	due	due	ADP
ap-766	75	19	to	to	ADP
ap-766	75	20	the	the	DET
ap-766	75	21	covariant	covariant	ADJ
ap-766	75	22	condition	condition	NOUN
ap-766	75	23	(	(	PUNCT
ap-766	75	24	3	3	NUM
ap-766	75	25	)	)	PUNCT
ap-766	75	26	.	.	PUNCT
ap-766	76	1	we	we	PRON
ap-766	76	2	will	will	AUX
ap-766	76	3	use	use	VERB
ap-766	76	4	the	the	DET
ap-766	76	5	following	follow	VERB
ap-766	76	6	notation	notation	NOUN
ap-766	76	7	a	a	DET
ap-766	76	8	j	j	PROPN
ap-766	76	9	z	z	PROPN
ap-766	76	10	j	j	PROPN
ap-766	77	1	j	j	PROPN
ap-766	77	2	j	j	PROPN
ap-766	77	3	j	j	PROPN
ap-766	78	1	j	j	PROPN
ap-766	78	2	j	j	PROPN
ap-766	79	1	d	d	PROPN
ap-766	79	2	b	b	PROPN
ap-766	79	3	j	j	PROPN
ap-766	79	4	z	z	PROPN
ap-766	79	5	d	d	PROPN
ap-766	79	6	n	n	PROPN
ap-766	79	7	n	n	CCONJ
ap-766	79	8	n	n	NOUN
ap-766	79	9	d	d	PROPN
ap-766	79	10	n	n	CCONJ
ap-766	79	11	�	�	PROPN
ap-766	79	12	�	�	PROPN
ap-766	79	13	�	�	PROPN
ap-766	79	14	�	�	PROPN
ap-766	79	15	�	�	PROPN
ap-766	79	16	�	�	PROPN
ap-766	79	17	�	�	PROPN
ap-766	79	18	�	�	PROPN
ap-766	79	19	�	�	PROPN
ap-766	79	20	�	�	PROPN
ap-766	79	21	{	{	PUNCT
ap-766	79	22	|	|	ADV
ap-766	79	23	(	(	PUNCT
ap-766	79	24	,	,	PUNCT
ap-766	79	25	,	,	PUNCT
ap-766	79	26	,	,	PUNCT
ap-766	79	27	)	)	PUNCT
ap-766	79	28	,	,	PUNCT
ap-766	79	29	}	}	PUNCT
ap-766	79	30	{	{	PUNCT
ap-766	79	31	|	|	ADV
ap-766	79	32	�	�	PROPN
ap-766	79	33	�	�	PROPN
ap-766	79	34	�	�	PROPN
ap-766	79	35	�	�	PROPN
ap-766	79	36	�	�	PROPN
ap-766	79	37	1	1	NUM
ap-766	79	38	22	22	NUM
ap-766	79	39	2	2	NUM
ap-766	79	40	3	3	NUM
ap-766	79	41	�	�	PROPN
ap-766	79	42	�	�	PROPN
ap-766	79	43	�	�	PROPN
ap-766	79	44	�	�	PROPN
ap-766	79	45	�	�	PROPN
ap-766	80	1	j	j	PROPN
ap-766	81	1	j	j	PROPN
ap-766	81	2	j	j	PROPN
ap-766	81	3	j	j	PROPN
ap-766	81	4	j	j	PROPN
ap-766	81	5	j	j	PROPN
ap-766	81	6	d	d	X
ap-766	81	7	j	j	PROPN
ap-766	81	8	n	n	CCONJ
ap-766	81	9	j	j	PROPN
ap-766	81	10	n	n	CCONJ
ap-766	81	11	n	n	CCONJ
ap-766	81	12	�	�	PROPN
ap-766	81	13	�	�	PROPN
ap-766	81	14	�	�	PROPN
ap-766	81	15	�	�	PROPN
ap-766	81	16	�	�	PROPN
ap-766	81	17	�	�	PROPN
ap-766	81	18	�	�	PROPN
ap-766	81	19	(	(	PUNCT
ap-766	81	20	,	,	PUNCT
ap-766	81	21	,	,	PUNCT
ap-766	81	22	)	)	PUNCT
ap-766	81	23	,	,	PUNCT
ap-766	81	24	}	}	PUNCT
ap-766	81	25	{	{	PUNCT
ap-766	81	26	}	}	PUNCT
ap-766	81	27	!	!	PUNCT
ap-766	82	1	sgn	sgn	NOUN
ap-766	82	2	(	(	PUNCT
ap-766	82	3	)	)	PUNCT
ap-766	82	4	)	)	PUNCT
ap-766	82	5	1	1	NUM
ap-766	82	6	1	1	NUM
ap-766	82	7	2	2	NUM
ap-766	82	8	1	1	NUM
ap-766	82	9	2	2	NUM
ap-766	82	10	1	1	NUM
ap-766	82	11	�	�	PROPN
ap-766	82	12	�	�	PROPN
ap-766	82	13	�	�	PROPN
ap-766	82	14	�	�	PROPN
ap-766	82	15	�	�	PROPN
ap-766	82	16	jn	jn	PROPN
ap-766	82	17	pn	pn	PROPN
ap-766	82	18	)	)	PUNCT
ap-766	82	19	,	,	PUNCT
ap-766	82	20	�	�	PROPN
ap-766	82	21	�	�	PROPN
ap-766	82	22	(	(	PUNCT
ap-766	82	23	10	10	NUM
ap-766	82	24	)	)	PUNCT
ap-766	82	25	where	where	SCONJ
ap-766	82	26	pn	pn	PROPN
ap-766	82	27	is	be	AUX
ap-766	82	28	a	a	DET
ap-766	82	29	group	group	NOUN
ap-766	82	30	of	of	ADP
ap-766	82	31	permutations	permutation	NOUN
ap-766	82	32	of	of	ADP
ap-766	82	33	n	n	DET
ap-766	82	34	elements	element	NOUN
ap-766	82	35	.	.	PUNCT
ap-766	83	1	the	the	DET
ap-766	83	2	output	output	NOUN
ap-766	83	3	states	state	NOUN
ap-766	83	4	of	of	ADP
ap-766	83	5	the	the	DET
ap-766	83	6	n	n	CCONJ
ap-766	83	7	-	-	PUNCT
ap-766	83	8	particle	particle	NOUN
ap-766	83	9	universal	universal	ADJ
ap-766	83	10	process	process	NOUN
ap-766	83	11	generating	generate	VERB
ap-766	83	12	totally	totally	ADV
ap-766	83	13	anti	anti	ADJ
ap-766	83	14	-	-	ADJ
ap-766	83	15	symmetric	symmetric	ADJ
ap-766	83	16	states	state	NOUN
ap-766	83	17	form	form	VERB
ap-766	83	18	a	a	DET
ap-766	83	19	one	one	NUM
ap-766	83	20	-	-	PUNCT
ap-766	83	21	parameter	parameter	NOUN
ap-766	83	22	family	family	NOUN
ap-766	83	23	and	and	CCONJ
ap-766	83	24	can	can	AUX
ap-766	83	25	be	be	AUX
ap-766	83	26	written	write	VERB
ap-766	83	27	in	in	ADP
ap-766	83	28	the	the	DET
ap-766	83	29	form	form	NOUN
ap-766	83	30	�	�	PROPN
ap-766	83	31	n	n	CCONJ
ap-766	83	32	anti	anti	X
ap-766	83	33	n	n	CCONJ
ap-766	83	34	n	n	CCONJ
ap-766	83	35	anti	anti	X
ap-766	83	36	n	n	CCONJ
ap-766	83	37	n	n	PRON
ap-766	83	38	antip	antip	NOUN
ap-766	83	39	p	p	X
ap-766	83	40	(	(	PUNCT
ap-766	83	41	)	)	PUNCT
ap-766	83	42	(	(	PUNCT
ap-766	83	43	)	)	PUNCT
ap-766	83	44	(	(	PUNCT
ap-766	83	45	)	)	PUNCT
ap-766	83	46	(	(	PUNCT
ap-766	83	47	)	)	PUNCT
ap-766	83	48	(	(	PUNCT
ap-766	83	49	)	)	PUNCT
ap-766	83	50	(	(	PUNCT
ap-766	83	51	)	)	PUNCT
ap-766	83	52	�	�	PROPN
ap-766	83	53	�	�	PROPN
ap-766	83	54	1	1	NUM
ap-766	83	55	,	,	PUNCT
ap-766	83	56	p	p	NOUN
ap-766	83	57	n	n	CCONJ
ap-766	83	58	(	(	PUNCT
ap-766	83	59	)	)	PUNCT
ap-766	83	60	,	,	PUNCT
ap-766	83	61	�	�	PROPN
ap-766	83	62	0	0	NUM
ap-766	83	63	1	1	NUM
ap-766	83	64	,	,	PUNCT
ap-766	83	65	(	(	PUNCT
ap-766	83	66	11	11	NUM
ap-766	83	67	)	)	PUNCT
ap-766	83	68	where	where	SCONJ
ap-766	83	69	the	the	DET
ap-766	83	70	matrices	matrix	NOUN
ap-766	83	71	n	n	X
ap-766	83	72	anti	anti	X
ap-766	83	73	(	(	PUNCT
ap-766	83	74	)	)	PUNCT
ap-766	83	75	and	and	CCONJ
ap-766	83	76	n	n	PRON
ap-766	83	77	anti	anti	ADJ
ap-766	83	78	(	(	PUNCT
ap-766	83	79	)	)	PUNCT
ap-766	83	80	are	be	AUX
ap-766	83	81	given	give	VERB
ap-766	83	82	by	by	ADP
ap-766	83	83	n	n	X
ap-766	83	84	anti	anti	PROPN
ap-766	83	85	j	j	PROPN
ap-766	83	86	a	a	PROPN
ap-766	83	87	n	n	X
ap-766	83	88	anti	anti	X
ap-766	83	89	n	n	PROPN
ap-766	83	90	d	d	PROPN
ap-766	83	91	d	d	PROPN
ap-766	83	92	n	n	PROPN
ap-766	84	1	j	j	PROPN
ap-766	84	2	j	j	PROPN
ap-766	84	3	d	d	PROPN
ap-766	84	4	(	(	PUNCT
ap-766	84	5	)	)	PUNCT
ap-766	84	6	(	(	PUNCT
ap-766	84	7	(	(	PUNCT
ap-766	84	8	)	)	PUNCT
ap-766	84	9	!	!	PUNCT
ap-766	85	1	(	(	PUNCT
ap-766	85	2	)	)	PUNCT
ap-766	85	3	(	(	PUNCT
ap-766	85	4	)	)	PUNCT
ap-766	85	5	{	{	PUNCT
ap-766	85	6	}	}	PUNCT
ap-766	85	7	{	{	PUNCT
ap-766	85	8	}	}	PUNCT
ap-766	85	9	,	,	PUNCT
ap-766	85	10	�	�	PROPN
ap-766	85	11	�	�	PROPN
ap-766	85	12	�	�	PROPN
ap-766	85	13	�	�	PROPN
ap-766	85	14	�	�	PROPN
ap-766	85	15	�	�	PROPN
ap-766	85	16	1	1	NUM
ap-766	85	17	1	1	NUM
ap-766	85	18	1	1	NUM
ap-766	85	19	�	�	PROPN
ap-766	85	20	�	�	PROPN
ap-766	85	21	�	�	PROPN
ap-766	85	22	�	�	PROPN
ap-766	85	23	)	)	PUNCT
ap-766	85	24	(	(	PUNCT
ap-766	85	25	)	)	PUNCT
ap-766	85	26	!	!	PUNCT
ap-766	86	1	(	(	PUNCT
ap-766	86	2	)	)	PUNCT
ap-766	86	3	(	(	PUNCT
ap-766	86	4	)	)	PUNCT
ap-766	86	5	{	{	PUNCT
ap-766	86	6	}	}	PUNCT
ap-766	86	7	{	{	PUNCT
ap-766	86	8	}	}	PUNCT
ap-766	86	9	.	.	PUNCT
ap-766	87	1	�	�	PROPN
ap-766	87	2	�	�	PROPN
ap-766	87	3	�	�	PROPN
ap-766	87	4	�	�	PROPN
ap-766	87	5	�	�	PROPN
ap-766	87	6	n	n	PROPN
ap-766	87	7	d	d	PROPN
ap-766	87	8	d	d	PROPN
ap-766	87	9	n	n	PROPN
ap-766	87	10	j	j	PROPN
ap-766	87	11	j	j	PROPN
ap-766	87	12	j	j	PROPN
ap-766	87	13	bd	bd	PROPN
ap-766	87	14	1	1	NUM
ap-766	87	15	1	1	NUM
ap-766	87	16	�	�	PROPN
ap-766	87	17	�	�	PROPN
ap-766	87	18	�	�	PROPN
ap-766	87	19	�	�	PROPN
ap-766	87	20	(	(	PUNCT
ap-766	87	21	12	12	NUM
ap-766	87	22	)	)	PUNCT
ap-766	87	23	in	in	ADP
ap-766	87	24	the	the	DET
ap-766	87	25	case	case	NOUN
ap-766	87	26	n	n	PRON
ap-766	87	27	�	�	PROPN
ap-766	87	28	d	d	PROPN
ap-766	87	29	,	,	PUNCT
ap-766	87	30	i.e.	i.e.	X
ap-766	87	31	when	when	SCONJ
ap-766	87	32	the	the	DET
ap-766	87	33	number	number	NOUN
ap-766	87	34	of	of	ADP
ap-766	87	35	particles	particle	NOUN
ap-766	87	36	is	be	AUX
ap-766	87	37	equal	equal	ADJ
ap-766	87	38	to	to	ADP
ap-766	87	39	the	the	DET
ap-766	87	40	dimension	dimension	NOUN
ap-766	87	41	of	of	ADP
ap-766	87	42	the	the	DET
ap-766	87	43	one	one	NUM
ap-766	87	44	-	-	PUNCT
ap-766	87	45	particle	particle	NOUN
ap-766	87	46	hilbert	hilbert	NOUN
ap-766	87	47	space	space	NOUN
ap-766	87	48	,	,	PUNCT
ap-766	87	49	we	we	PRON
ap-766	87	50	have	have	VERB
ap-766	87	51	to	to	PART
ap-766	87	52	put	put	VERB
ap-766	87	53	p	p	NOUN
ap-766	87	54	n	n	CCONJ
ap-766	87	55	(	(	PUNCT
ap-766	87	56	)	)	PUNCT
ap-766	87	57	�	�	PROPN
ap-766	87	58	0	0	NUM
ap-766	87	59	and	and	CCONJ
ap-766	87	60	the	the	DET
ap-766	87	61	one	one	NUM
ap-766	87	62	-	-	PUNCT
ap-766	87	63	parameter	parameter	NOUN
ap-766	87	64	family	family	NOUN
ap-766	87	65	collapses	collapse	VERB
ap-766	87	66	to	to	ADP
ap-766	87	67	a	a	DET
ap-766	87	68	single	single	ADJ
ap-766	87	69	process	process	NOUN
ap-766	87	70	generating	generate	VERB
ap-766	87	71	an	an	DET
ap-766	87	72	n	n	CCONJ
ap-766	87	73	-	-	PUNCT
ap-766	87	74	particle	particle	NOUN
ap-766	87	75	singlet	singlet	NOUN
ap-766	87	76	state	state	NOUN
ap-766	87	77	.	.	PUNCT
ap-766	88	1	this	this	PRON
ap-766	88	2	is	be	AUX
ap-766	88	3	the	the	DET
ap-766	88	4	only	only	ADJ
ap-766	88	5	case	case	NOUN
ap-766	88	6	when	when	SCONJ
ap-766	88	7	the	the	DET
ap-766	88	8	one	one	NUM
ap-766	88	9	-	-	PUNCT
ap-766	88	10	parameter	parameter	NOUN
ap-766	88	11	family	family	NOUN
ap-766	88	12	produces	produce	VERB
ap-766	88	13	a	a	DET
ap-766	88	14	pure	pure	ADJ
ap-766	88	15	state	state	NOUN
ap-766	88	16	,	,	PUNCT
ap-766	88	17	while	while	SCONJ
ap-766	88	18	in	in	ADP
ap-766	88	19	all	all	DET
ap-766	88	20	other	other	ADJ
ap-766	88	21	possible	possible	ADJ
ap-766	88	22	cases	case	NOUN
ap-766	88	23	the	the	DET
ap-766	88	24	output	output	NOUN
ap-766	88	25	state	state	PROPN
ap-766	88	26	�	�	PROPN
ap-766	88	27	n	n	CCONJ
ap-766	88	28	anti	anti	NOUN
ap-766	88	29	(	(	PUNCT
ap-766	88	30	)	)	PUNCT
ap-766	88	31	is	be	AUX
ap-766	88	32	always	always	ADV
ap-766	88	33	mixed	mixed	ADJ
ap-766	88	34	.	.	PUNCT
ap-766	89	1	the	the	DET
ap-766	89	2	maximally	maximally	ADV
ap-766	89	3	mixed	mixed	ADJ
ap-766	89	4	state	state	NOUN
ap-766	89	5	is	be	AUX
ap-766	89	6	described	describe	VERB
ap-766	89	7	by	by	ADP
ap-766	89	8	the	the	DET
ap-766	89	9	parameter	parameter	NOUN
ap-766	89	10	p	p	PROPN
ap-766	89	11	d	d	PROPN
ap-766	89	12	n	n	PRON
ap-766	89	13	dn	dn	PROPN
ap-766	89	14	(	(	PUNCT
ap-766	89	15	)	)	PUNCT
ap-766	89	16	�	�	PROPN
ap-766	89	17	�	�	PROPN
ap-766	89	18	and	and	CCONJ
ap-766	89	19	the	the	DET
ap-766	89	20	output	output	NOUN
ap-766	89	21	density	density	NOUN
ap-766	89	22	matrix	matrix	NOUN
ap-766	89	23	involves	involve	VERB
ap-766	89	24	all	all	DET
ap-766	89	25	d	d	PROPN
ap-766	89	26	n	n	CCONJ
ap-766	89	27	�	�	PROPN
ap-766	89	28	�	�	PROPN
ap-766	89	29	�	�	PROPN
ap-766	89	30	�	�	PROPN
ap-766	89	31	�	�	PROPN
ap-766	89	32	n	n	CCONJ
ap-766	89	33	-	-	PUNCT
ap-766	89	34	particles	particle	NOUN
ap-766	89	35	anti	anti	ADJ
ap-766	89	36	-	-	ADJ
ap-766	89	37	symmetric	symmetric	ADJ
ap-766	89	38	states	state	NOUN
ap-766	89	39	with	with	ADP
ap-766	89	40	the	the	DET
ap-766	89	41	same	same	ADJ
ap-766	89	42	probability	probability	NOUN
ap-766	89	43	.	.	PUNCT
ap-766	90	1	in	in	ADP
ap-766	90	2	this	this	DET
ap-766	90	3	case	case	NOUN
ap-766	90	4	the	the	DET
ap-766	90	5	output	output	NOUN
ap-766	90	6	density	density	NOUN
ap-766	90	7	matrix	matrix	NOUN
ap-766	90	8	has	have	VERB
ap-766	90	9	the	the	DET
ap-766	90	10	form	form	NOUN
ap-766	90	11	�	�	NOUN
ap-766	90	12	n	n	CCONJ
ap-766	90	13	anti	anti	X
ap-766	90	14	n	n	X
ap-766	90	15	j	j	PROPN
ap-766	90	16	c	c	PROPN
ap-766	90	17	p	p	PROPN
ap-766	90	18	d	d	PROPN
ap-766	90	19	n	n	PROPN
ap-766	90	20	d	d	PROPN
ap-766	90	21	d	d	PROPN
ap-766	90	22	n	n	PROPN
ap-766	90	23	j	j	PROPN
ap-766	90	24	j	j	PROPN
ap-766	90	25	d	d	PROPN
ap-766	90	26	(	(	PUNCT
ap-766	90	27	)	)	PUNCT
ap-766	90	28	(	(	PUNCT
ap-766	90	29	)	)	PUNCT
ap-766	90	30	{	{	PUNCT
ap-766	90	31	}	}	PUNCT
ap-766	90	32	{	{	PUNCT
ap-766	90	33	}	}	PUNCT
ap-766	90	34	�	�	PROPN
ap-766	90	35	�	�	PROPN
ap-766	90	36	�	�	PROPN
ap-766	90	37	�	�	PROPN
ap-766	90	38	�	�	PROPN
ap-766	90	39	�	�	PROPN
ap-766	90	40	�	�	PROPN
ap-766	90	41	�	�	PROPN
ap-766	90	42	�	�	PROPN
ap-766	90	43	�	�	PROPN
ap-766	90	44	�	�	PROPN
ap-766	90	45	�	�	PROPN
ap-766	90	46	�	�	PROPN
ap-766	90	47	�	�	PROPN
ap-766	90	48	�	�	PROPN
ap-766	90	49	1	1	NUM
ap-766	90	50	�	�	PROPN
ap-766	90	51	�	�	PROPN
ap-766	90	52	�	�	PROPN
ap-766	90	53	,	,	PUNCT
ap-766	90	54	(	(	PUNCT
ap-766	90	55	13	13	NUM
ap-766	90	56	)	)	PUNCT
ap-766	90	57	where	where	SCONJ
ap-766	90	58	the	the	DET
ap-766	90	59	set	set	NOUN
ap-766	90	60	cd	cd	NOUN
ap-766	90	61	is	be	AUX
ap-766	90	62	defined	define	VERB
ap-766	90	63	as	as	ADP
ap-766	90	64	c	c	PROPN
ap-766	90	65	j	j	PROPN
ap-766	90	66	z	z	PROPN
ap-766	90	67	j	j	PROPN
ap-766	90	68	j	j	PROPN
ap-766	90	69	j	j	PROPN
ap-766	90	70	dd	dd	PROPN
ap-766	90	71	n	n	CCONJ
ap-766	90	72	n	n	CCONJ
ap-766	90	73	�	�	PROPN
ap-766	90	74	�	�	PROPN
ap-766	90	75	�	�	PROPN
ap-766	90	76	�	�	PROPN
ap-766	90	77	�	�	PROPN
ap-766	90	78	�	�	PROPN
ap-766	90	79	�	�	PROPN
ap-766	90	80	{	{	PUNCT
ap-766	90	81	|	|	ADV
ap-766	90	82	}	}	PUNCT
ap-766	90	83	�	�	PROPN
ap-766	90	84	�	�	PROPN
ap-766	90	85	1	1	NUM
ap-766	90	86	1	1	NUM
ap-766	90	87	2	2	NUM
ap-766	90	88	.	.	PUNCT
ap-766	91	1	(	(	PUNCT
ap-766	91	2	14	14	NUM
ap-766	91	3	)	)	PUNCT
ap-766	91	4	©	©	PROPN
ap-766	91	5	czech	czech	PROPN
ap-766	91	6	technical	technical	PROPN
ap-766	91	7	university	university	PROPN
ap-766	91	8	publishing	publishing	NOUN
ap-766	91	9	house	house	NOUN
ap-766	91	10	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-766	91	11	35	35	NUM
ap-766	91	12	czech	czech	PROPN
ap-766	91	13	technical	technical	PROPN
ap-766	91	14	university	university	PROPN
ap-766	91	15	in	in	ADP
ap-766	91	16	prague	prague	PROPN
ap-766	91	17	acta	acta	PROPN
ap-766	91	18	polytechnica	polytechnica	PROPN
ap-766	91	19	vol	vol	NOUN
ap-766	91	20	.	.	PROPN
ap-766	92	1	45	45	NUM
ap-766	92	2	no	no	NOUN
ap-766	92	3	.	.	PUNCT
ap-766	93	1	5/2005	5/2005	NUM
ap-766	93	2	this	this	DET
ap-766	93	3	state	state	NOUN
ap-766	93	4	is	be	AUX
ap-766	93	5	invariant	invariant	ADJ
ap-766	93	6	under	under	ADP
ap-766	93	7	the	the	DET
ap-766	93	8	transformation	transformation	NOUN
ap-766	93	9	of	of	ADP
ap-766	93	10	the	the	DET
ap-766	93	11	type	type	NOUN
ap-766	93	12	u	u	PROPN
ap-766	93	13	n	n	CCONJ
ap-766	93	14	�	�	PROPN
ap-766	93	15	and	and	CCONJ
ap-766	93	16	therefore	therefore	ADV
ap-766	93	17	this	this	DET
ap-766	93	18	particular	particular	ADJ
ap-766	93	19	process	process	NOUN
ap-766	93	20	involves	involve	VERB
ap-766	93	21	only	only	ADV
ap-766	93	22	the	the	DET
ap-766	93	23	scalar	scalar	ADJ
ap-766	93	24	part	part	NOUN
ap-766	93	25	.	.	PUNCT
ap-766	94	1	reduced	reduce	VERB
ap-766	94	2	states	state	NOUN
ap-766	94	3	of	of	ADP
ap-766	94	4	k	k	PROPN
ap-766	94	5	particles	particle	NOUN
ap-766	94	6	are	be	AUX
ap-766	94	7	the	the	DET
ap-766	94	8	same	same	ADJ
ap-766	94	9	for	for	ADP
ap-766	94	10	all	all	DET
ap-766	94	11	k	k	ADJ
ap-766	94	12	-	-	ADJ
ap-766	94	13	particle	particle	NOUN
ap-766	94	14	subsystems	subsystem	NOUN
ap-766	94	15	and	and	CCONJ
ap-766	94	16	have	have	VERB
ap-766	94	17	the	the	DET
ap-766	94	18	same	same	ADJ
ap-766	94	19	form	form	NOUN
ap-766	94	20	as	as	ADP
ap-766	94	21	the	the	DET
ap-766	94	22	output	output	NOUN
ap-766	94	23	state	state	NOUN
ap-766	94	24	of	of	ADP
ap-766	94	25	the	the	DET
ap-766	94	26	k	k	ADJ
ap-766	94	27	-	-	PUNCT
ap-766	94	28	particle	particle	NOUN
ap-766	94	29	universal	universal	ADJ
ap-766	94	30	process	process	NOUN
ap-766	94	31	.	.	PUNCT
ap-766	95	1	the	the	DET
ap-766	95	2	only	only	ADJ
ap-766	95	3	difference	difference	NOUN
ap-766	95	4	is	be	AUX
ap-766	95	5	that	that	SCONJ
ap-766	95	6	the	the	DET
ap-766	95	7	parameter	parameter	NOUN
ap-766	95	8	p	p	PROPN
ap-766	95	9	k	k	PROPN
ap-766	95	10	(	(	PUNCT
ap-766	95	11	)	)	PUNCT
ap-766	95	12	has	have	VERB
ap-766	95	13	to	to	PART
ap-766	95	14	be	be	AUX
ap-766	95	15	replaced	replace	VERB
ap-766	95	16	by	by	ADP
ap-766	95	17	p	p	PROPN
ap-766	95	18	n	n	ADV
ap-766	95	19	k	k	PROPN
ap-766	95	20	(	(	PUNCT
ap-766	95	21	)	)	PUNCT
ap-766	95	22	(	(	PUNCT
ap-766	95	23	)	)	PUNCT
ap-766	95	24	,	,	PUNCT
ap-766	95	25	which	which	PRON
ap-766	95	26	is	be	AUX
ap-766	95	27	given	give	VERB
ap-766	95	28	by	by	ADP
ap-766	95	29	p	p	PROPN
ap-766	95	30	k	k	PROPN
ap-766	95	31	n	n	PROPN
ap-766	95	32	k	k	PROPN
ap-766	95	33	nn	nn	PROPN
ap-766	95	34	k	k	PROPN
ap-766	95	35	p	p	PROPN
ap-766	95	36	n	n	PROPN
ap-766	95	37	(	(	PUNCT
ap-766	95	38	)	)	PUNCT
ap-766	95	39	(	(	PUNCT
ap-766	95	40	)	)	PUNCT
ap-766	95	41	(	(	PUNCT
ap-766	95	42	)	)	PUNCT
ap-766	95	43	(	(	PUNCT
ap-766	95	44	)	)	PUNCT
ap-766	95	45	�	�	PROPN
ap-766	95	46	�	�	PROPN
ap-766	95	47	�	�	PROPN
ap-766	95	48	.	.	PUNCT
ap-766	96	1	(	(	PUNCT
ap-766	96	2	15	15	X
ap-766	96	3	)	)	PUNCT
ap-766	96	4	the	the	DET
ap-766	96	5	properties	property	NOUN
ap-766	96	6	of	of	ADP
ap-766	96	7	the	the	DET
ap-766	96	8	two	two	NUM
ap-766	96	9	-	-	PUNCT
ap-766	96	10	particle	particle	NOUN
ap-766	96	11	subsystems	subsystem	NOUN
ap-766	96	12	are	be	AUX
ap-766	96	13	described	describe	VERB
ap-766	96	14	by	by	ADP
ap-766	96	15	the	the	DET
ap-766	96	16	parameter	parameter	NOUN
ap-766	96	17	p	p	PROPN
ap-766	96	18	n	n	CCONJ
ap-766	96	19	(	(	PUNCT
ap-766	96	20	)	)	PUNCT
ap-766	96	21	(	(	PUNCT
ap-766	96	22	)	)	PUNCT
ap-766	96	23	2	2	X
ap-766	96	24	.	.	PUNCT
ap-766	97	1	the	the	DET
ap-766	97	2	entanglement	entanglement	NOUN
ap-766	97	3	of	of	ADP
ap-766	97	4	two	two	NUM
ap-766	97	5	-	-	PUNCT
ap-766	97	6	particle	particle	NOUN
ap-766	97	7	subsystems	subsystem	NOUN
ap-766	97	8	is	be	AUX
ap-766	97	9	quantified	quantify	VERB
ap-766	97	10	by	by	ADP
ap-766	97	11	the	the	DET
ap-766	97	12	negativity	negativity	NOUN
ap-766	97	13	[	[	X
ap-766	97	14	5	5	NUM
ap-766	97	15	]	]	PUNCT
ap-766	97	16	.	.	PUNCT
ap-766	98	1	for	for	ADP
ap-766	98	2	this	this	DET
ap-766	98	3	one	one	NUM
ap-766	98	4	-	-	PUNCT
ap-766	98	5	parameter	parameter	NOUN
ap-766	98	6	family	family	NOUN
ap-766	98	7	this	this	DET
ap-766	98	8	function	function	NOUN
ap-766	98	9	is	be	AUX
ap-766	98	10	given	give	VERB
ap-766	98	11	by	by	ADP
ap-766	98	12	(	(	PUNCT
ap-766	98	13	c.f	c.f	PROPN
ap-766	98	14	.	.	PUNCT
ap-766	99	1	[	[	X
ap-766	99	2	4	4	NUM
ap-766	99	3	]	]	SYM
ap-766	99	4	)	)	PUNCT
ap-766	99	5	�	�	PROPN
ap-766	99	6	�	�	PROPN
ap-766	99	7	n	n	CCONJ
ap-766	99	8	p	p	X
ap-766	99	9	p	p	X
ap-766	100	1	d	d	X
ap-766	100	2	p	p	PROPN
ap-766	100	3	d	d	X
ap-766	100	4	p	p	X
ap-766	100	5	d	d	PROPN
ap-766	100	6	(	(	PUNCT
ap-766	100	7	)	)	PUNCT
ap-766	100	8	(	(	PUNCT
ap-766	100	9	)	)	PUNCT
ap-766	100	10	(	(	PUNCT
ap-766	100	11	)	)	PUNCT
ap-766	100	12	(	(	PUNCT
ap-766	100	13	)	)	PUNCT
ap-766	100	14	(	(	PUNCT
ap-766	100	15	)	)	PUNCT
ap-766	100	16	(	(	PUNCT
ap-766	100	17	)	)	PUNCT
ap-766	100	18	(	(	PUNCT
ap-766	100	19	)	)	PUNCT
ap-766	100	20	2	2	NUM
ap-766	100	21	2	2	NUM
ap-766	100	22	2	2	NUM
ap-766	100	23	2	2	NUM
ap-766	100	24	2	2	NUM
ap-766	100	25	2	2	NUM
ap-766	100	26	2	2	NUM
ap-766	100	27	2	2	NUM
ap-766	100	28	1	1	NUM
ap-766	100	29	1	1	NUM
ap-766	100	30	2	2	NUM
ap-766	100	31	1	1	NUM
ap-766	100	32	1	1	NUM
ap-766	100	33	1	1	NUM
ap-766	100	34	�	�	PROPN
ap-766	100	35	�	�	PROPN
ap-766	100	36	�	�	PROPN
ap-766	100	37	�	�	PROPN
ap-766	100	38	�	�	PROPN
ap-766	100	39	�	�	PROPN
ap-766	100	40	�	�	PROPN
ap-766	100	41	.	.	PUNCT
ap-766	101	1	(	(	PUNCT
ap-766	101	2	16	16	NUM
ap-766	101	3	)	)	PUNCT
ap-766	101	4	the	the	DET
ap-766	101	5	negativity	negativity	NOUN
ap-766	101	6	of	of	ADP
ap-766	101	7	the	the	DET
ap-766	101	8	two	two	NUM
ap-766	101	9	-	-	PUNCT
ap-766	101	10	particle	particle	NOUN
ap-766	101	11	subsystems	subsystem	NOUN
ap-766	101	12	of	of	ADP
ap-766	101	13	the	the	DET
ap-766	101	14	n	n	CCONJ
ap-766	101	15	-	-	PUNCT
ap-766	101	16	particle	particle	NOUN
ap-766	101	17	universal	universal	ADJ
ap-766	101	18	process	process	NOUN
ap-766	101	19	generating	generate	VERB
ap-766	101	20	totally	totally	ADV
ap-766	101	21	anti	anti	ADJ
ap-766	101	22	-	-	ADJ
ap-766	101	23	symmetric	symmetric	ADJ
ap-766	101	24	states	state	NOUN
ap-766	101	25	is	be	AUX
ap-766	101	26	then	then	ADV
ap-766	101	27	given	give	VERB
ap-766	101	28	by	by	ADP
ap-766	101	29	n	n	PRON
ap-766	101	30	p	p	NOUN
ap-766	101	31	n	n	PROPN
ap-766	101	32	d	d	PROPN
ap-766	101	33	n	n	CCONJ
ap-766	101	34	p	p	NOUN
ap-766	101	35	dp	dp	NOUN
ap-766	102	1	n	n	NOUN
ap-766	102	2	d	d	PROPN
ap-766	102	3	p	p	PROPN
ap-766	102	4	n	n	CCONJ
ap-766	102	5	n	n	CCONJ
ap-766	102	6	n	n	CCONJ
ap-766	102	7	n	n	CCONJ
ap-766	102	8	n	n	PROPN
ap-766	102	9	(	(	PUNCT
ap-766	102	10	)	)	PUNCT
ap-766	102	11	(	(	PUNCT
ap-766	102	12	)	)	PUNCT
ap-766	102	13	(	(	PUNCT
ap-766	102	14	)	)	PUNCT
ap-766	102	15	(	(	PUNCT
ap-766	102	16	)	)	PUNCT
ap-766	102	17	(	(	PUNCT
ap-766	102	18	)	)	PUNCT
ap-766	102	19	(	(	PUNCT
ap-766	102	20	)	)	PUNCT
ap-766	102	21	(	(	PUNCT
ap-766	102	22	)	)	PUNCT
ap-766	102	23	�	�	PROPN
ap-766	102	24	�	�	PROPN
ap-766	102	25	�	�	PROPN
ap-766	102	26	�	�	PROPN
ap-766	102	27	�	�	PROPN
ap-766	102	28	�	�	PROPN
ap-766	102	29	�	�	PROPN
ap-766	102	30	�	�	PROPN
ap-766	102	31	�	�	PROPN
ap-766	102	32	�	�	PROPN
ap-766	102	33	1	1	NUM
ap-766	102	34	2	2	NUM
ap-766	102	35	1	1	NUM
ap-766	102	36	2	2	NUM
ap-766	102	37	2	2	NUM
ap-766	102	38	4	4	NUM
ap-766	102	39	4	4	NUM
ap-766	102	40	22	22	NUM
ap-766	102	41	2	2	NUM
ap-766	102	42	4	4	NUM
ap-766	102	43	4	4	NUM
ap-766	102	44	�	�	PROPN
ap-766	102	45	�	�	PROPN
ap-766	102	46	�	�	PROPN
ap-766	102	47	�	�	PROPN
ap-766	102	48	�	�	PROPN
ap-766	102	49	n	n	PROPN
ap-766	102	50	d	d	NOUN
ap-766	102	51	.	.	PUNCT
ap-766	103	1	(	(	PUNCT
ap-766	103	2	17	17	NUM
ap-766	103	3	)	)	PUNCT
ap-766	103	4	this	this	DET
ap-766	103	5	function	function	NOUN
ap-766	103	6	has	have	VERB
ap-766	103	7	a	a	DET
ap-766	103	8	minimum	minimum	NOUN
ap-766	103	9	for	for	ADP
ap-766	103	10	p	p	PROPN
ap-766	103	11	d	d	PROPN
ap-766	103	12	n	n	X
ap-766	103	13	nn	nn	PROPN
ap-766	103	14	(	(	PUNCT
ap-766	103	15	)	)	PUNCT
ap-766	103	16	�	�	PROPN
ap-766	103	17	�	�	PROPN
ap-766	103	18	,	,	PUNCT
ap-766	103	19	(	(	PUNCT
ap-766	103	20	18	18	NUM
ap-766	103	21	)	)	PUNCT
ap-766	103	22	i.e.	i.e.	X
ap-766	103	23	the	the	DET
ap-766	103	24	scalar	scalar	ADJ
ap-766	103	25	process	process	NOUN
ap-766	103	26	that	that	PRON
ap-766	103	27	produces	produce	VERB
ap-766	103	28	the	the	DET
ap-766	103	29	most	most	ADV
ap-766	103	30	disordered	disordered	ADJ
ap-766	103	31	state	state	NOUN
ap-766	103	32	also	also	ADV
ap-766	103	33	produces	produce	VERB
ap-766	103	34	the	the	DET
ap-766	103	35	state	state	NOUN
ap-766	103	36	with	with	ADP
ap-766	103	37	the	the	DET
ap-766	103	38	least	least	ADV
ap-766	103	39	entangled	entangle	VERB
ap-766	103	40	two	two	NUM
ap-766	103	41	-	-	PUNCT
ap-766	103	42	particle	particle	NOUN
ap-766	103	43	subsystems	subsystem	NOUN
ap-766	103	44	.	.	PUNCT
ap-766	104	1	the	the	DET
ap-766	104	2	maximal	maximal	ADJ
ap-766	104	3	value	value	NOUN
ap-766	104	4	of	of	ADP
ap-766	104	5	negativity	negativity	NOUN
ap-766	104	6	is	be	AUX
ap-766	104	7	obtained	obtain	VERB
ap-766	104	8	for	for	ADP
ap-766	104	9	p	p	PROPN
ap-766	104	10	n	n	X
ap-766	104	11	(	(	PUNCT
ap-766	104	12	)	)	PUNCT
ap-766	104	13	�	�	PROPN
ap-766	104	14	1	1	NUM
ap-766	104	15	or	or	CCONJ
ap-766	104	16	p	p	NOUN
ap-766	104	17	n	n	CCONJ
ap-766	104	18	(	(	PUNCT
ap-766	104	19	)	)	PUNCT
ap-766	104	20	�	�	PROPN
ap-766	104	21	0	0	NUM
ap-766	104	22	,	,	PUNCT
ap-766	104	23	depending	depend	VERB
ap-766	104	24	on	on	ADP
ap-766	104	25	the	the	DET
ap-766	104	26	relation	relation	NOUN
ap-766	104	27	between	between	ADP
ap-766	104	28	n	n	PROPN
ap-766	104	29	and	and	CCONJ
ap-766	104	30	d.	d.	NOUN
ap-766	104	31	for	for	ADP
ap-766	104	32	d	d	PROPN
ap-766	104	33	>	>	X
ap-766	104	34	2n	2n	NUM
ap-766	104	35	�	�	PROPN
ap-766	104	36	1	1	NUM
ap-766	104	37	the	the	DET
ap-766	104	38	maximum	maximum	NOUN
ap-766	104	39	is	be	AUX
ap-766	104	40	at	at	ADP
ap-766	104	41	the	the	DET
ap-766	104	42	point	point	NOUN
ap-766	104	43	p	p	NOUN
ap-766	104	44	n	n	CCONJ
ap-766	104	45	(	(	PUNCT
ap-766	104	46	)	)	PUNCT
ap-766	104	47	�	�	PROPN
ap-766	104	48	0	0	NUM
ap-766	104	49	and	and	CCONJ
ap-766	104	50	has	have	VERB
ap-766	104	51	the	the	DET
ap-766	104	52	value	value	NOUN
ap-766	105	1	n	n	NOUN
ap-766	105	2	d	d	X
ap-766	105	3	n	n	CCONJ
ap-766	105	4	n	n	NOUN
ap-766	105	5	d	d	PROPN
ap-766	105	6	n	n	CCONJ
ap-766	105	7	n	n	CCONJ
ap-766	105	8	n	n	ADV
ap-766	105	9	dmax	dmax	X
ap-766	105	10	(	(	PUNCT
ap-766	105	11	)	)	PUNCT
ap-766	105	12	(	(	PUNCT
ap-766	105	13	)	)	PUNCT
ap-766	105	14	(	(	PUNCT
ap-766	105	15	)	)	PUNCT
ap-766	105	16	�	�	PROPN
ap-766	105	17	�	�	PROPN
ap-766	105	18	�	�	PROPN
ap-766	105	19	�	�	PROPN
ap-766	105	20	�	�	PROPN
ap-766	105	21	�	�	PROPN
ap-766	105	22	�	�	PROPN
ap-766	105	23	�	�	PROPN
ap-766	105	24	2	2	NUM
ap-766	105	25	1	1	NUM
ap-766	105	26	2	2	NUM
ap-766	105	27	4	4	NUM
ap-766	105	28	4	4	NUM
ap-766	105	29	2	2	NUM
ap-766	105	30	1	1	NUM
ap-766	105	31	.	.	PUNCT
ap-766	106	1	(	(	PUNCT
ap-766	106	2	19	19	NUM
ap-766	106	3	)	)	PUNCT
ap-766	106	4	for	for	ADP
ap-766	106	5	d	d	X
ap-766	106	6	<	<	X
ap-766	106	7	2n	2n	NUM
ap-766	106	8	�	�	NOUN
ap-766	106	9	1	1	NUM
ap-766	106	10	the	the	DET
ap-766	106	11	maximum	maximum	NOUN
ap-766	106	12	is	be	AUX
ap-766	106	13	at	at	ADP
ap-766	106	14	the	the	DET
ap-766	106	15	point	point	NOUN
ap-766	106	16	p	p	NOUN
ap-766	106	17	n	n	CCONJ
ap-766	106	18	(	(	PUNCT
ap-766	106	19	)	)	PUNCT
ap-766	106	20	�	�	PROPN
ap-766	106	21	1	1	NUM
ap-766	106	22	and	and	CCONJ
ap-766	106	23	is	be	AUX
ap-766	106	24	given	give	VERB
ap-766	106	25	by	by	ADP
ap-766	106	26	n	n	PROPN
ap-766	106	27	d	d	PROPN
ap-766	106	28	n	n	ADV
ap-766	106	29	dmax	dmax	ADJ
ap-766	106	30	(	(	PUNCT
ap-766	106	31	)	)	PUNCT
ap-766	106	32	�	�	PROPN
ap-766	106	33	�	�	PROPN
ap-766	106	34	�	�	PROPN
ap-766	106	35	�	�	PROPN
ap-766	106	36	2	2	NUM
ap-766	106	37	1	1	NUM
ap-766	106	38	1	1	NUM
ap-766	106	39	1	1	NUM
ap-766	106	40	.	.	PUNCT
ap-766	107	1	(	(	PUNCT
ap-766	107	2	20	20	NUM
ap-766	107	3	)	)	PUNCT
ap-766	107	4	in	in	ADP
ap-766	107	5	the	the	DET
ap-766	107	6	case	case	NOUN
ap-766	107	7	when	when	SCONJ
ap-766	107	8	d	d	PROPN
ap-766	107	9	�	�	PROPN
ap-766	107	10	2n	2n	NUM
ap-766	107	11	�	�	PROPN
ap-766	107	12	1	1	NUM
ap-766	107	13	the	the	DET
ap-766	107	14	values	value	NOUN
ap-766	107	15	of	of	ADP
ap-766	107	16	negativity	negativity	NOUN
ap-766	107	17	at	at	ADP
ap-766	107	18	the	the	DET
ap-766	107	19	points	point	NOUN
ap-766	107	20	p	p	NOUN
ap-766	107	21	n	n	CCONJ
ap-766	107	22	(	(	PUNCT
ap-766	107	23	)	)	PUNCT
ap-766	107	24	�	�	PROPN
ap-766	107	25	0and	0and	PROPN
ap-766	107	26	p	p	PROPN
ap-766	107	27	n	n	CCONJ
ap-766	107	28	(	(	PUNCT
ap-766	107	29	)	)	PUNCT
ap-766	107	30	�	�	PROPN
ap-766	107	31	1are	1are	NOUN
ap-766	107	32	equal	equal	ADJ
ap-766	107	33	,	,	PUNCT
ap-766	107	34	so	so	SCONJ
ap-766	107	35	the	the	DET
ap-766	107	36	function	function	NOUN
ap-766	107	37	n	n	CCONJ
ap-766	107	38	p	p	NOUN
ap-766	107	39	n	n	X
ap-766	107	40	(	(	PUNCT
ap-766	107	41	)	)	PUNCT
ap-766	107	42	(	(	PUNCT
ap-766	107	43	)	)	PUNCT
ap-766	107	44	has	have	VERB
ap-766	107	45	two	two	NUM
ap-766	107	46	equal	equal	ADJ
ap-766	107	47	peaks	peak	NOUN
ap-766	107	48	.	.	PUNCT
ap-766	108	1	the	the	DET
ap-766	108	2	output	output	NOUN
ap-766	108	3	density	density	NOUN
ap-766	108	4	matrix	matrix	NOUN
ap-766	108	5	(	(	PUNCT
ap-766	108	6	11	11	NUM
ap-766	108	7	)	)	PUNCT
ap-766	108	8	has	have	VERB
ap-766	108	9	the	the	DET
ap-766	108	10	form	form	NOUN
ap-766	108	11	of	of	ADP
ap-766	108	12	the	the	DET
ap-766	108	13	convex	convex	ADJ
ap-766	108	14	sum	sum	NOUN
ap-766	108	15	of	of	ADP
ap-766	108	16	two	two	NUM
ap-766	108	17	density	density	NOUN
ap-766	108	18	matrices	matrix	NOUN
ap-766	108	19	,	,	PUNCT
ap-766	108	20	n	n	X
ap-766	108	21	anti	anti	ADJ
ap-766	108	22	(	(	PUNCT
ap-766	108	23	)	)	PUNCT
ap-766	108	24	is	be	AUX
ap-766	108	25	the	the	DET
ap-766	108	26	sum	sum	NOUN
ap-766	108	27	of	of	ADP
ap-766	108	28	the	the	DET
ap-766	108	29	projectors	projector	NOUN
ap-766	108	30	onto	onto	ADP
ap-766	108	31	the	the	DET
ap-766	108	32	anti	anti	ADJ
ap-766	108	33	-	-	ADJ
ap-766	108	34	symmetric	symmetric	ADJ
ap-766	108	35	subspace	subspace	NOUN
ap-766	108	36	involving	involve	VERB
ap-766	108	37	the	the	DET
ap-766	108	38	initial	initial	ADJ
ap-766	108	39	state	state	NOUN
ap-766	108	40	1	1	NUM
ap-766	108	41	,	,	PUNCT
ap-766	108	42	n	n	CCONJ
ap-766	108	43	anti	anti	ADJ
ap-766	108	44	(	(	PUNCT
ap-766	108	45	)	)	PUNCT
ap-766	108	46	involves	involve	VERB
ap-766	108	47	the	the	DET
ap-766	108	48	complementary	complementary	ADJ
ap-766	108	49	projectors	projector	NOUN
ap-766	108	50	to	to	ADP
ap-766	108	51	those	those	PRON
ap-766	108	52	in	in	ADP
ap-766	108	53	n	n	X
ap-766	108	54	anti	anti	ADJ
ap-766	108	55	(	(	PUNCT
ap-766	108	56	)	)	PUNCT
ap-766	108	57	on	on	ADP
ap-766	108	58	the	the	DET
ap-766	108	59	n	n	CCONJ
ap-766	108	60	-	-	PUNCT
ap-766	108	61	particle	particle	NOUN
ap-766	108	62	anti	anti	ADJ
ap-766	108	63	-	-	ADJ
ap-766	108	64	symmetric	symmetric	ADJ
ap-766	108	65	subspace	subspace	NOUN
ap-766	108	66	.	.	PUNCT
ap-766	109	1	for	for	ADP
ap-766	109	2	the	the	DET
ap-766	109	3	special	special	ADJ
ap-766	109	4	case	case	NOUN
ap-766	109	5	of	of	ADP
ap-766	109	6	p	p	PROPN
ap-766	109	7	n	n	CCONJ
ap-766	109	8	(	(	PUNCT
ap-766	109	9	)	)	PUNCT
ap-766	109	10	�	�	PROPN
ap-766	109	11	0	0	NUM
ap-766	109	12	only	only	ADV
ap-766	109	13	the	the	DET
ap-766	109	14	matrix	matrix	NOUN
ap-766	109	15	n	n	CCONJ
ap-766	109	16	anti	anti	X
ap-766	109	17	(	(	PUNCT
ap-766	109	18	)	)	PUNCT
ap-766	109	19	is	be	AUX
ap-766	109	20	involved	involve	VERB
ap-766	109	21	and	and	CCONJ
ap-766	109	22	the	the	DET
ap-766	109	23	output	output	NOUN
ap-766	109	24	density	density	NOUN
ap-766	109	25	matrix	matrix	NOUN
ap-766	109	26	can	can	AUX
ap-766	109	27	be	be	AUX
ap-766	109	28	written	write	VERB
ap-766	109	29	as	as	ADP
ap-766	109	30	�	�	NOUN
ap-766	109	31	n	n	CCONJ
ap-766	109	32	anti	anti	X
ap-766	109	33	n	n	X
ap-766	109	34	in	in	ADP
ap-766	109	35	n	n	CCONJ
ap-766	109	36	n	n	NOUN
ap-766	109	37	d	d	PROPN
ap-766	109	38	d	d	PROPN
ap-766	109	39	n	n	PROPN
ap-766	109	40	a	a	DET
ap-766	109	41	a	a	X
ap-766	109	42	(	(	PUNCT
ap-766	109	43	)	)	PUNCT
ap-766	109	44	(	(	PUNCT
ap-766	109	45	)	)	PUNCT
ap-766	109	46	!	!	PUNCT
ap-766	110	1	(	(	PUNCT
ap-766	110	2	)	)	PUNCT
ap-766	110	3	(	(	PUNCT
ap-766	110	4	)	)	PUNCT
ap-766	110	5	�	�	PROPN
ap-766	110	6	�	�	PROPN
ap-766	110	7	�	�	PROPN
ap-766	110	8	�	�	PROPN
ap-766	110	9	�	�	PROPN
ap-766	110	10	1	1	NUM
ap-766	110	11	1	1	NUM
ap-766	110	12	1	1	NUM
ap-766	110	13	�	�	PROPN
ap-766	110	14	,	,	PUNCT
ap-766	110	15	(	(	PUNCT
ap-766	110	16	21	21	NUM
ap-766	110	17	)	)	PUNCT
ap-766	110	18	where	where	SCONJ
ap-766	110	19	an	an	PRON
ap-766	110	20	is	be	AUX
ap-766	110	21	the	the	DET
ap-766	110	22	projection	projection	NOUN
ap-766	110	23	operator	operator	NOUN
ap-766	110	24	onto	onto	ADP
ap-766	110	25	the	the	DET
ap-766	110	26	anti	anti	ADJ
ap-766	110	27	-	-	ADJ
ap-766	110	28	symmetric	symmetric	ADJ
ap-766	110	29	subspace	subspace	NOUN
ap-766	110	30	of	of	ADP
ap-766	110	31	the	the	DET
ap-766	110	32	n	n	CCONJ
ap-766	110	33	-	-	PUNCT
ap-766	110	34	particle	particle	NOUN
ap-766	110	35	hilbert	hilbert	NOUN
ap-766	110	36	space	space	NOUN
ap-766	110	37	.	.	PUNCT
ap-766	111	1	hence	hence	ADV
ap-766	111	2	this	this	DET
ap-766	111	3	particular	particular	ADJ
ap-766	111	4	process	process	NOUN
ap-766	111	5	can	can	AUX
ap-766	111	6	be	be	AUX
ap-766	111	7	realized	realize	VERB
ap-766	111	8	by	by	ADP
ap-766	111	9	a	a	DET
ap-766	111	10	certain	certain	ADJ
ap-766	111	11	projector	projector	NOUN
ap-766	111	12	acting	act	VERB
ap-766	111	13	on	on	ADP
ap-766	111	14	the	the	DET
ap-766	111	15	initial	initial	ADJ
ap-766	111	16	state	state	NOUN
ap-766	111	17	.	.	PUNCT
ap-766	112	1	universal	universal	ADJ
ap-766	112	2	processes	process	NOUN
ap-766	112	3	with	with	ADP
ap-766	112	4	this	this	DET
ap-766	112	5	property	property	NOUN
ap-766	112	6	will	will	AUX
ap-766	112	7	be	be	AUX
ap-766	112	8	studied	study	VERB
ap-766	112	9	in	in	ADP
ap-766	112	10	the	the	DET
ap-766	112	11	following	follow	VERB
ap-766	112	12	section	section	NOUN
ap-766	112	13	.	.	PUNCT
ap-766	113	1	4	4	NUM
ap-766	113	2	realization	realization	NOUN
ap-766	113	3	of	of	ADP
ap-766	113	4	universal	universal	ADJ
ap-766	113	5	processes	process	NOUN
ap-766	113	6	as	as	SCONJ
ap-766	113	7	was	be	AUX
ap-766	113	8	shown	show	VERB
ap-766	113	9	above	above	ADP
ap-766	113	10	,	,	PUNCT
ap-766	113	11	some	some	DET
ap-766	113	12	important	important	ADJ
ap-766	113	13	universal	universal	ADJ
ap-766	113	14	processes	process	NOUN
ap-766	113	15	can	can	AUX
ap-766	113	16	be	be	AUX
ap-766	113	17	realized	realize	VERB
ap-766	113	18	by	by	ADP
ap-766	113	19	the	the	DET
ap-766	113	20	action	action	NOUN
ap-766	113	21	of	of	ADP
ap-766	113	22	certain	certain	ADJ
ap-766	113	23	projectors	projector	NOUN
ap-766	113	24	on	on	ADP
ap-766	113	25	the	the	DET
ap-766	113	26	input	input	NOUN
ap-766	113	27	state	state	NOUN
ap-766	113	28	.	.	PUNCT
ap-766	114	1	besides	besides	SCONJ
ap-766	114	2	the	the	DET
ap-766	114	3	example	example	NOUN
ap-766	114	4	in	in	ADP
ap-766	114	5	the	the	DET
ap-766	114	6	previous	previous	ADJ
ap-766	114	7	section	section	NOUN
ap-766	114	8	,	,	PUNCT
ap-766	114	9	where	where	SCONJ
ap-766	114	10	the	the	DET
ap-766	114	11	projector	projector	NOUN
ap-766	114	12	on	on	ADP
ap-766	114	13	the	the	DET
ap-766	114	14	anti	anti	ADJ
ap-766	114	15	-	-	ADJ
ap-766	114	16	symmetric	symmetric	ADJ
ap-766	114	17	subspace	subspace	NOUN
ap-766	114	18	of	of	ADP
ap-766	114	19	the	the	DET
ap-766	114	20	n	n	CCONJ
ap-766	114	21	-	-	PUNCT
ap-766	114	22	particle	particle	NOUN
ap-766	114	23	hilbert	hilbert	NOUN
ap-766	114	24	space	space	NOUN
ap-766	114	25	was	be	AUX
ap-766	114	26	used	use	VERB
ap-766	114	27	,	,	PUNCT
ap-766	114	28	we	we	PRON
ap-766	114	29	can	can	AUX
ap-766	114	30	mention	mention	VERB
ap-766	114	31	the	the	DET
ap-766	114	32	optimal	optimal	ADJ
ap-766	114	33	universal	universal	ADJ
ap-766	114	34	copying	copying	NOUN
ap-766	114	35	process	process	NOUN
ap-766	114	36	from	from	ADP
ap-766	114	37	one	one	NUM
ap-766	114	38	to	to	ADP
ap-766	114	39	n	n	PRON
ap-766	114	40	particles	particle	NOUN
ap-766	114	41	,	,	PUNCT
ap-766	114	42	which	which	PRON
ap-766	114	43	can	can	AUX
ap-766	114	44	be	be	AUX
ap-766	114	45	implemented	implement	VERB
ap-766	114	46	by	by	ADP
ap-766	114	47	using	use	VERB
ap-766	114	48	a	a	DET
ap-766	114	49	projector	projector	NOUN
ap-766	114	50	on	on	ADP
ap-766	114	51	the	the	DET
ap-766	114	52	symmetric	symmetric	ADJ
ap-766	114	53	subspace	subspace	NOUN
ap-766	114	54	of	of	ADP
ap-766	114	55	the	the	DET
ap-766	114	56	n	n	CCONJ
ap-766	114	57	-	-	PUNCT
ap-766	114	58	particle	particle	NOUN
ap-766	114	59	hilbert	hilbert	NOUN
ap-766	114	60	space	space	NOUN
ap-766	114	61	[	[	X
ap-766	114	62	2	2	NUM
ap-766	114	63	]	]	PUNCT
ap-766	114	64	.	.	PUNCT
ap-766	115	1	these	these	DET
ap-766	115	2	projectors	projector	NOUN
ap-766	115	3	play	play	VERB
ap-766	115	4	the	the	DET
ap-766	115	5	role	role	NOUN
ap-766	115	6	of	of	ADP
ap-766	115	7	kraus	kraus	PROPN
ap-766	115	8	operators	operators	PROPN
ap-766	115	9	for	for	ADP
ap-766	115	10	a	a	DET
ap-766	115	11	given	give	VERB
ap-766	115	12	processes	process	NOUN
ap-766	115	13	and	and	CCONJ
ap-766	115	14	can	can	AUX
ap-766	115	15	be	be	AUX
ap-766	115	16	used	use	VERB
ap-766	115	17	to	to	PART
ap-766	115	18	construct	construct	VERB
ap-766	115	19	a	a	DET
ap-766	115	20	unitary	unitary	ADJ
ap-766	115	21	evolution	evolution	NOUN
ap-766	115	22	operator	operator	NOUN
ap-766	115	23	in	in	ADP
ap-766	115	24	the	the	DET
ap-766	115	25	canonical	canonical	ADJ
ap-766	115	26	way	way	NOUN
ap-766	116	1	[	[	X
ap-766	116	2	7	7	NUM
ap-766	116	3	]	]	X
ap-766	116	4	,	,	PUNCT
ap-766	116	5	as	as	SCONJ
ap-766	116	6	will	will	AUX
ap-766	116	7	be	be	AUX
ap-766	116	8	shown	show	VERB
ap-766	116	9	below	below	ADP
ap-766	116	10	.	.	PUNCT
ap-766	117	1	the	the	DET
ap-766	117	2	natural	natural	ADJ
ap-766	117	3	question	question	NOUN
ap-766	117	4	arises	arise	VERB
ap-766	117	5	what	what	DET
ap-766	117	6	class	class	NOUN
ap-766	117	7	of	of	ADP
ap-766	117	8	projectors	projector	NOUN
ap-766	117	9	have	have	VERB
ap-766	117	10	this	this	DET
ap-766	117	11	property	property	NOUN
ap-766	117	12	of	of	ADP
ap-766	117	13	realizing	realize	VERB
ap-766	117	14	covariant	covariant	ADJ
ap-766	117	15	processes	process	NOUN
ap-766	117	16	.	.	PUNCT
ap-766	118	1	let	let	VERB
ap-766	118	2	t	t	PROPN
ap-766	118	3	be	be	AUX
ap-766	118	4	a	a	DET
ap-766	118	5	projector	projector	NOUN
ap-766	118	6	on	on	ADP
ap-766	118	7	some	some	DET
ap-766	118	8	subspace	subspace	NOUN
ap-766	118	9	of	of	ADP
ap-766	118	10	the	the	DET
ap-766	118	11	n	n	CCONJ
ap-766	118	12	-	-	PUNCT
ap-766	118	13	particle	particle	NOUN
ap-766	118	14	hilbert	hilbert	NOUN
ap-766	118	15	space	space	NOUN
ap-766	118	16	and	and	CCONJ
ap-766	118	17	�	�	PROPN
ap-766	118	18	in	in	ADP
ap-766	118	19	.	.	PUNCT
ap-766	119	1	the	the	DET
ap-766	119	2	mapping	mapping	NOUN
ap-766	119	3	on	on	ADP
ap-766	119	4	the	the	DET
ap-766	119	5	density	density	NOUN
ap-766	119	6	operators	operator	NOUN
ap-766	119	7	�	�	PROPN
ap-766	119	8	�	�	PROPN
ap-766	119	9	out	out	ADP
ap-766	119	10	int	int	NOUN
ap-766	119	11	t	t	PROPN
ap-766	119	12	�	�	PROPN
ap-766	119	13	�	�	PROPN
ap-766	119	14	,	,	PUNCT
ap-766	119	15	where	where	SCONJ
ap-766	119	16	�	�	PROPN
ap-766	119	17	is	be	AUX
ap-766	119	18	normalizing	normalize	VERB
ap-766	119	19	factor	factor	NOUN
ap-766	119	20	�	�	NOUN
ap-766	119	21	out	out	ADP
ap-766	119	22	to	to	PART
ap-766	119	23	be	be	AUX
ap-766	119	24	a	a	DET
ap-766	119	25	density	density	NOUN
ap-766	119	26	matrix	matrix	NOUN
ap-766	119	27	,	,	PUNCT
ap-766	119	28	fulfills	fulfill	VERB
ap-766	119	29	the	the	DET
ap-766	119	30	covariant	covariant	ADJ
ap-766	119	31	condition	condition	NOUN
ap-766	119	32	if	if	SCONJ
ap-766	119	33	the	the	DET
ap-766	119	34	following	follow	VERB
ap-766	119	35	equality	equality	NOUN
ap-766	119	36	is	be	AUX
ap-766	119	37	satisfied	satisfied	ADJ
ap-766	119	38	for	for	ADP
ap-766	119	39	all	all	DET
ap-766	119	40	one	one	NUM
ap-766	119	41	-	-	PUNCT
ap-766	119	42	particle	particle	NOUN
ap-766	119	43	unitary	unitary	ADJ
ap-766	119	44	transformations	transformation	NOUN
ap-766	119	45	u	u	NOUN
ap-766	119	46	and	and	CCONJ
ap-766	119	47	for	for	ADP
ap-766	119	48	all	all	DET
ap-766	119	49	one	one	NUM
ap-766	119	50	-	-	PUNCT
ap-766	119	51	particle	particle	NOUN
ap-766	119	52	pure	pure	ADJ
ap-766	119	53	input	input	NOUN
ap-766	119	54	states	state	NOUN
ap-766	120	1	p	p	NOUN
ap-766	120	2	p	p	X
ap-766	120	3	:	:	PUNCT
ap-766	120	4	t	t	PROPN
ap-766	120	5	u	u	X
ap-766	120	6	u	u	INTJ
ap-766	120	7	i	i	PRON
ap-766	120	8	t	t	VERB
ap-766	121	1	u	u	NOUN
ap-766	122	1	t	t	X
ap-766	123	1	i	i	PRON
ap-766	123	2	tu	tu	PROPN
ap-766	123	3	n	n	CCONJ
ap-766	123	4	n	n	CCONJ
ap-766	123	5	n	n	CCONJ
ap-766	123	6	n	n	PROPN
ap-766	123	7	(	(	PUNCT
ap-766	123	8	)	)	PUNCT
ap-766	123	9	†	†	PROPN
ap-766	123	10	(	(	PUNCT
ap-766	123	11	)	)	PUNCT
ap-766	123	12	(	(	PUNCT
ap-766	123	13	)	)	PUNCT
ap-766	123	14	(	(	PUNCT
ap-766	123	15	)	)	PUNCT
ap-766	123	16	†	†	PROPN
ap-766	124	1	p	p	X
ap-766	124	2	p	p	X
ap-766	124	3	p	p	X
ap-766	124	4	p	p	X
ap-766	124	5	�	�	PROPN
ap-766	124	6	�	�	PROPN
ap-766	124	7	�	�	PROPN
ap-766	124	8	�	�	PROPN
ap-766	124	9	�	�	PROPN
ap-766	124	10	�	�	PROPN
ap-766	124	11	�	�	PROPN
ap-766	124	12	�	�	PROPN
ap-766	124	13	�	�	PROPN
ap-766	124	14	1	1	NUM
ap-766	124	15	1	1	NUM
ap-766	124	16	(	(	PUNCT
ap-766	124	17	22	22	NUM
ap-766	124	18	)	)	PUNCT
ap-766	124	19	a	a	DET
ap-766	124	20	sufficient	sufficient	ADJ
ap-766	124	21	condition	condition	NOUN
ap-766	124	22	for	for	SCONJ
ap-766	124	23	t	t	PROPN
ap-766	124	24	to	to	PART
ap-766	124	25	satisfy	satisfy	VERB
ap-766	124	26	(	(	PUNCT
ap-766	124	27	22	22	NUM
ap-766	124	28	)	)	PUNCT
ap-766	124	29	is	be	AUX
ap-766	124	30	u	u	PROPN
ap-766	124	31	t	t	PROPN
ap-766	124	32	tun	tun	PROPN
ap-766	124	33	n	n	CCONJ
ap-766	124	34	�	�	PROPN
ap-766	124	35	�	�	PROPN
ap-766	124	36	�	�	PROPN
ap-766	124	37	(	(	PUNCT
ap-766	124	38	)	)	PUNCT
ap-766	124	39	(	(	PUNCT
ap-766	124	40	)	)	PUNCT
ap-766	124	41	,	,	PUNCT
ap-766	124	42	(	(	PUNCT
ap-766	124	43	23	23	NUM
ap-766	124	44	)	)	PUNCT
ap-766	124	45	i.e.	i.e.	X
ap-766	124	46	t	t	PROPN
ap-766	124	47	must	must	AUX
ap-766	124	48	commute	commute	VERB
ap-766	124	49	with	with	ADP
ap-766	124	50	all	all	DET
ap-766	124	51	unitary	unitary	ADJ
ap-766	124	52	transformations	transformation	NOUN
ap-766	124	53	of	of	ADP
ap-766	124	54	the	the	DET
ap-766	124	55	form	form	NOUN
ap-766	124	56	u	u	PROPN
ap-766	124	57	n	n	PRON
ap-766	124	58	�	�	PROPN
ap-766	124	59	(	(	PUNCT
ap-766	124	60	)	)	PUNCT
ap-766	124	61	.	.	PUNCT
ap-766	125	1	all	all	DET
ap-766	125	2	n	n	CCONJ
ap-766	125	3	-	-	PUNCT
ap-766	125	4	particle	particle	NOUN
ap-766	125	5	transformations	transformation	NOUN
ap-766	125	6	u	u	PROPN
ap-766	125	7	n	n	PRON
ap-766	125	8	�	�	PROPN
ap-766	125	9	(	(	PUNCT
ap-766	125	10	)	)	PUNCT
ap-766	125	11	form	form	VERB
ap-766	125	12	an	an	DET
ap-766	125	13	n	n	CCONJ
ap-766	125	14	-	-	PUNCT
ap-766	125	15	particle	particle	NOUN
ap-766	125	16	representation	representation	NOUN
ap-766	125	17	of	of	ADP
ap-766	125	18	a	a	DET
ap-766	125	19	one	one	NUM
ap-766	125	20	-	-	PUNCT
ap-766	125	21	particle	particle	NOUN
ap-766	125	22	unitary	unitary	ADJ
ap-766	125	23	group	group	NOUN
ap-766	125	24	.	.	PUNCT
ap-766	126	1	this	this	DET
ap-766	126	2	representation	representation	NOUN
ap-766	126	3	is	be	AUX
ap-766	126	4	generally	generally	ADV
ap-766	126	5	reducible	reducible	ADJ
ap-766	126	6	for	for	ADP
ap-766	126	7	n	n	X
ap-766	126	8	�	�	PROPN
ap-766	126	9	2	2	NUM
ap-766	126	10	.	.	PROPN
ap-766	126	11	from	from	ADP
ap-766	126	12	schur	schur	PROPN
ap-766	126	13	’s	’s	PART
ap-766	126	14	lemma	lemma	PROPN
ap-766	126	15	,	,	PUNCT
ap-766	126	16	which	which	PRON
ap-766	126	17	states	state	VERB
ap-766	126	18	that	that	SCONJ
ap-766	126	19	a	a	DET
ap-766	126	20	representation	representation	NOUN
ap-766	126	21	is	be	AUX
ap-766	126	22	irreducible	irreducible	ADJ
ap-766	126	23	if	if	SCONJ
ap-766	126	24	and	and	CCONJ
ap-766	126	25	only	only	ADV
ap-766	126	26	if	if	SCONJ
ap-766	126	27	the	the	DET
ap-766	126	28	only	only	ADJ
ap-766	126	29	matrix	matrix	NOUN
ap-766	126	30	commuting	commute	VERB
ap-766	126	31	with	with	ADP
ap-766	126	32	all	all	DET
ap-766	126	33	members	member	NOUN
ap-766	126	34	of	of	ADP
ap-766	126	35	the	the	DET
ap-766	126	36	representation	representation	NOUN
ap-766	126	37	is	be	AUX
ap-766	126	38	proportional	proportional	ADJ
ap-766	126	39	to	to	ADP
ap-766	126	40	the	the	DET
ap-766	126	41	identity	identity	NOUN
ap-766	126	42	,	,	PUNCT
ap-766	126	43	we	we	PRON
ap-766	126	44	can	can	AUX
ap-766	126	45	deduce	deduce	VERB
ap-766	126	46	that	that	SCONJ
ap-766	126	47	if	if	SCONJ
ap-766	126	48	t	t	PROPN
ap-766	126	49	is	be	AUX
ap-766	126	50	proportional	proportional	ADJ
ap-766	126	51	to	to	ADP
ap-766	126	52	the	the	DET
ap-766	126	53	projector	projector	NOUN
ap-766	126	54	on	on	ADP
ap-766	126	55	invariant	invariant	ADJ
ap-766	126	56	subspace	subspace	NOUN
ap-766	126	57	of	of	ADP
ap-766	126	58	the	the	DET
ap-766	126	59	reducible	reducible	ADJ
ap-766	126	60	representation	representation	NOUN
ap-766	126	61	then	then	ADV
ap-766	126	62	condition	condition	NOUN
ap-766	126	63	(	(	PUNCT
ap-766	126	64	23	23	NUM
ap-766	126	65	)	)	PUNCT
ap-766	126	66	is	be	AUX
ap-766	126	67	satisfied	satisfied	ADJ
ap-766	126	68	.	.	PUNCT
ap-766	127	1	more	more	ADV
ap-766	127	2	generally	generally	ADV
ap-766	127	3	,	,	PUNCT
ap-766	127	4	let	let	VERB
ap-766	127	5	{	{	PUNCT
ap-766	127	6	}	}	PUNCT
ap-766	127	7	p	p	X
ap-766	127	8	�	�	PROPN
ap-766	127	9	be	be	AUX
ap-766	127	10	a	a	DET
ap-766	127	11	set	set	NOUN
ap-766	127	12	of	of	ADP
ap-766	127	13	all	all	DET
ap-766	127	14	projectors	projector	NOUN
ap-766	127	15	on	on	ADP
ap-766	127	16	the	the	DET
ap-766	127	17	minimal	minimal	ADJ
ap-766	127	18	invariant	invariant	ADJ
ap-766	127	19	subspaces	subspace	NOUN
ap-766	127	20	,	,	PUNCT
ap-766	127	21	then	then	ADV
ap-766	127	22	operator	operator	NOUN
ap-766	127	23	t	t	PROPN
ap-766	127	24	,	,	PUNCT
ap-766	127	25	which	which	PRON
ap-766	127	26	is	be	AUX
ap-766	127	27	defined	define	VERB
ap-766	127	28	as	as	ADP
ap-766	127	29	t	t	PROPN
ap-766	127	30	p	p	PROPN
ap-766	127	31	�	�	PROPN
ap-766	127	32	�	�	PROPN
ap-766	127	33	�	�	PROPN
ap-766	127	34	�	�	PROPN
ap-766	127	35	,	,	PUNCT
ap-766	127	36	(	(	PUNCT
ap-766	127	37	24	24	NUM
ap-766	127	38	)	)	PUNCT
ap-766	127	39	commutes	commute	NOUN
ap-766	127	40	with	with	ADP
ap-766	127	41	all	all	DET
ap-766	127	42	unitary	unitary	ADJ
ap-766	127	43	operators	operator	NOUN
ap-766	127	44	of	of	ADP
ap-766	127	45	the	the	DET
ap-766	127	46	form	form	NOUN
ap-766	127	47	u	u	PROPN
ap-766	127	48	n	n	PRON
ap-766	127	49	�	�	PROPN
ap-766	127	50	(	(	PUNCT
ap-766	127	51	)	)	PUNCT
ap-766	127	52	,	,	PUNCT
ap-766	127	53	for	for	ADP
ap-766	127	54	arbitrary	arbitrary	ADJ
ap-766	127	55	�	�	PROPN
ap-766	127	56	�	�	PROPN
ap-766	127	57	�	�	PROPN
ap-766	127	58	.	.	PUNCT
ap-766	128	1	now	now	ADV
ap-766	128	2	it	it	PRON
ap-766	128	3	is	be	AUX
ap-766	128	4	obvious	obvious	ADJ
ap-766	128	5	that	that	SCONJ
ap-766	128	6	the	the	DET
ap-766	128	7	mapping	mapping	NOUN
ap-766	128	8	~t	~t	PUNCT
ap-766	128	9	�	�	PROPN
ap-766	128	10	out	out	ADP
ap-766	128	11	n	n	ADP
ap-766	128	12	nt	not	PART
ap-766	128	13	t	t	PROPN
ap-766	129	1	i	i	PRON
ap-766	129	2	t	t	NOUN
ap-766	130	1	t	t	X
ap-766	131	1	i	i	PRON
ap-766	131	2	t	t	PROPN
ap-766	131	3	�	�	PROPN
ap-766	131	4	�	�	PROPN
ap-766	131	5	�	�	PROPN
ap-766	131	6	�	�	PROPN
ap-766	131	7	�	�	PROPN
ap-766	131	8	�	�	PROPN
ap-766	131	9	�	�	PROPN
ap-766	131	10	�	�	PROPN
ap-766	131	11	~	~	PROPN
ap-766	131	12	(	(	PUNCT
ap-766	131	13	)	)	PUNCT
ap-766	131	14	(	(	PUNCT
ap-766	131	15	)	)	PUNCT
ap-766	131	16	[	[	PUNCT
ap-766	131	17	(	(	PUNCT
ap-766	131	18	)	)	PUNCT
ap-766	131	19	]	]	PUNCT
ap-766	131	20	(	(	PUNCT
ap-766	131	21	)	)	PUNCT
ap-766	131	22	†	†	X
ap-766	131	23	(	(	PUNCT
ap-766	131	24	)	)	PUNCT
ap-766	131	25	†p	†p	X
ap-766	131	26	p	p	X
ap-766	131	27	p	p	X
ap-766	131	28	p	p	X
ap-766	131	29	p	p	X
ap-766	131	30	p	p	X
ap-766	131	31	1	1	NUM
ap-766	131	32	1tr	1tr	NOUN
ap-766	131	33	,	,	PUNCT
ap-766	131	34	(	(	PUNCT
ap-766	131	35	25	25	NUM
ap-766	131	36	)	)	PUNCT
ap-766	131	37	where	where	SCONJ
ap-766	131	38	t	t	PROPN
ap-766	131	39	is	be	AUX
ap-766	131	40	of	of	ADP
ap-766	131	41	the	the	DET
ap-766	131	42	form	form	NOUN
ap-766	131	43	(	(	PUNCT
ap-766	131	44	24	24	NUM
ap-766	131	45	)	)	PUNCT
ap-766	131	46	,	,	PUNCT
ap-766	131	47	from	from	ADP
ap-766	131	48	the	the	DET
ap-766	131	49	pure	pure	ADJ
ap-766	131	50	one	one	NUM
ap-766	131	51	-	-	PUNCT
ap-766	131	52	particle	particle	NOUN
ap-766	131	53	input	input	NOUN
ap-766	131	54	states	state	NOUN
ap-766	131	55	to	to	ADP
ap-766	131	56	the	the	DET
ap-766	131	57	n	n	CCONJ
ap-766	131	58	-	-	PUNCT
ap-766	131	59	particle	particle	NOUN
ap-766	131	60	output	output	NOUN
ap-766	131	61	density	density	NOUN
ap-766	131	62	operators	operator	NOUN
ap-766	131	63	satisfies	satisfy	VERB
ap-766	131	64	condition	condition	NOUN
ap-766	131	65	(	(	PUNCT
ap-766	131	66	22	22	NUM
ap-766	131	67	)	)	PUNCT
ap-766	131	68	.	.	PUNCT
ap-766	132	1	the	the	DET
ap-766	132	2	next	next	ADJ
ap-766	132	3	simple	simple	ADJ
ap-766	132	4	consequence	consequence	NOUN
ap-766	132	5	of	of	ADP
ap-766	132	6	the	the	DET
ap-766	132	7	presented	present	VERB
ap-766	132	8	construction	construction	NOUN
ap-766	132	9	is	be	AUX
ap-766	132	10	that	that	SCONJ
ap-766	132	11	any	any	DET
ap-766	132	12	convex	convex	ADJ
ap-766	132	13	combination	combination	NOUN
ap-766	132	14	of	of	ADP
ap-766	132	15	transformations	transformation	NOUN
ap-766	132	16	of	of	ADP
ap-766	132	17	the	the	DET
ap-766	132	18	form	form	NOUN
ap-766	132	19	(	(	PUNCT
ap-766	132	20	25	25	NUM
ap-766	132	21	)	)	PUNCT
ap-766	132	22	also	also	ADV
ap-766	132	23	satisfies	satisfy	VERB
ap-766	132	24	(	(	PUNCT
ap-766	132	25	22	22	NUM
ap-766	132	26	)	)	PUNCT
ap-766	132	27	.	.	PUNCT
ap-766	133	1	even	even	ADV
ap-766	133	2	though	though	SCONJ
ap-766	133	3	transformation	transformation	NOUN
ap-766	133	4	(	(	PUNCT
ap-766	133	5	25	25	NUM
ap-766	133	6	)	)	PUNCT
ap-766	133	7	fulfils	fulfil	VERB
ap-766	133	8	covariant	covariant	ADJ
ap-766	133	9	condition	condition	NOUN
ap-766	133	10	(	(	PUNCT
ap-766	133	11	22	22	NUM
ap-766	133	12	)	)	PUNCT
ap-766	133	13	it	it	PRON
ap-766	133	14	need	need	AUX
ap-766	133	15	not	not	PART
ap-766	133	16	be	be	AUX
ap-766	133	17	completely	completely	ADV
ap-766	133	18	positive	positive	ADJ
ap-766	133	19	,	,	PUNCT
ap-766	133	20	which	which	PRON
ap-766	133	21	is	be	AUX
ap-766	133	22	a	a	DET
ap-766	133	23	necessary	necessary	ADJ
ap-766	133	24	condition	condition	NOUN
ap-766	133	25	for	for	ADP
ap-766	133	26	the	the	DET
ap-766	133	27	physical	physical	ADJ
ap-766	133	28	acceptability	acceptability	NOUN
ap-766	133	29	of	of	ADP
ap-766	133	30	this	this	DET
ap-766	133	31	mapping	mapping	NOUN
ap-766	133	32	.	.	PUNCT
ap-766	134	1	36	36	NUM
ap-766	135	1	©	©	PROPN
ap-766	135	2	czech	czech	PROPN
ap-766	135	3	technical	technical	PROPN
ap-766	135	4	university	university	PROPN
ap-766	135	5	publishing	publishing	NOUN
ap-766	135	6	house	house	NOUN
ap-766	135	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-766	135	8	acta	acta	PROPN
ap-766	135	9	polytechnica	polytechnica	PROPN
ap-766	135	10	vol	vol	NOUN
ap-766	135	11	.	.	PROPN
ap-766	136	1	45	45	NUM
ap-766	136	2	no	no	NOUN
ap-766	136	3	.	.	PUNCT
ap-766	137	1	5/2005	5/2005	NUM
ap-766	137	2	czech	czech	PROPN
ap-766	137	3	technical	technical	PROPN
ap-766	137	4	university	university	PROPN
ap-766	137	5	in	in	ADP
ap-766	137	6	prague	prague	PROPN
ap-766	137	7	from	from	ADP
ap-766	137	8	the	the	DET
ap-766	137	9	kraus	kraus	PROPN
ap-766	137	10	theorem	theorem	PROPN
ap-766	137	11	we	we	PRON
ap-766	137	12	have	have	VERB
ap-766	137	13	the	the	DET
ap-766	137	14	following	follow	VERB
ap-766	137	15	criterion	criterion	NOUN
ap-766	137	16	[	[	X
ap-766	137	17	8	8	NUM
ap-766	137	18	]	]	PUNCT
ap-766	137	19	:	:	PUNCT
ap-766	137	20	linear	linear	PROPN
ap-766	137	21	mapping	mapping	NOUN
ap-766	137	22	p	p	NOUN
ap-766	137	23	from	from	ADP
ap-766	137	24	the	the	DET
ap-766	137	25	density	density	NOUN
ap-766	137	26	matrices	matrix	NOUN
ap-766	137	27	on	on	ADP
ap-766	137	28	the	the	DET
ap-766	137	29	input	input	NOUN
ap-766	137	30	hilbert	hilbert	NOUN
ap-766	137	31	space	space	NOUN
ap-766	137	32	to	to	ADP
ap-766	137	33	the	the	DET
ap-766	137	34	density	density	NOUN
ap-766	137	35	matrices	matrix	NOUN
ap-766	137	36	on	on	ADP
ap-766	137	37	the	the	DET
ap-766	137	38	output	output	NOUN
ap-766	137	39	hilbert	hilbert	NOUN
ap-766	137	40	space	space	NOUN
ap-766	137	41	is	be	AUX
ap-766	137	42	completely	completely	ADV
ap-766	137	43	positive	positive	ADJ
ap-766	137	44	if	if	SCONJ
ap-766	138	1	and	and	CCONJ
ap-766	138	2	only	only	ADV
ap-766	138	3	if	if	SCONJ
ap-766	138	4	there	there	PRON
ap-766	138	5	exists	exist	VERB
ap-766	138	6	a	a	DET
ap-766	138	7	so	so	ADV
ap-766	138	8	called	call	VERB
ap-766	138	9	kraus	kraus	PROPN
ap-766	138	10	decomposition	decomposition	NOUN
ap-766	138	11	of	of	ADP
ap-766	138	12	a	a	DET
ap-766	138	13	given	give	VERB
ap-766	138	14	transformation	transformation	NOUN
ap-766	138	15	,	,	PUNCT
ap-766	138	16	i.e.	i.e.	X
ap-766	138	17	if	if	SCONJ
ap-766	138	18	there	there	PRON
ap-766	138	19	exists	exist	VERB
ap-766	138	20	a	a	DET
ap-766	138	21	set	set	NOUN
ap-766	138	22	of	of	ADP
ap-766	138	23	linear	linear	PROPN
ap-766	138	24	mappings	mapping	NOUN
ap-766	138	25	,	,	PUNCT
ap-766	138	26	kraus	kraus	PROPN
ap-766	138	27	operators	operators	PROPN
ap-766	138	28	,	,	PUNCT
ap-766	138	29	{	{	PUNCT
ap-766	138	30	}	}	PUNCT
ap-766	138	31	ek	ek	AUX
ap-766	138	32	satisfying	satisfy	VERB
ap-766	138	33	the	the	DET
ap-766	138	34	two	two	NUM
ap-766	138	35	following	follow	VERB
ap-766	138	36	conditions	condition	NOUN
ap-766	138	37	for	for	ADP
ap-766	138	38	any	any	DET
ap-766	138	39	input	input	NOUN
ap-766	138	40	density	density	NOUN
ap-766	138	41	operator	operator	NOUN
ap-766	138	42	,	,	PUNCT
ap-766	138	43	�	�	PROPN
ap-766	138	44	�	�	PROPN
ap-766	138	45	p	p	NOUN
ap-766	138	46	e	e	X
ap-766	138	47	e	e	X
ap-766	138	48	e	e	X
ap-766	138	49	e	e	X
ap-766	138	50	k	k	PROPN
ap-766	138	51	kk	kk	PROPN
ap-766	138	52	k	k	PROPN
ap-766	138	53	kk	kk	PROPN
ap-766	138	54	(	(	PUNCT
ap-766	138	55	)	)	PUNCT
ap-766	138	56	†	†	PROPN
ap-766	138	57	†	†	X
ap-766	138	58	�	�	PROPN
ap-766	138	59	tr	tr	VERB
ap-766	138	60	(	(	PUNCT
ap-766	138	61	26	26	NUM
ap-766	138	62	)	)	PUNCT
ap-766	138	63	e	e	NOUN
ap-766	138	64	e	e	X
ap-766	138	65	ik	ik	PROPN
ap-766	138	66	k	k	PROPN
ap-766	138	67	k	k	PROPN
ap-766	138	68	†	†	PROPN
ap-766	138	69	�	�	PROPN
ap-766	138	70	.	.	PUNCT
ap-766	139	1	(	(	PUNCT
ap-766	139	2	27	27	NUM
ap-766	139	3	)	)	PUNCT
ap-766	139	4	the	the	DET
ap-766	139	5	definition	definition	NOUN
ap-766	139	6	of	of	ADP
ap-766	139	7	transformation	transformation	NOUN
ap-766	139	8	~t	~t	PUNCT
ap-766	139	9	guarantees	guarantee	VERB
ap-766	139	10	fulfillment	fulfillment	NOUN
ap-766	139	11	of	of	ADP
ap-766	139	12	the	the	DET
ap-766	139	13	first	first	ADJ
ap-766	139	14	condition	condition	NOUN
ap-766	139	15	(	(	PUNCT
ap-766	139	16	26	26	NUM
ap-766	139	17	)	)	PUNCT
ap-766	139	18	.	.	PUNCT
ap-766	140	1	to	to	PART
ap-766	140	2	satisfy	satisfy	VERB
ap-766	140	3	(	(	PUNCT
ap-766	140	4	27	27	NUM
ap-766	140	5	)	)	PUNCT
ap-766	140	6	we	we	PRON
ap-766	140	7	must	must	AUX
ap-766	140	8	restrict	restrict	VERB
ap-766	140	9	the	the	DET
ap-766	140	10	range	range	NOUN
ap-766	140	11	of	of	ADP
ap-766	140	12	parameters	parameter	NOUN
ap-766	140	13	�	�	PROPN
ap-766	140	14	in	in	ADP
ap-766	140	15	(	(	PUNCT
ap-766	140	16	24	24	NUM
ap-766	140	17	)	)	PUNCT
ap-766	140	18	to	to	PART
ap-766	140	19	inequality	inequality	VERB
ap-766	140	20	�	�	PROPN
ap-766	140	21	�	�	PROPN
ap-766	140	22	1for	1for	PROPN
ap-766	140	23	all	all	DET
ap-766	140	24	�	�	PROPN
ap-766	140	25	.	.	PUNCT
ap-766	141	1	the	the	DET
ap-766	141	2	construction	construction	NOUN
ap-766	141	3	of	of	ADP
ap-766	141	4	the	the	DET
ap-766	141	5	completely	completely	ADV
ap-766	141	6	positive	positive	ADJ
ap-766	141	7	universal	universal	ADJ
ap-766	141	8	processes	process	NOUN
ap-766	141	9	which	which	PRON
ap-766	141	10	was	be	AUX
ap-766	141	11	described	describe	VERB
ap-766	141	12	above	above	ADV
ap-766	141	13	can	can	AUX
ap-766	141	14	still	still	ADV
ap-766	141	15	be	be	AUX
ap-766	141	16	generalized	generalize	VERB
ap-766	141	17	.	.	PUNCT
ap-766	142	1	the	the	DET
ap-766	142	2	transformation	transformation	NOUN
ap-766	142	3	of	of	ADP
ap-766	142	4	the	the	DET
ap-766	142	5	form	form	NOUN
ap-766	142	6	(	(	PUNCT
ap-766	142	7	25	25	NUM
ap-766	142	8	)	)	PUNCT
ap-766	142	9	describes	describe	VERB
ap-766	142	10	the	the	DET
ap-766	142	11	universal	universal	ADJ
ap-766	142	12	process	process	NOUN
ap-766	142	13	from	from	ADP
ap-766	142	14	one	one	NUM
ap-766	142	15	to	to	ADP
ap-766	142	16	n	n	NOUN
ap-766	142	17	particles	particle	NOUN
ap-766	142	18	.	.	PUNCT
ap-766	143	1	by	by	ADP
ap-766	143	2	applying	apply	VERB
ap-766	143	3	the	the	DET
ap-766	143	4	partial	partial	ADJ
ap-766	143	5	trace	trace	NOUN
ap-766	143	6	operation	operation	NOUN
ap-766	143	7	over	over	ADP
ap-766	143	8	arbitrary	arbitrary	ADJ
ap-766	143	9	m	m	NOUN
ap-766	143	10	particles	particle	NOUN
ap-766	143	11	,	,	PUNCT
ap-766	143	12	m	m	VERB
ap-766	143	13	<	<	X
ap-766	143	14	n	n	CCONJ
ap-766	143	15	,	,	PUNCT
ap-766	143	16	to	to	ADP
ap-766	143	17	the	the	DET
ap-766	143	18	n	n	CCONJ
ap-766	143	19	-	-	PUNCT
ap-766	143	20	particle	particle	NOUN
ap-766	143	21	output	output	NOUN
ap-766	143	22	state	state	NOUN
ap-766	143	23	of	of	ADP
ap-766	143	24	transformation	transformation	NOUN
ap-766	143	25	(	(	PUNCT
ap-766	143	26	25	25	NUM
ap-766	143	27	)	)	PUNCT
ap-766	143	28	we	we	PRON
ap-766	143	29	get	get	VERB
ap-766	143	30	the	the	DET
ap-766	143	31	transformation	transformation	NOUN
ap-766	143	32	from	from	ADP
ap-766	143	33	one	one	NUM
ap-766	143	34	particle	particle	NOUN
ap-766	143	35	pure	pure	ADJ
ap-766	143	36	states	state	NOUN
ap-766	143	37	to	to	ADP
ap-766	143	38	an	an	DET
ap-766	143	39	(	(	PUNCT
ap-766	143	40	n	n	X
ap-766	143	41	�	�	PROPN
ap-766	143	42	m)-particle	m)-particle	NOUN
ap-766	143	43	.	.	PUNCT
ap-766	144	1	it	it	PRON
ap-766	144	2	is	be	AUX
ap-766	144	3	easy	easy	ADJ
ap-766	144	4	to	to	PART
ap-766	144	5	see	see	VERB
ap-766	144	6	that	that	SCONJ
ap-766	144	7	in	in	ADP
ap-766	144	8	this	this	DET
ap-766	144	9	case	case	NOUN
ap-766	144	10	the	the	DET
ap-766	144	11	covariant	covariant	ADJ
ap-766	144	12	condition	condition	NOUN
ap-766	144	13	remains	remain	VERB
ap-766	144	14	satisfied	satisfied	ADJ
ap-766	144	15	and	and	CCONJ
ap-766	144	16	we	we	PRON
ap-766	144	17	get	get	VERB
ap-766	144	18	the	the	DET
ap-766	144	19	completely	completely	ADV
ap-766	144	20	positive	positive	ADJ
ap-766	144	21	universal	universal	ADJ
ap-766	144	22	process	process	NOUN
ap-766	144	23	on	on	ADP
ap-766	144	24	n	n	DET
ap-766	144	25	�	�	PROPN
ap-766	144	26	m	m	PROPN
ap-766	144	27	particles	particle	NOUN
ap-766	144	28	.	.	PUNCT
ap-766	145	1	the	the	DET
ap-766	145	2	last	last	ADJ
ap-766	145	3	form	form	NOUN
ap-766	145	4	of	of	ADP
ap-766	145	5	the	the	DET
ap-766	145	6	universal	universal	ADJ
ap-766	145	7	process	process	NOUN
ap-766	145	8	on	on	ADP
ap-766	145	9	n	n	DET
ap-766	145	10	particles	particle	NOUN
ap-766	145	11	built	build	VERB
ap-766	145	12	up	up	ADP
ap-766	145	13	of	of	ADP
ap-766	145	14	projectors	projector	NOUN
ap-766	145	15	is	be	AUX
ap-766	145	16	therefore	therefore	ADV
ap-766	145	17	the	the	DET
ap-766	145	18	following	follow	VERB
ap-766	145	19	�	�	PROPN
ap-766	145	20	�	�	PROPN
ap-766	145	21	�	�	PROPN
ap-766	145	22	�	�	PROPN
ap-766	145	23	�	�	PROPN
ap-766	145	24	out	out	ADP
ap-766	145	25	i	i	PRON
ap-766	146	1	i	i	PROPN
ap-766	147	1	l	l	VERB
ap-766	147	2	in	in	ADP
ap-766	147	3	l	l	PROPN
ap-766	147	4	l	l	X
ap-766	147	5	l	l	NOUN
ap-766	147	6	in	in	ADP
ap-766	147	7	m	m	PROPN
ap-766	147	8	t	t	NOUN
ap-766	148	1	i	i	PRON
ap-766	148	2	t	t	PROPN
ap-766	149	1	t	t	X
ap-766	150	1	i	i	PRON
ap-766	150	2	�	�	PROPN
ap-766	150	3	�	�	PROPN
ap-766	150	4	�	�	PROPN
ap-766	150	5	�	�	PROPN
ap-766	150	6	�	�	PROPN
ap-766	150	7	�	�	PROPN
ap-766	150	8	tr	tr	VERB
ap-766	150	9	tr	tr	VERB
ap-766	150	10	1	1	NUM
ap-766	150	11	1	1	NUM
ap-766	150	12	,	,	PUNCT
ap-766	150	13	,	,	PUNCT
ap-766	150	14	(	(	PUNCT
ap-766	150	15	)	)	PUNCT
ap-766	150	16	(	(	PUNCT
ap-766	150	17	)	)	PUNCT
ap-766	150	18	(	(	PUNCT
ap-766	150	19	)	)	PUNCT
ap-766	150	20	†	†	X
ap-766	150	21	(	(	PUNCT
ap-766	150	22	)	)	PUNCT
ap-766	150	23	(	(	PUNCT
ap-766	150	24	(	(	PUNCT
ap-766	150	25	)	)	PUNCT
ap-766	150	26	(	(	PUNCT
ap-766	150	27	�	�	PROPN
ap-766	150	28	�	�	PROPN
ap-766	150	29	�	�	PROPN
ap-766	150	30	l	l	PROPN
ap-766	150	31	lt	lt	PROPN
ap-766	150	32	�	�	PROPN
ap-766	150	33	1	1	NUM
ap-766	150	34	)	)	PUNCT
ap-766	150	35	(	(	PUNCT
ap-766	150	36	)	)	PUNCT
ap-766	150	37	†	†	NOUN
ap-766	150	38	)	)	PUNCT
ap-766	150	39	,	,	PUNCT
ap-766	150	40	(	(	PUNCT
ap-766	150	41	28	28	NUM
ap-766	150	42	)	)	PUNCT
ap-766	150	43	where	where	SCONJ
ap-766	150	44	m	m	VERB
ap-766	150	45	�	�	PROPN
ap-766	150	46	�	�	PROPN
ap-766	150	47	0	0	NUM
ap-766	150	48	,	,	PUNCT
ap-766	150	49	l	l	PROPN
ap-766	150	50	�	�	PROPN
ap-766	150	51	n	n	CCONJ
ap-766	150	52	�	�	PROPN
ap-766	150	53	m	m	PROPN
ap-766	150	54	,	,	PUNCT
ap-766	150	55	{	{	PUNCT
ap-766	150	56	,	,	PUNCT
ap-766	150	57	,	,	PUNCT
ap-766	150	58	}	}	PUNCT
ap-766	150	59	{	{	PUNCT
ap-766	150	60	,	,	PUNCT
ap-766	150	61	,	,	PUNCT
ap-766	150	62	}	}	PUNCT
ap-766	150	63	i	i	PRON
ap-766	150	64	i	i	PRON
ap-766	150	65	lm1	lm1	VERB
ap-766	150	66	1	1	NUM
ap-766	150	67	�	�	PROPN
ap-766	150	68	�	�	PROPN
ap-766	150	69	�	�	PROPN
ap-766	150	70	and	and	CCONJ
ap-766	150	71	t	t	PROPN
ap-766	150	72	(	(	PUNCT
ap-766	150	73	l	l	NOUN
ap-766	150	74	)	)	PUNCT
ap-766	150	75	is	be	AUX
ap-766	150	76	the	the	DET
ap-766	150	77	transformation	transformation	NOUN
ap-766	150	78	of	of	ADP
ap-766	150	79	the	the	DET
ap-766	150	80	form	form	NOUN
ap-766	150	81	(	(	PUNCT
ap-766	150	82	24	24	NUM
ap-766	150	83	)	)	PUNCT
ap-766	150	84	on	on	ADP
ap-766	150	85	the	the	DET
ap-766	150	86	l	l	NOUN
ap-766	150	87	-	-	ADJ
ap-766	150	88	particle	particle	NOUN
ap-766	150	89	hilbert	hilbert	NOUN
ap-766	150	90	space	space	NOUN
ap-766	150	91	,	,	PUNCT
ap-766	150	92	where	where	SCONJ
ap-766	150	93	the	the	DET
ap-766	150	94	condition	condition	NOUN
ap-766	150	95	�	�	PROPN
ap-766	150	96	�	�	PROPN
ap-766	150	97	1	1	NUM
ap-766	150	98	is	be	AUX
ap-766	150	99	required	require	VERB
ap-766	150	100	for	for	ADP
ap-766	150	101	all	all	DET
ap-766	150	102	�	�	PROPN
ap-766	150	103	.	.	PUNCT
ap-766	151	1	note	note	VERB
ap-766	151	2	that	that	SCONJ
ap-766	151	3	by	by	ADP
ap-766	151	4	tracing	trace	VERB
ap-766	151	5	out	out	ADP
ap-766	151	6	different	different	ADJ
ap-766	151	7	particles	particle	NOUN
ap-766	151	8	we	we	PRON
ap-766	151	9	can	can	AUX
ap-766	151	10	generally	generally	ADV
ap-766	151	11	get	get	VERB
ap-766	151	12	a	a	DET
ap-766	151	13	different	different	ADJ
ap-766	151	14	classes	class	NOUN
ap-766	151	15	of	of	ADP
ap-766	151	16	processes	process	NOUN
ap-766	151	17	[	[	X
ap-766	151	18	9	9	NUM
ap-766	151	19	]	]	PUNCT
ap-766	151	20	.	.	PUNCT
ap-766	152	1	the	the	DET
ap-766	152	2	simple	simple	ADJ
ap-766	152	3	consequence	consequence	NOUN
ap-766	152	4	of	of	ADP
ap-766	152	5	the	the	DET
ap-766	152	6	linearity	linearity	NOUN
ap-766	152	7	of	of	ADP
ap-766	152	8	quantum	quantum	NOUN
ap-766	152	9	theory	theory	NOUN
ap-766	152	10	is	be	AUX
ap-766	152	11	that	that	SCONJ
ap-766	152	12	the	the	DET
ap-766	152	13	convex	convex	ADJ
ap-766	152	14	combination	combination	NOUN
ap-766	152	15	of	of	ADP
ap-766	152	16	the	the	DET
ap-766	152	17	processes	process	NOUN
ap-766	152	18	of	of	ADP
ap-766	152	19	the	the	DET
ap-766	152	20	form	form	NOUN
ap-766	152	21	(	(	PUNCT
ap-766	152	22	28	28	NUM
ap-766	152	23	)	)	PUNCT
ap-766	152	24	is	be	AUX
ap-766	152	25	also	also	ADV
ap-766	152	26	a	a	DET
ap-766	152	27	completely	completely	ADV
ap-766	152	28	positive	positive	ADJ
ap-766	152	29	universal	universal	ADJ
ap-766	152	30	process	process	NOUN
ap-766	152	31	.	.	PUNCT
ap-766	153	1	in	in	ADP
ap-766	153	2	the	the	DET
ap-766	153	3	case	case	NOUN
ap-766	153	4	of	of	ADP
ap-766	153	5	formula	formula	NOUN
ap-766	153	6	(	(	PUNCT
ap-766	153	7	28	28	NUM
ap-766	153	8	)	)	PUNCT
ap-766	153	9	the	the	DET
ap-766	153	10	mapping	mapping	NOUN
ap-766	153	11	t	t	PROPN
ap-766	153	12	l	l	PROPN
ap-766	153	13	(	(	PUNCT
ap-766	153	14	)	)	PUNCT
ap-766	153	15	does	do	AUX
ap-766	153	16	not	not	PART
ap-766	153	17	play	play	VERB
ap-766	153	18	the	the	DET
ap-766	153	19	role	role	NOUN
ap-766	153	20	of	of	ADP
ap-766	153	21	the	the	DET
ap-766	153	22	kraus	kraus	PROPN
ap-766	153	23	operator	operator	NOUN
ap-766	153	24	of	of	ADP
ap-766	153	25	the	the	DET
ap-766	153	26	universal	universal	ADJ
ap-766	153	27	process	process	NOUN
ap-766	153	28	(	(	PUNCT
ap-766	153	29	except	except	SCONJ
ap-766	153	30	the	the	DET
ap-766	153	31	case	case	NOUN
ap-766	153	32	m	m	VERB
ap-766	153	33	�	�	PROPN
ap-766	153	34	0	0	NUM
ap-766	153	35	)	)	PUNCT
ap-766	153	36	,	,	PUNCT
ap-766	153	37	but	but	CCONJ
ap-766	153	38	(	(	PUNCT
ap-766	153	39	28	28	NUM
ap-766	153	40	)	)	PUNCT
ap-766	153	41	can	can	AUX
ap-766	153	42	be	be	AUX
ap-766	153	43	further	far	ADV
ap-766	153	44	rewritten	rewrite	VERB
ap-766	153	45	in	in	ADP
ap-766	153	46	the	the	DET
ap-766	153	47	following	following	ADJ
ap-766	153	48	way	way	NOUN
ap-766	153	49	:	:	PUNCT
ap-766	153	50	�	�	PROPN
ap-766	153	51	�	�	PROPN
ap-766	153	52	out	out	ADP
ap-766	154	1	j	j	PROPN
ap-766	154	2	j	j	PROPN
ap-766	155	1	k	k	PROPN
ap-766	155	2	k	k	PROPN
ap-766	156	1	i	i	PRON
ap-766	157	1	i	i	PRON
ap-766	157	2	in	in	ADP
ap-766	157	3	n	n	PRON
ap-766	157	4	j	j	PROPN
ap-766	158	1	j	j	PROPN
ap-766	158	2	k	k	PROPN
ap-766	158	3	km	km	PROPN
ap-766	158	4	m	m	VERB
ap-766	158	5	m	m	VERB
ap-766	158	6	m	m	VERB
ap-766	158	7	m	m	VERB
ap-766	158	8	i	i	PRON
ap-766	158	9	�	�	PROPN
ap-766	158	10	�	�	PROPN
ap-766	158	11	�	�	PROPN
ap-766	158	12	�	�	PROPN
ap-766	158	13	�	�	PROPN
ap-766	158	14	�	�	PROPN
ap-766	158	15	1	1	NUM
ap-766	158	16	1	1	NUM
ap-766	158	17	1	1	NUM
ap-766	158	18	1	1	NUM
ap-766	158	19	1	1	NUM
ap-766	158	20	1	1	NUM
ap-766	158	21	,	,	PUNCT
ap-766	158	22	,	,	PUNCT
ap-766	158	23	,	,	PUNCT
ap-766	158	24	,	,	PUNCT
ap-766	158	25	(	(	PUNCT
ap-766	158	26	)	)	PUNCT
ap-766	158	27	,	,	PUNCT
ap-766	158	28	,	,	PUNCT
ap-766	158	29	,	,	PUNCT
ap-766	158	30	�	�	PROPN
ap-766	158	31	�	�	PROPN
ap-766	158	32	�	�	PROPN
ap-766	158	33	�	�	PROPN
ap-766	158	34	�	�	PROPN
ap-766	158	35	�	�	PROPN
ap-766	158	36	�	�	PROPN
ap-766	159	1	i	i	PRON
ap-766	159	2	i	i	PRON
ap-766	160	1	j	j	PROPN
ap-766	161	1	j	j	PROPN
ap-766	162	1	k	k	PROPN
ap-766	162	2	k	k	PROPN
ap-766	162	3	d	d	PROPN
ap-766	162	4	l	l	NOUN
ap-766	162	5	in	in	ADP
ap-766	162	6	l	l	PROPN
ap-766	162	7	l	l	X
ap-766	162	8	m	m	VERB
ap-766	162	9	m	m	VERB
ap-766	162	10	m	m	VERB
ap-766	163	1	t	t	NOUN
ap-766	164	1	i	i	PRON
ap-766	164	2	t	t	NOUN
ap-766	164	3	1	1	NUM
ap-766	164	4	1	1	NUM
ap-766	164	5	1	1	NUM
ap-766	164	6	1	1	NUM
ap-766	164	7	1	1	NUM
ap-766	164	8	1	1	NUM
ap-766	164	9	,	,	PUNCT
ap-766	164	10	†	†	PROPN
ap-766	164	11	,	,	PUNCT
ap-766	164	12	,	,	PUNCT
ap-766	164	13	(	(	PUNCT
ap-766	164	14	)	)	PUNCT
ap-766	164	15	(	(	PUNCT
ap-766	164	16	)	)	PUNCT
ap-766	164	17	(	(	PUNCT
ap-766	164	18	)	)	PUNCT
ap-766	164	19	†	†	X
ap-766	164	20	(	(	PUNCT
ap-766	164	21	)	)	PUNCT
ap-766	164	22	�	�	PROPN
ap-766	164	23	�	�	PROPN
ap-766	164	24	�	�	PROPN
ap-766	164	25	�	�	PROPN
ap-766	164	26	�	�	PROPN
ap-766	164	27	�	�	PROPN
ap-766	164	28	�	�	PROPN
ap-766	164	29	�	�	PROPN
ap-766	164	30	tr	tr	VERB
ap-766	164	31	�	�	PROPN
ap-766	164	32	(	(	PUNCT
ap-766	164	33	29	29	NUM
ap-766	164	34	)	)	PUNCT
ap-766	164	35	where	where	SCONJ
ap-766	164	36	d	d	NOUN
ap-766	164	37	is	be	AUX
ap-766	164	38	a	a	DET
ap-766	164	39	dimension	dimension	NOUN
ap-766	164	40	of	of	ADP
ap-766	164	41	the	the	DET
ap-766	164	42	one	one	NUM
ap-766	164	43	-	-	PUNCT
ap-766	164	44	particle	particle	NOUN
ap-766	164	45	hilbert	hilbert	NOUN
ap-766	164	46	space	space	NOUN
ap-766	164	47	and	and	CCONJ
ap-766	164	48	�	�	PROPN
ap-766	165	1	j	j	PROPN
ap-766	165	2	j	j	PROPN
ap-766	166	1	k	k	PROPN
ap-766	166	2	k	k	PROPN
ap-766	167	1	i	i	PRON
ap-766	168	1	i	i	PRON
ap-766	168	2	m	m	VERB
ap-766	168	3	m	m	VERB
ap-766	168	4	m	m	VERB
ap-766	168	5	1	1	NUM
ap-766	168	6	1	1	NUM
ap-766	168	7	1	1	NUM
ap-766	168	8	,	,	PUNCT
ap-766	168	9	,	,	PUNCT
ap-766	168	10	,	,	PUNCT
ap-766	168	11	,	,	PUNCT
ap-766	168	12	�	�	PROPN
ap-766	168	13	�	�	PROPN
ap-766	168	14	�	�	PROPN
ap-766	168	15	are	be	AUX
ap-766	168	16	the	the	DET
ap-766	168	17	linear	linear	ADJ
ap-766	168	18	operators	operator	NOUN
ap-766	168	19	on	on	ADP
ap-766	168	20	the	the	DET
ap-766	168	21	n	n	CCONJ
ap-766	168	22	-	-	PUNCT
ap-766	168	23	particle	particle	NOUN
ap-766	168	24	hilbert	hilbert	NOUN
ap-766	168	25	space	space	NOUN
ap-766	168	26	,	,	PUNCT
ap-766	168	27	which	which	PRON
ap-766	168	28	are	be	AUX
ap-766	168	29	defined	define	VERB
ap-766	168	30	�	�	PROPN
ap-766	169	1	j	j	PROPN
ap-766	169	2	j	j	PROPN
ap-766	170	1	k	k	PROPN
ap-766	170	2	k	k	PROPN
ap-766	171	1	i	i	PRON
ap-766	172	1	i	i	PRON
ap-766	173	1	i	i	PRON
ap-766	173	2	m	m	VERB
ap-766	173	3	i	i	VERB
ap-766	173	4	l	l	NOUN
ap-766	173	5	m	m	VERB
ap-766	173	6	m	m	VERB
ap-766	173	7	m	m	VERB
ap-766	173	8	m	m	VERB
ap-766	173	9	m	m	PROPN
ap-766	173	10	j	j	PROPN
ap-766	173	11	j	j	PROPN
ap-766	173	12	p	p	PROPN
ap-766	173	13	k	k	PROPN
ap-766	173	14	k	k	PROPN
ap-766	173	15	1	1	NUM
ap-766	173	16	1	1	NUM
ap-766	173	17	1	1	NUM
ap-766	173	18	1	1	NUM
ap-766	173	19	1	1	NUM
ap-766	173	20	1	1	NUM
ap-766	173	21	,	,	PUNCT
ap-766	173	22	,	,	PUNCT
ap-766	173	23	,	,	PUNCT
ap-766	173	24	,	,	PUNCT
ap-766	173	25	(	(	PUNCT
ap-766	173	26	)	)	PUNCT
ap-766	173	27	.	.	PUNCT
ap-766	174	1	�	�	PROPN
ap-766	174	2	�	�	PROPN
ap-766	174	3	�	�	PROPN
ap-766	174	4	�	�	PROPN
ap-766	174	5	�	�	PROPN
ap-766	174	6	�	�	PROPN
ap-766	174	7	�	�	PROPN
ap-766	174	8	�	�	PROPN
ap-766	174	9	�	�	PROPN
ap-766	174	10	�	�	PROPN
ap-766	174	11	�	�	PROPN
ap-766	174	12	�	�	PROPN
ap-766	174	13	�	�	PROPN
ap-766	174	14	(	(	PUNCT
ap-766	174	15	30	30	NUM
ap-766	174	16	)	)	PUNCT
ap-766	174	17	subscription	subscription	NOUN
ap-766	174	18	by	by	ADP
ap-766	174	19	the	the	DET
ap-766	174	20	bra	bra	NOUN
ap-766	174	21	-	-	PUNCT
ap-766	174	22	vector	vector	NOUN
ap-766	174	23	i	i	PRON
ap-766	174	24	j	j	PROPN
ap-766	174	25	means	mean	VERB
ap-766	174	26	that	that	SCONJ
ap-766	174	27	i	i	PRON
ap-766	174	28	acts	act	VERB
ap-766	174	29	on	on	ADP
ap-766	174	30	the	the	DET
ap-766	174	31	j	j	PROPN
ap-766	174	32	-	-	PUNCT
ap-766	174	33	th	th	VERB
ap-766	174	34	component	component	NOUN
ap-766	174	35	of	of	ADP
ap-766	174	36	the	the	DET
ap-766	174	37	tensor	tensor	NOUN
ap-766	174	38	product	product	NOUN
ap-766	174	39	,	,	PUNCT
ap-766	174	40	i.e.	i.e.	X
ap-766	174	41	on	on	ADP
ap-766	174	42	the	the	DET
ap-766	174	43	j	j	PROPN
ap-766	174	44	-	-	PUNCT
ap-766	174	45	th	th	VERB
ap-766	174	46	particle	particle	NOUN
ap-766	174	47	.	.	PUNCT
ap-766	175	1	the	the	DET
ap-766	175	2	operators	operator	NOUN
ap-766	175	3	defined	define	VERB
ap-766	175	4	by	by	ADP
ap-766	175	5	equation	equation	NOUN
ap-766	175	6	(	(	PUNCT
ap-766	175	7	30	30	NUM
ap-766	175	8	)	)	PUNCT
ap-766	175	9	form	form	NOUN
ap-766	175	10	the	the	DET
ap-766	175	11	set	set	NOUN
ap-766	175	12	of	of	ADP
ap-766	175	13	kraus	kraus	PROPN
ap-766	175	14	operators	operators	PROPN
ap-766	175	15	of	of	ADP
ap-766	175	16	the	the	DET
ap-766	175	17	universal	universal	ADJ
ap-766	175	18	process	process	NOUN
ap-766	175	19	(	(	PUNCT
ap-766	175	20	28	28	NUM
ap-766	175	21	)	)	PUNCT
ap-766	175	22	.	.	PUNCT
ap-766	176	1	we	we	PRON
ap-766	176	2	generalize	generalize	VERB
ap-766	176	3	the	the	DET
ap-766	176	4	bipartite	bipartite	ADJ
ap-766	176	5	universal	universal	ADJ
ap-766	176	6	processes	process	NOUN
ap-766	176	7	to	to	ADP
ap-766	176	8	the	the	DET
ap-766	176	9	subclass	subclass	NOUN
ap-766	176	10	of	of	ADP
ap-766	176	11	the	the	DET
ap-766	176	12	multi	multi	ADJ
ap-766	176	13	-	-	ADJ
ap-766	176	14	particle	particle	ADJ
ap-766	176	15	universal	universal	ADJ
ap-766	176	16	processes	process	NOUN
ap-766	176	17	from	from	ADP
ap-766	176	18	one	one	NUM
ap-766	176	19	to	to	ADP
ap-766	176	20	n	n	NOUN
ap-766	176	21	particles	particle	NOUN
ap-766	176	22	.	.	PUNCT
ap-766	177	1	we	we	PRON
ap-766	177	2	show	show	VERB
ap-766	177	3	how	how	SCONJ
ap-766	177	4	the	the	DET
ap-766	177	5	general	general	ADJ
ap-766	177	6	statement	statement	NOUN
ap-766	177	7	for	for	ADP
ap-766	177	8	a	a	DET
ap-766	177	9	multi	multi	ADJ
ap-766	177	10	-	-	ADJ
ap-766	177	11	particle	particle	ADJ
ap-766	177	12	universal	universal	ADJ
ap-766	177	13	process	process	NOUN
ap-766	177	14	can	can	AUX
ap-766	177	15	be	be	AUX
ap-766	177	16	constructed	construct	VERB
ap-766	177	17	.	.	PUNCT
ap-766	178	1	the	the	DET
ap-766	178	2	one	one	NUM
ap-766	178	3	-	-	PUNCT
ap-766	178	4	parameter	parameter	NOUN
ap-766	178	5	family	family	NOUN
ap-766	178	6	of	of	ADP
ap-766	178	7	processes	process	NOUN
ap-766	178	8	generating	generate	VERB
ap-766	178	9	totally	totally	ADV
ap-766	178	10	anti	anti	ADJ
ap-766	178	11	-	-	ADJ
ap-766	178	12	symmetric	symmetric	ADJ
ap-766	178	13	states	state	NOUN
ap-766	178	14	was	be	AUX
ap-766	178	15	generalized	generalize	VERB
ap-766	178	16	to	to	ADP
ap-766	178	17	a	a	DET
ap-766	178	18	multi	multi	ADJ
ap-766	178	19	-	-	ADJ
ap-766	178	20	particle	particle	ADJ
ap-766	178	21	regime	regime	NOUN
ap-766	178	22	and	and	CCONJ
ap-766	178	23	its	its	PRON
ap-766	178	24	entanglement	entanglement	NOUN
ap-766	178	25	properties	property	NOUN
ap-766	178	26	were	be	AUX
ap-766	178	27	studied	study	VERB
ap-766	178	28	.	.	PUNCT
ap-766	179	1	a	a	DET
ap-766	179	2	view	view	NOUN
ap-766	179	3	on	on	ADP
ap-766	179	4	the	the	DET
ap-766	179	5	complete	complete	ADJ
ap-766	179	6	positivity	positivity	NOUN
ap-766	179	7	and	and	CCONJ
ap-766	179	8	the	the	DET
ap-766	179	9	possible	possible	ADJ
ap-766	179	10	physical	physical	ADJ
ap-766	179	11	realization	realization	NOUN
ap-766	179	12	of	of	ADP
ap-766	179	13	the	the	DET
ap-766	179	14	universal	universal	ADJ
ap-766	179	15	processes	process	NOUN
ap-766	179	16	is	be	AUX
ap-766	179	17	given	give	VERB
ap-766	179	18	.	.	PUNCT
ap-766	180	1	5	5	NUM
ap-766	180	2	conclusions	conclusion	NOUN
ap-766	180	3	universal	universal	ADJ
ap-766	180	4	processes	process	NOUN
ap-766	180	5	may	may	AUX
ap-766	180	6	play	play	VERB
ap-766	180	7	an	an	DET
ap-766	180	8	important	important	ADJ
ap-766	180	9	role	role	NOUN
ap-766	180	10	in	in	ADP
ap-766	180	11	various	various	ADJ
ap-766	180	12	branches	branch	NOUN
ap-766	180	13	of	of	ADP
ap-766	180	14	quantum	quantum	ADJ
ap-766	180	15	information	information	NOUN
ap-766	180	16	processing	processing	NOUN
ap-766	180	17	,	,	PUNCT
ap-766	180	18	e.	e.	PROPN
ap-766	180	19	g.	g.	PROPN
ap-766	180	20	in	in	ADP
ap-766	180	21	preparation	preparation	NOUN
ap-766	180	22	of	of	ADP
ap-766	180	23	entangled	entangled	ADJ
ap-766	180	24	states	state	NOUN
ap-766	180	25	or	or	CCONJ
ap-766	180	26	copies	copy	NOUN
ap-766	180	27	of	of	ADP
ap-766	180	28	the	the	DET
ap-766	180	29	input	input	NOUN
ap-766	180	30	state	state	NOUN
ap-766	180	31	.	.	PUNCT
ap-766	181	1	in	in	ADP
ap-766	181	2	addition	addition	NOUN
ap-766	181	3	to	to	ADP
ap-766	181	4	operations	operation	NOUN
ap-766	181	5	with	with	ADP
ap-766	181	6	two	two	NUM
ap-766	181	7	particles	particle	NOUN
ap-766	181	8	,	,	PUNCT
ap-766	181	9	multi	multi	ADJ
ap-766	181	10	-	-	ADJ
ap-766	181	11	particle	particle	ADJ
ap-766	181	12	operations	operation	NOUN
ap-766	181	13	are	be	AUX
ap-766	181	14	also	also	ADV
ap-766	181	15	of	of	ADP
ap-766	181	16	interest	interest	NOUN
ap-766	181	17	.	.	PUNCT
ap-766	182	1	for	for	ADP
ap-766	182	2	this	this	DET
ap-766	182	3	purpose	purpose	NOUN
ap-766	182	4	we	we	PRON
ap-766	182	5	have	have	AUX
ap-766	182	6	generalized	generalize	VERB
ap-766	182	7	the	the	DET
ap-766	182	8	two	two	NUM
ap-766	182	9	-	-	PUNCT
ap-766	182	10	particle	particle	NOUN
ap-766	182	11	universal	universal	ADJ
ap-766	182	12	processes	process	NOUN
ap-766	182	13	to	to	ADP
ap-766	182	14	a	a	DET
ap-766	182	15	multi	multi	ADJ
ap-766	182	16	-	-	ADJ
ap-766	182	17	particle	particle	ADJ
ap-766	182	18	regime	regime	NOUN
ap-766	182	19	and	and	CCONJ
ap-766	182	20	we	we	PRON
ap-766	182	21	have	have	AUX
ap-766	182	22	shown	show	VERB
ap-766	182	23	how	how	SCONJ
ap-766	182	24	the	the	DET
ap-766	182	25	general	general	ADJ
ap-766	182	26	statement	statement	NOUN
ap-766	182	27	for	for	ADP
ap-766	182	28	the	the	DET
ap-766	182	29	multi	multi	ADJ
ap-766	182	30	-	-	ADJ
ap-766	182	31	particle	particle	ADJ
ap-766	182	32	universal	universal	ADJ
ap-766	182	33	process	process	NOUN
ap-766	182	34	can	can	AUX
ap-766	182	35	be	be	AUX
ap-766	182	36	constructed	construct	VERB
ap-766	182	37	using	use	VERB
ap-766	182	38	the	the	DET
ap-766	182	39	results	result	NOUN
ap-766	182	40	for	for	ADP
ap-766	182	41	two	two	NUM
ap-766	182	42	-	-	PUNCT
ap-766	182	43	particle	particle	NOUN
ap-766	182	44	universal	universal	ADJ
ap-766	182	45	processes	process	NOUN
ap-766	182	46	.	.	PUNCT
ap-766	183	1	for	for	ADP
ap-766	183	2	the	the	DET
ap-766	183	3	preparation	preparation	NOUN
ap-766	183	4	of	of	ADP
ap-766	183	5	multi	multi	ADJ
ap-766	183	6	-	-	ADJ
ap-766	183	7	particle	particle	ADJ
ap-766	183	8	entangled	entangle	VERB
ap-766	183	9	states	state	NOUN
ap-766	183	10	we	we	PRON
ap-766	183	11	generalized	generalize	VERB
ap-766	183	12	the	the	DET
ap-766	183	13	one	one	NUM
ap-766	183	14	-	-	PUNCT
ap-766	183	15	parameter	parameter	NOUN
ap-766	183	16	family	family	NOUN
ap-766	183	17	of	of	ADP
ap-766	183	18	processes	process	NOUN
ap-766	183	19	generating	generate	VERB
ap-766	183	20	totally	totally	ADV
ap-766	183	21	anti	anti	ADJ
ap-766	183	22	-	-	ADJ
ap-766	183	23	symmetric	symmetric	ADJ
ap-766	183	24	states	state	NOUN
ap-766	183	25	to	to	ADP
ap-766	183	26	a	a	DET
ap-766	183	27	multi	multi	ADJ
ap-766	183	28	-	-	ADJ
ap-766	183	29	particle	particle	ADJ
ap-766	183	30	regime	regime	NOUN
ap-766	183	31	and	and	CCONJ
ap-766	183	32	studied	study	VERB
ap-766	183	33	its	its	PRON
ap-766	183	34	bipartite	bipartite	ADJ
ap-766	183	35	entanglement	entanglement	NOUN
ap-766	183	36	properties	property	NOUN
ap-766	183	37	.	.	PUNCT
ap-766	184	1	this	this	DET
ap-766	184	2	one	one	NUM
ap-766	184	3	-	-	PUNCT
ap-766	184	4	parameter	parameter	NOUN
ap-766	184	5	class	class	NOUN
ap-766	184	6	generates	generate	VERB
ap-766	184	7	entangled	entangle	VERB
ap-766	184	8	states	state	NOUN
ap-766	184	9	with	with	ADP
ap-766	184	10	equal	equal	ADJ
ap-766	184	11	reduced	reduce	VERB
ap-766	184	12	states	state	NOUN
ap-766	184	13	,	,	PUNCT
ap-766	184	14	thus	thus	ADV
ap-766	184	15	the	the	DET
ap-766	184	16	entanglement	entanglement	NOUN
ap-766	184	17	is	be	AUX
ap-766	184	18	shared	share	VERB
ap-766	184	19	uniformly	uniformly	ADV
ap-766	184	20	between	between	ADP
ap-766	184	21	all	all	DET
ap-766	184	22	pairs	pair	NOUN
ap-766	184	23	of	of	ADP
ap-766	184	24	particles	particle	NOUN
ap-766	184	25	.	.	PUNCT
ap-766	185	1	a	a	DET
ap-766	185	2	particular	particular	ADJ
ap-766	185	3	process	process	NOUN
ap-766	185	4	of	of	ADP
ap-766	185	5	this	this	DET
ap-766	185	6	one	one	NUM
ap-766	185	7	-	-	PUNCT
ap-766	185	8	parameter	parameter	NOUN
ap-766	185	9	family	family	NOUN
ap-766	185	10	can	can	AUX
ap-766	185	11	be	be	AUX
ap-766	185	12	realized	realize	VERB
ap-766	185	13	by	by	ADP
ap-766	185	14	a	a	DET
ap-766	185	15	simple	simple	ADJ
ap-766	185	16	action	action	NOUN
ap-766	185	17	of	of	ADP
ap-766	185	18	a	a	DET
ap-766	185	19	projection	projection	NOUN
ap-766	185	20	operator	operator	NOUN
ap-766	185	21	.	.	PUNCT
ap-766	186	1	for	for	ADP
ap-766	186	2	processes	process	NOUN
ap-766	186	3	of	of	ADP
ap-766	186	4	this	this	DET
ap-766	186	5	kind	kind	NOUN
ap-766	186	6	we	we	PRON
ap-766	186	7	can	can	AUX
ap-766	186	8	in	in	ADP
ap-766	186	9	a	a	DET
ap-766	186	10	canonical	canonical	ADJ
ap-766	186	11	way	way	NOUN
ap-766	186	12	construct	construct	VERB
ap-766	186	13	a	a	DET
ap-766	186	14	unitary	unitary	ADJ
ap-766	186	15	evolution	evolution	NOUN
ap-766	186	16	operator	operator	NOUN
ap-766	186	17	,	,	PUNCT
ap-766	186	18	thus	thus	ADV
ap-766	186	19	they	they	PRON
ap-766	186	20	are	be	AUX
ap-766	186	21	completely	completely	ADV
ap-766	186	22	positive	positive	ADJ
ap-766	186	23	.	.	PUNCT
ap-766	187	1	an	an	DET
ap-766	187	2	open	open	ADJ
ap-766	187	3	question	question	NOUN
ap-766	187	4	is	be	AUX
ap-766	187	5	whether	whether	SCONJ
ap-766	187	6	other	other	ADJ
ap-766	187	7	universal	universal	ADJ
ap-766	187	8	processes	process	NOUN
ap-766	187	9	can	can	AUX
ap-766	187	10	be	be	AUX
ap-766	187	11	performed	perform	VERB
ap-766	187	12	by	by	ADP
ap-766	187	13	an	an	DET
ap-766	187	14	action	action	NOUN
ap-766	187	15	of	of	ADP
ap-766	187	16	a	a	DET
ap-766	187	17	certain	certain	ADJ
ap-766	187	18	projector	projector	NOUN
ap-766	187	19	,	,	PUNCT
ap-766	187	20	possibly	possibly	ADV
ap-766	187	21	on	on	ADP
ap-766	187	22	a	a	DET
ap-766	187	23	larger	large	ADJ
ap-766	187	24	hilbert	hilbert	NOUN
ap-766	187	25	space	space	NOUN
ap-766	187	26	(	(	PUNCT
ap-766	187	27	i.	i.	PROPN
ap-766	187	28	e.	e.	PROPN
ap-766	187	29	with	with	ADP
ap-766	187	30	more	more	ADJ
ap-766	187	31	particles	particle	NOUN
ap-766	187	32	)	)	PUNCT
ap-766	187	33	and	and	CCONJ
ap-766	187	34	then	then	ADV
ap-766	187	35	tracing	trace	VERB
ap-766	187	36	over	over	ADP
ap-766	187	37	some	some	PRON
ap-766	187	38	of	of	ADP
ap-766	187	39	the	the	DET
ap-766	187	40	particles	particle	NOUN
ap-766	187	41	.	.	PUNCT
ap-766	188	1	such	such	ADJ
ap-766	188	2	processes	process	NOUN
ap-766	188	3	will	will	AUX
ap-766	188	4	also	also	ADV
ap-766	188	5	be	be	AUX
ap-766	188	6	completely	completely	ADV
ap-766	188	7	positive	positive	ADJ
ap-766	188	8	,	,	PUNCT
ap-766	188	9	and	and	CCONJ
ap-766	188	10	therefore	therefore	ADV
ap-766	188	11	physically	physically	ADV
ap-766	188	12	feasible	feasible	ADJ
ap-766	188	13	,	,	PUNCT
ap-766	188	14	which	which	PRON
ap-766	188	15	makes	make	VERB
ap-766	188	16	them	they	PRON
ap-766	188	17	very	very	ADV
ap-766	188	18	interesting	interesting	ADJ
ap-766	188	19	for	for	ADP
ap-766	188	20	the	the	DET
ap-766	188	21	possible	possible	ADJ
ap-766	188	22	future	future	ADJ
ap-766	188	23	realization	realization	NOUN
ap-766	188	24	of	of	ADP
ap-766	188	25	a	a	DET
ap-766	188	26	quantum	quantum	ADJ
ap-766	188	27	computer	computer	NOUN
ap-766	188	28	.	.	PUNCT
ap-766	189	1	6	6	NUM
ap-766	189	2	acknowledgment	acknowledgment	NOUN
ap-766	189	3	the	the	DET
ap-766	189	4	authors	author	NOUN
ap-766	189	5	would	would	AUX
ap-766	189	6	like	like	VERB
ap-766	189	7	to	to	PART
ap-766	189	8	thank	thank	VERB
ap-766	189	9	prof	prof	PROPN
ap-766	189	10	.	.	PUNCT
ap-766	189	11	igor	igor	PROPN
ap-766	189	12	jex	jex	PROPN
ap-766	189	13	from	from	ADP
ap-766	189	14	ctu	ctu	NOUN
ap-766	189	15	in	in	ADP
ap-766	189	16	prague	prague	NOUN
ap-766	189	17	and	and	CCONJ
ap-766	189	18	prof	prof	PROPN
ap-766	189	19	.	.	PUNCT
ap-766	190	1	gernot	gernot	PROPN
ap-766	190	2	alber	alber	PROPN
ap-766	190	3	from	from	ADP
ap-766	190	4	tu	tu	PROPN
ap-766	190	5	darmstadt	darmstadt	PROPN
ap-766	190	6	for	for	ADP
ap-766	190	7	many	many	ADJ
ap-766	190	8	stimulating	stimulating	ADJ
ap-766	190	9	discussions	discussion	NOUN
ap-766	190	10	.	.	PUNCT
ap-766	191	1	references	reference	NOUN
ap-766	191	2	[	[	X
ap-766	191	3	1	1	NUM
ap-766	191	4	]	]	PUNCT
ap-766	191	5	wooters	wooter	NOUN
ap-766	191	6	,	,	PUNCT
ap-766	191	7	w.	w.	PROPN
ap-766	191	8	k.	k.	PROPN
ap-766	191	9	,	,	PUNCT
ap-766	191	10	zurek	zurek	PROPN
ap-766	191	11	w.	w.	PROPN
ap-766	191	12	h.	h.	PROPN
ap-766	191	13	:	:	PUNCT
ap-766	191	14	“	"	PUNCT
ap-766	191	15	a	a	DET
ap-766	191	16	single	single	ADJ
ap-766	191	17	quantum	quantum	NOUN
ap-766	191	18	can	can	AUX
ap-766	191	19	not	not	PART
ap-766	191	20	be	be	AUX
ap-766	191	21	cloned	clone	VERB
ap-766	191	22	.	.	PUNCT
ap-766	191	23	”	"	PUNCT
ap-766	192	1	nature	nature	NOUN
ap-766	192	2	299	299	NUM
ap-766	192	3	(	(	PUNCT
ap-766	192	4	1982	1982	NUM
ap-766	192	5	)	)	PUNCT
ap-766	192	6	802	802	NUM
ap-766	192	7	.	.	PUNCT
ap-766	193	1	[	[	X
ap-766	193	2	2	2	NUM
ap-766	193	3	]	]	PUNCT
ap-766	193	4	werner	werner	NOUN
ap-766	193	5	,	,	PUNCT
ap-766	193	6	r.	r.	PROPN
ap-766	193	7	f.	f.	PROPN
ap-766	193	8	:	:	PUNCT
ap-766	193	9	“	"	PUNCT
ap-766	193	10	optimal	optimal	ADJ
ap-766	193	11	cloning	cloning	NOUN
ap-766	193	12	of	of	ADP
ap-766	193	13	pure	pure	ADJ
ap-766	193	14	states	state	NOUN
ap-766	193	15	.	.	PUNCT
ap-766	193	16	”	"	PUNCT
ap-766	194	1	phys	phy	NOUN
ap-766	194	2	.	.	PUNCT
ap-766	195	1	rev	rev	PROPN
ap-766	195	2	.	.	PUNCT
ap-766	196	1	a	a	DET
ap-766	196	2	58	58	NUM
ap-766	196	3	,	,	PUNCT
ap-766	196	4	(	(	PUNCT
ap-766	196	5	1998	1998	NUM
ap-766	196	6	)	)	PUNCT
ap-766	196	7	1827–1832	1827–1832	NUM
ap-766	196	8	.	.	PUNCT
ap-766	197	1	[	[	X
ap-766	197	2	3	3	NUM
ap-766	197	3	]	]	X
ap-766	197	4	novotný	novotný	PROPN
ap-766	197	5	,	,	PUNCT
ap-766	197	6	j.	j.	PROPN
ap-766	197	7	,	,	PUNCT
ap-766	197	8	alber	alber	PROPN
ap-766	197	9	,	,	PUNCT
ap-766	197	10	g.	g.	PROPN
ap-766	197	11	,	,	PUNCT
ap-766	197	12	jex	jex	PROPN
ap-766	197	13	,	,	PUNCT
ap-766	197	14	i.	i.	PROPN
ap-766	197	15	:	:	PUNCT
ap-766	197	16	“	"	PUNCT
ap-766	197	17	optimal	optimal	ADJ
ap-766	197	18	copying	copying	NOUN
ap-766	197	19	of	of	ADP
ap-766	197	20	entangled	entangle	VERB
ap-766	197	21	two	two	NUM
ap-766	197	22	-	-	PUNCT
ap-766	197	23	qubit	qubit	NOUN
ap-766	197	24	states	state	NOUN
ap-766	197	25	.	.	PUNCT
ap-766	197	26	”	"	PUNCT
ap-766	197	27	phys	phy	NOUN
ap-766	197	28	.	.	PUNCT
ap-766	198	1	rev	rev	PROPN
ap-766	198	2	.	.	PUNCT
ap-766	199	1	a	a	DET
ap-766	199	2	71	71	NUM
ap-766	199	3	,	,	PUNCT
ap-766	199	4	(	(	PUNCT
ap-766	199	5	2005	2005	NUM
ap-766	199	6	)	)	PUNCT
ap-766	199	7	,	,	PUNCT
ap-766	199	8	042332	042332	NUM
ap-766	199	9	.	.	PUNCT
ap-766	200	1	[	[	X
ap-766	200	2	4	4	NUM
ap-766	200	3	]	]	PUNCT
ap-766	200	4	alber	alber	PROPN
ap-766	200	5	,	,	PUNCT
ap-766	200	6	g.	g.	PROPN
ap-766	200	7	,	,	PUNCT
ap-766	200	8	delgado	delgado	PROPN
ap-766	200	9	,	,	PUNCT
ap-766	200	10	d.	d.	PROPN
ap-766	200	11	,	,	PUNCT
ap-766	200	12	jex	jex	PROPN
ap-766	200	13	,	,	PUNCT
ap-766	200	14	i.	i.	PROPN
ap-766	200	15	:	:	PUNCT
ap-766	200	16	“	"	PUNCT
ap-766	200	17	optimal	optimal	ADJ
ap-766	200	18	universal	universal	ADJ
ap-766	200	19	two	two	NUM
ap-766	200	20	-	-	PUNCT
ap-766	200	21	particle	particle	NOUN
ap-766	200	22	processes	process	NOUN
ap-766	200	23	in	in	ADP
ap-766	200	24	arbitrary	arbitrary	ADJ
ap-766	200	25	dimensional	dimensional	ADJ
ap-766	200	26	hilbert	hilbert	NOUN
ap-766	200	27	spaces	space	NOUN
ap-766	200	28	.	.	PUNCT
ap-766	200	29	”	"	PUNCT
ap-766	200	30	qic	qic	VERB
ap-766	200	31	1	1	NUM
ap-766	200	32	(	(	PUNCT
ap-766	200	33	2001	2001	NUM
ap-766	200	34	)	)	PUNCT
ap-766	200	35	33	33	NUM
ap-766	200	36	.	.	PUNCT
ap-766	201	1	[	[	X
ap-766	201	2	5	5	NUM
ap-766	201	3	]	]	PUNCT
ap-766	201	4	vidal	vidal	NOUN
ap-766	201	5	,	,	PUNCT
ap-766	201	6	g.	g.	PROPN
ap-766	201	7	,	,	PUNCT
ap-766	201	8	werner	werner	PROPN
ap-766	201	9	,	,	PUNCT
ap-766	201	10	r.	r.	PROPN
ap-766	201	11	f.	f.	PROPN
ap-766	201	12	:	:	PUNCT
ap-766	201	13	“	"	PUNCT
ap-766	201	14	computable	computable	ADJ
ap-766	201	15	measure	measure	NOUN
ap-766	201	16	of	of	ADP
ap-766	201	17	entanglement	entanglement	NOUN
ap-766	201	18	.	.	PUNCT
ap-766	201	19	”	"	PUNCT
ap-766	201	20	phys	phy	NOUN
ap-766	201	21	.	.	PUNCT
ap-766	202	1	rev	rev	PROPN
ap-766	202	2	.	.	PUNCT
ap-766	203	1	a	a	DET
ap-766	203	2	65	65	NUM
ap-766	203	3	,	,	PUNCT
ap-766	203	4	(	(	PUNCT
ap-766	203	5	2002	2002	NUM
ap-766	203	6	)	)	PUNCT
ap-766	203	7	,	,	PUNCT
ap-766	203	8	032314	032314	NUM
ap-766	203	9	.	.	PUNCT
ap-766	204	1	[	[	X
ap-766	204	2	6	6	NUM
ap-766	204	3	]	]	PUNCT
ap-766	204	4	m.	m.	NOUN
ap-766	204	5	štefaňák	štefaňák	NOUN
ap-766	204	6	:	:	PUNCT
ap-766	204	7	“	"	PUNCT
ap-766	204	8	many	many	ADJ
ap-766	204	9	particle	particle	NOUN
ap-766	204	10	universal	universal	ADJ
ap-766	204	11	processes	process	NOUN
ap-766	204	12	.	.	PUNCT
ap-766	204	13	”	"	PUNCT
ap-766	205	1	diploma	diploma	NOUN
ap-766	205	2	thesis	thesis	NOUN
ap-766	205	3	,	,	PUNCT
ap-766	205	4	fjfi	fjfi	PROPN
ap-766	205	5	,	,	PUNCT
ap-766	205	6	(	(	PUNCT
ap-766	205	7	2003	2003	NUM
ap-766	205	8	)	)	PUNCT
ap-766	205	9	.	.	PUNCT
ap-766	206	1	©	©	PROPN
ap-766	206	2	czech	czech	PROPN
ap-766	206	3	technical	technical	PROPN
ap-766	206	4	university	university	PROPN
ap-766	206	5	publishing	publishing	NOUN
ap-766	206	6	house	house	NOUN
ap-766	206	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-766	206	8	37	37	NUM
ap-766	206	9	czech	czech	PROPN
ap-766	206	10	technical	technical	PROPN
ap-766	206	11	university	university	PROPN
ap-766	206	12	in	in	ADP
ap-766	206	13	prague	prague	PROPN
ap-766	206	14	acta	acta	PROPN
ap-766	206	15	polytechnica	polytechnica	PROPN
ap-766	206	16	vol	vol	NOUN
ap-766	206	17	.	.	PROPN
ap-766	207	1	45	45	NUM
ap-766	207	2	no	no	NOUN
ap-766	207	3	.	.	PUNCT
ap-766	208	1	5/2005	5/2005	NUM
ap-766	209	1	[	[	X
ap-766	209	2	7	7	NUM
ap-766	209	3	]	]	X
ap-766	209	4	nielsen	nielsen	PROPN
ap-766	209	5	,	,	PUNCT
ap-766	209	6	m.	m.	NOUN
ap-766	209	7	a.	a.	PROPN
ap-766	209	8	,	,	PUNCT
ap-766	209	9	chuang	chuang	PROPN
ap-766	209	10	,	,	PUNCT
ap-766	209	11	i.	i.	PROPN
ap-766	209	12	l.	l.	PROPN
ap-766	209	13	:	:	PUNCT
ap-766	209	14	quantum	quantum	ADJ
ap-766	209	15	computation	computation	NOUN
ap-766	209	16	and	and	CCONJ
ap-766	209	17	quantum	quantum	NOUN
ap-766	209	18	information	information	NOUN
ap-766	209	19	.	.	PUNCT
ap-766	210	1	cambridge	cambridge	PROPN
ap-766	210	2	university	university	PROPN
ap-766	210	3	press	press	PROPN
ap-766	210	4	,	,	PUNCT
ap-766	210	5	cambridge	cambridge	PROPN
ap-766	210	6	,	,	PUNCT
ap-766	210	7	2000	2000	NUM
ap-766	210	8	.	.	PUNCT
ap-766	211	1	[	[	X
ap-766	211	2	8	8	NUM
ap-766	211	3	]	]	X
ap-766	211	4	kraus	kraus	PROPN
ap-766	211	5	,	,	PUNCT
ap-766	211	6	k.	k.	PROPN
ap-766	211	7	:	:	PUNCT
ap-766	211	8	states	state	NOUN
ap-766	211	9	,	,	PUNCT
ap-766	211	10	effects	effect	NOUN
ap-766	211	11	,	,	PUNCT
ap-766	211	12	operations	operation	NOUN
ap-766	211	13	:	:	PUNCT
ap-766	211	14	fundamental	fundamental	ADJ
ap-766	211	15	notions	notion	NOUN
ap-766	211	16	of	of	ADP
ap-766	211	17	quantum	quantum	NOUN
ap-766	211	18	theory	theory	NOUN
ap-766	211	19	.	.	PUNCT
ap-766	212	1	springer	springer	NOUN
ap-766	212	2	-	-	PUNCT
ap-766	212	3	verlag	verlag	PROPN
ap-766	212	4	,	,	PUNCT
ap-766	212	5	berlin	berlin	PROPN
ap-766	212	6	,	,	PUNCT
ap-766	212	7	1983	1983	NUM
ap-766	212	8	.	.	PUNCT
ap-766	213	1	[	[	X
ap-766	213	2	9	9	NUM
ap-766	213	3	]	]	X
ap-766	213	4	košt’ák	košt’ák	PROPN
ap-766	213	5	,	,	PUNCT
ap-766	213	6	v.	v.	ADV
ap-766	213	7	:	:	PUNCT
ap-766	213	8	“	"	PUNCT
ap-766	213	9	vlastnosti	vlastnosti	VERB
ap-766	213	10	a	a	DET
ap-766	213	11	implementace	implementace	NOUN
ap-766	213	12	univerzálních	univerzálních	ADJ
ap-766	213	13	procesů	procesů	NOUN
ap-766	213	14	pro	pro	X
ap-766	213	15	více	více	PROPN
ap-766	213	16	částic	částic	ADJ
ap-766	213	17	.	.	PUNCT
ap-766	213	18	”	"	PUNCT
ap-766	214	1	(	(	PUNCT
ap-766	214	2	in	in	ADP
ap-766	214	3	czech	czech	PROPN
ap-766	214	4	)	)	PUNCT
ap-766	214	5	diploma	diploma	NOUN
ap-766	214	6	thesis	thesis	NOUN
ap-766	214	7	,	,	PUNCT
ap-766	214	8	fjfi	fjfi	PROPN
ap-766	214	9	,	,	PUNCT
ap-766	214	10	ctu	ctu	NOUN
ap-766	214	11	in	in	ADP
ap-766	214	12	prague	prague	PROPN
ap-766	214	13	,	,	PUNCT
ap-766	214	14	2005	2005	NUM
ap-766	214	15	.	.	PUNCT
ap-766	215	1	ing	ing	ADJ
ap-766	215	2	.	.	PUNCT
ap-766	216	1	jaroslav	jaroslav	PROPN
ap-766	216	2	novotný	novotný	PROPN
ap-766	216	3	e	e	PROPN
ap-766	216	4	-	-	NOUN
ap-766	216	5	mail	mail	NOUN
ap-766	216	6	:	:	PUNCT
ap-766	216	7	novotny.jaroslav@seznam.cz	novotny.jaroslav@seznam.cz	NOUN
ap-766	216	8	ing	ing	PROPN
ap-766	216	9	.	.	PUNCT
ap-766	217	1	martin	martin	PROPN
ap-766	217	2	štefaňák	štefaňák	PROPN
ap-766	217	3	e	e	NOUN
ap-766	217	4	-	-	NOUN
ap-766	217	5	mail	mail	NOUN
ap-766	217	6	:	:	PUNCT
ap-766	217	7	stefanak.m@seznam.cz	stefanak.m@seznam.cz	ADJ
ap-766	217	8	vojtěch	vojtěch	NOUN
ap-766	217	9	košt’ák	košt’ák	PROPN
ap-766	217	10	e	e	NOUN
ap-766	217	11	-	-	NOUN
ap-766	217	12	mail	mail	NOUN
ap-766	217	13	:	:	PUNCT
ap-766	217	14	vojtech.kostak@centrum.cz	vojtech.kostak@centrum.cz	NOUN
ap-766	217	15	department	department	PROPN
ap-766	217	16	of	of	ADP
ap-766	217	17	physics	physics	PROPN
ap-766	217	18	czech	czech	PROPN
ap-766	217	19	technical	technical	PROPN
ap-766	217	20	university	university	PROPN
ap-766	217	21	in	in	ADP
ap-766	217	22	prague	prague	PROPN
ap-766	217	23	faculty	faculty	NOUN
ap-766	217	24	of	of	ADP
ap-766	217	25	nuclear	nuclear	ADJ
ap-766	217	26	sciences	science	NOUN
ap-766	217	27	and	and	CCONJ
ap-766	217	28	physical	physical	ADJ
ap-766	217	29	engineering	engineering	NOUN
ap-766	217	30	břehová	břehová	VERB
ap-766	217	31	7	7	NUM
ap-766	217	32	115	115	NUM
ap-766	217	33	19	19	NUM
ap-766	217	34	prague	prague	NOUN
ap-766	217	35	1	1	NUM
ap-766	217	36	,	,	PUNCT
ap-766	217	37	czech	czech	PROPN
ap-766	217	38	republic	republic	NOUN
ap-766	217	39	38	38	NUM
ap-766	217	40	©	©	PROPN
ap-766	217	41	czech	czech	PROPN
ap-766	217	42	technical	technical	PROPN
ap-766	217	43	university	university	PROPN
ap-766	217	44	publishing	publishing	NOUN
ap-766	217	45	house	house	NOUN
ap-766	217	46	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-766	217	47	acta	acta	PROPN
ap-766	217	48	polytechnica	polytechnica	PROPN
ap-766	217	49	vol	vol	NOUN
ap-766	217	50	.	.	PROPN
ap-766	218	1	45	45	NUM
ap-766	218	2	no	no	NOUN
ap-766	218	3	.	.	PUNCT
ap-766	219	1	5/2005	5/2005	NUM
ap-766	219	2	czech	czech	PROPN
ap-766	219	3	technical	technical	PROPN
ap-766	219	4	university	university	PROPN
ap-766	219	5	in	in	ADP
ap-766	219	6	prague	prague	NOUN