id	sid	tid	token	lemma	pos
asir-4528	1	1	applied	apply	VERB
asir-4528	1	2	science	science	NOUN
asir-4528	1	3	and	and	CCONJ
asir-4528	1	4	innovative	innovative	ADJ
asir-4528	1	5	research	research	NOUN
asir-4528	1	6	issn	issn	VERB
asir-4528	1	7	2474	2474	NUM
asir-4528	1	8	-	-	SYM
asir-4528	1	9	4972	4972	NUM
asir-4528	1	10	(	(	PUNCT
asir-4528	1	11	print	print	NOUN
asir-4528	1	12	)	)	PUNCT
asir-4528	1	13	issn	issn	VERB
asir-4528	1	14	2474	2474	NUM
asir-4528	1	15	-	-	SYM
asir-4528	1	16	4980	4980	NUM
asir-4528	1	17	(	(	PUNCT
asir-4528	1	18	online	online	ADJ
asir-4528	1	19	)	)	PUNCT
asir-4528	1	20	vol	vol	NOUN
asir-4528	1	21	.	.	PROPN
asir-4528	2	1	6	6	NUM
asir-4528	2	2	,	,	PUNCT
asir-4528	2	3	no	no	INTJ
asir-4528	2	4	.	.	NOUN
asir-4528	2	5	1	1	NUM
asir-4528	2	6	,	,	PUNCT
asir-4528	2	7	2022	2022	NUM
asir-4528	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-4528	2	9	46	46	NUM
asir-4528	2	10	original	original	ADJ
asir-4528	2	11	paper	paper	NOUN
asir-4528	2	12	explaining	explain	VERB
asir-4528	2	13	double	double	ADJ
asir-4528	2	14	split	split	ADJ
asir-4528	2	15	experiment	experiment	NOUN
asir-4528	2	16	with	with	ADP
asir-4528	2	17	geometrical	geometrical	ADJ
asir-4528	2	18	algebra	algebra	NOUN
asir-4528	2	19	formalism	formalism	NOUN
asir-4528	2	20	alexander	alexander	NOUN
asir-4528	2	21	soiguine1	soiguine1	PROPN
asir-4528	2	22	*	*	PROPN
asir-4528	2	23	1	1	NUM
asir-4528	2	24	soiguine	soiguine	ADJ
asir-4528	2	25	quantum	quantum	NOUN
asir-4528	2	26	computing	computing	NOUN
asir-4528	2	27	,	,	PUNCT
asir-4528	2	28	31	31	NUM
asir-4528	2	29	aurora	aurora	PROPN
asir-4528	2	30	,	,	PUNCT
asir-4528	2	31	aliso	aliso	PROPN
asir-4528	2	32	viejo	viejo	PROPN
asir-4528	2	33	,	,	PUNCT
asir-4528	2	34	ca	ca	PROPN
asir-4528	2	35	,	,	PUNCT
asir-4528	2	36	usa	usa	PROPN
asir-4528	2	37	*	*	PUNCT
asir-4528	2	38	e	e	PROPN
asir-4528	2	39	-	-	NOUN
asir-4528	2	40	mail	mail	NOUN
asir-4528	2	41	:	:	PUNCT
asir-4528	2	42	alex@soiguine.com	alex@soiguine.com	X
asir-4528	2	43	received	receive	VERB
asir-4528	2	44	:	:	PUNCT
asir-4528	2	45	february	february	NOUN
asir-4528	2	46	8	8	NUM
asir-4528	2	47	,	,	PUNCT
asir-4528	2	48	2022	2022	NUM
asir-4528	2	49	accepted	accept	VERB
asir-4528	2	50	:	:	PUNCT
asir-4528	2	51	february	february	PROPN
asir-4528	2	52	15	15	NUM
asir-4528	2	53	,	,	PUNCT
asir-4528	2	54	2022	2022	NUM
asir-4528	2	55	online	online	ADV
asir-4528	2	56	published	publish	VERB
asir-4528	2	57	:	:	PUNCT
asir-4528	2	58	february	february	PROPN
asir-4528	2	59	18	18	NUM
asir-4528	2	60	,	,	PUNCT
asir-4528	2	61	2022	2022	NUM
asir-4528	2	62	doi:10.22158	doi:10.22158	NOUN
asir-4528	2	63	/	/	SYM
asir-4528	2	64	asir.v6n1p46	asir.v6n1p46	NOUN
asir-4528	2	65	url	url	NOUN
asir-4528	2	66	:	:	PUNCT
asir-4528	2	67	http://doi.org/10.22158/asir.v6n1p46	http://doi.org/10.22158/asir.v6n1p46	ADV
asir-4528	2	68	abstract	abstract	ADJ
asir-4528	2	69	the	the	DET
asir-4528	2	70	geometric	geometric	ADJ
asir-4528	2	71	algebra	algebra	NOUN
asir-4528	2	72	formalism	formalism	NOUN
asir-4528	2	73	opens	open	VERB
asir-4528	2	74	the	the	DET
asir-4528	2	75	door	door	NOUN
asir-4528	2	76	to	to	ADP
asir-4528	2	77	developing	develop	VERB
asir-4528	2	78	a	a	DET
asir-4528	2	79	theory	theory	NOUN
asir-4528	2	80	upgrading	upgrade	VERB
asir-4528	2	81	conventional	conventional	ADJ
asir-4528	2	82	quantum	quantum	ADJ
asir-4528	2	83	mechanics	mechanic	NOUN
asir-4528	2	84	.	.	PUNCT
asir-4528	3	1	generalizations	generalization	NOUN
asir-4528	3	2	,	,	PUNCT
asir-4528	3	3	stemming	stem	VERB
asir-4528	3	4	from	from	ADP
asir-4528	3	5	implementation	implementation	NOUN
asir-4528	3	6	of	of	ADP
asir-4528	3	7	complex	complex	ADJ
asir-4528	3	8	numbers	number	NOUN
asir-4528	3	9	as	as	ADP
asir-4528	3	10	geometrically	geometrically	ADV
asir-4528	3	11	feasible	feasible	ADJ
asir-4528	3	12	objects	object	NOUN
asir-4528	3	13	in	in	ADP
asir-4528	3	14	three	three	NUM
asir-4528	3	15	dimensions	dimension	NOUN
asir-4528	3	16	;	;	PUNCT
asir-4528	3	17	unambiguous	unambiguous	ADJ
asir-4528	3	18	definition	definition	NOUN
asir-4528	3	19	of	of	ADP
asir-4528	3	20	states	state	NOUN
asir-4528	3	21	,	,	PUNCT
asir-4528	3	22	observables	observable	NOUN
asir-4528	3	23	,	,	PUNCT
asir-4528	3	24	measurements	measurement	NOUN
asir-4528	3	25	bring	bring	VERB
asir-4528	3	26	into	into	ADP
asir-4528	3	27	reality	reality	NOUN
asir-4528	3	28	clear	clear	ADJ
asir-4528	3	29	explanations	explanation	NOUN
asir-4528	3	30	of	of	ADP
asir-4528	3	31	conventional	conventional	ADJ
asir-4528	3	32	weird	weird	ADJ
asir-4528	3	33	quantum	quantum	ADJ
asir-4528	3	34	mechanical	mechanical	ADJ
asir-4528	3	35	features	feature	NOUN
asir-4528	3	36	,	,	PUNCT
asir-4528	3	37	particularly	particularly	ADV
asir-4528	3	38	the	the	DET
asir-4528	3	39	results	result	NOUN
asir-4528	3	40	of	of	ADP
asir-4528	3	41	double	double	ADJ
asir-4528	3	42	split	split	ADJ
asir-4528	3	43	experiments	experiment	NOUN
asir-4528	3	44	where	where	SCONJ
asir-4528	3	45	particles	particle	NOUN
asir-4528	3	46	create	create	VERB
asir-4528	3	47	diffraction	diffraction	NOUN
asir-4528	3	48	patterns	pattern	NOUN
asir-4528	3	49	inherent	inherent	ADJ
asir-4528	3	50	to	to	PART
asir-4528	3	51	wave	wave	VERB
asir-4528	3	52	diffraction	diffraction	NOUN
asir-4528	3	53	.	.	PUNCT
asir-4528	4	1	this	this	DET
asir-4528	4	2	weirdness	weirdness	NOUN
asir-4528	4	3	of	of	ADP
asir-4528	4	4	the	the	DET
asir-4528	4	5	double	double	ADJ
asir-4528	4	6	split	split	NOUN
asir-4528	4	7	experiment	experiment	NOUN
asir-4528	4	8	is	be	AUX
asir-4528	4	9	milestone	milestone	NOUN
asir-4528	4	10	of	of	ADP
asir-4528	4	11	all	all	DET
asir-4528	4	12	further	further	ADJ
asir-4528	4	13	difficulties	difficulty	NOUN
asir-4528	4	14	in	in	ADP
asir-4528	4	15	interpretation	interpretation	NOUN
asir-4528	4	16	of	of	ADP
asir-4528	4	17	quantum	quantum	ADJ
asir-4528	4	18	mechanics	mechanic	NOUN
asir-4528	4	19	.	.	PUNCT
asir-4528	5	1	keywords	keyword	VERB
asir-4528	5	2	geometric	geometric	ADJ
asir-4528	5	3	algebra	algebra	NOUN
asir-4528	5	4	,	,	PUNCT
asir-4528	5	5	quantum	quantum	ADJ
asir-4528	5	6	states	state	NOUN
asir-4528	5	7	,	,	PUNCT
asir-4528	5	8	observables	observable	NOUN
asir-4528	5	9	,	,	PUNCT
asir-4528	5	10	measurements	measurement	NOUN
asir-4528	5	11	1	1	NUM
asir-4528	5	12	.	.	PUNCT
asir-4528	5	13	introduction	introduction	NOUN
asir-4528	5	14	.	.	PUNCT
asir-4528	6	1	working	work	VERB
asir-4528	6	2	with	with	ADP
asir-4528	6	3	g	g	NOUN
asir-4528	6	4	-	-	PUNCT
asir-4528	6	5	qubits	qubit	NOUN
asir-4528	6	6	instead	instead	ADV
asir-4528	6	7	of	of	ADP
asir-4528	6	8	qubits	qubit	NOUN
asir-4528	6	9	theory	theory	NOUN
asir-4528	6	10	of	of	ADP
asir-4528	6	11	upgrading	upgrade	VERB
asir-4528	6	12	conventional	conventional	ADJ
asir-4528	6	13	quantum	quantum	ADJ
asir-4528	6	14	mechanics	mechanic	NOUN
asir-4528	6	15	has	have	AUX
asir-4528	6	16	been	be	AUX
asir-4528	6	17	under	under	ADP
asir-4528	6	18	development	development	NOUN
asir-4528	6	19	(	(	PUNCT
asir-4528	6	20	soiguine	soiguine	NOUN
asir-4528	6	21	,	,	PUNCT
asir-4528	6	22	1996	1996	NUM
asir-4528	6	23	,	,	PUNCT
asir-4528	6	24	2014	2014	NUM
asir-4528	6	25	,	,	PUNCT
asir-4528	6	26	2015	2015	NUM
asir-4528	6	27	,	,	PUNCT
asir-4528	6	28	2020	2020	NUM
asir-4528	6	29	)	)	PUNCT
asir-4528	6	30	.	.	PUNCT
asir-4528	7	1	the	the	DET
asir-4528	7	2	main	main	ADJ
asir-4528	7	3	novel	novel	NOUN
asir-4528	7	4	features	feature	NOUN
asir-4528	7	5	are	be	AUX
asir-4528	7	6	:	:	PUNCT
asir-4528	7	7	replacing	replace	VERB
asir-4528	7	8	complex	complex	ADJ
asir-4528	7	9	numbers	number	NOUN
asir-4528	7	10	with	with	ADP
asir-4528	7	11	elements	element	NOUN
asir-4528	7	12	of	of	ADP
asir-4528	7	13	even	even	ADJ
asir-4528	7	14	subalgebra	subalgebra	NOUN
asir-4528	7	15	of	of	ADP
asir-4528	7	16	geometric	geometric	ADJ
asir-4528	7	17	algebra	algebra	NOUN
asir-4528	7	18	in	in	ADP
asir-4528	7	19	three	three	NUM
asir-4528	7	20	dimensions	dimension	NOUN
asir-4528	7	21	,	,	PUNCT
asir-4528	7	22	that	that	PRON
asir-4528	7	23	’s	’s	ADV
asir-4528	7	24	by	by	ADP
asir-4528	7	25	elements	element	NOUN
asir-4528	7	26	of	of	ADP
asir-4528	7	27	the	the	DET
asir-4528	7	28	form	form	NOUN
asir-4528	7	29	“	"	PUNCT
asir-4528	7	30	scalar	scalar	ADJ
asir-4528	7	31	plus	plus	CCONJ
asir-4528	7	32	bivector	bivector	NOUN
asir-4528	7	33	”	"	PUNCT
asir-4528	7	34	.	.	PUNCT
asir-4528	8	1	the	the	DET
asir-4528	8	2	objects	object	NOUN
asir-4528	8	3	identifying	identify	VERB
asir-4528	8	4	physical	physical	ADJ
asir-4528	8	5	media	medium	NOUN
asir-4528	8	6	are	be	AUX
asir-4528	8	7	of	of	ADP
asir-4528	8	8	the	the	DET
asir-4528	8	9	same	same	ADJ
asir-4528	8	10	structure	structure	NOUN
asir-4528	8	11	:	:	PUNCT
asir-4528	8	12	explicitly	explicitly	ADV
asir-4528	8	13	defined	define	VERB
asir-4528	8	14	plane	plane	NOUN
asir-4528	8	15	along	along	ADP
asir-4528	8	16	with	with	ADP
asir-4528	8	17	angle	angle	NOUN
asir-4528	8	18	of	of	ADP
asir-4528	8	19	rotation	rotation	NOUN
asir-4528	8	20	in	in	ADP
asir-4528	8	21	that	that	DET
asir-4528	8	22	plane	plane	NOUN
asir-4528	8	23	.	.	PUNCT
asir-4528	9	1	operators	operator	NOUN
asir-4528	9	2	acting	act	VERB
asir-4528	9	3	on	on	ADP
asir-4528	9	4	the	the	DET
asir-4528	9	5	objects	object	NOUN
asir-4528	9	6	are	be	AUX
asir-4528	9	7	operators	operator	NOUN
asir-4528	9	8	of	of	ADP
asir-4528	9	9	rotation	rotation	NOUN
asir-4528	9	10	having	have	VERB
asir-4528	9	11	the	the	DET
asir-4528	9	12	same	same	ADJ
asir-4528	9	13	structure	structure	NOUN
asir-4528	9	14	:	:	PUNCT
asir-4528	9	15	scalar	scalar	ADJ
asir-4528	9	16	plus	plus	CCONJ
asir-4528	9	17	bivector	bivector	NOUN
asir-4528	9	18	.	.	PUNCT
asir-4528	10	1	that	that	PRON
asir-4528	10	2	is	be	AUX
asir-4528	10	3	the	the	DET
asir-4528	10	4	measurement	measurement	NOUN
asir-4528	10	5	operation	operation	NOUN
asir-4528	10	6	.	.	PUNCT
asir-4528	11	1	mapping	mapping	NOUN
asir-4528	11	2	of	of	ADP
asir-4528	11	3	operator	operator	NOUN
asir-4528	11	4	to	to	ADP
asir-4528	11	5	the	the	DET
asir-4528	11	6	result	result	NOUN
asir-4528	11	7	of	of	ADP
asir-4528	11	8	measurement	measurement	NOUN
asir-4528	11	9	,	,	PUNCT
asir-4528	11	10	that	that	PRON
asir-4528	11	11	is	be	AUX
asir-4528	11	12	collapse	collapse	NOUN
asir-4528	11	13	,	,	PUNCT
asir-4528	11	14	creates	create	VERB
asir-4528	11	15	a	a	DET
asir-4528	11	16	“	"	PUNCT
asir-4528	11	17	particle	particle	NOUN
asir-4528	11	18	”	"	PUNCT
asir-4528	11	19	.	.	PUNCT
asir-4528	12	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-4528	12	2	applied	apply	VERB
asir-4528	12	3	science	science	NOUN
asir-4528	12	4	and	and	CCONJ
asir-4528	12	5	innovative	innovative	ADJ
asir-4528	12	6	research	research	NOUN
asir-4528	12	7	vol	vol	NOUN
asir-4528	12	8	.	.	PROPN
asir-4528	13	1	6	6	NUM
asir-4528	13	2	,	,	PUNCT
asir-4528	13	3	no	no	INTJ
asir-4528	13	4	.	.	NOUN
asir-4528	13	5	1	1	NUM
asir-4528	13	6	,	,	PUNCT
asir-4528	13	7	2022	2022	NUM
asir-4528	13	8	47	47	NUM
asir-4528	13	9	published	publish	VERB
asir-4528	13	10	by	by	ADP
asir-4528	13	11	scholink	scholink	PROPN
asir-4528	13	12	inc	inc	PROPN
asir-4528	13	13	.	.	PUNCT
asir-4528	14	1	the	the	DET
asir-4528	14	2	operators	operator	NOUN
asir-4528	14	3	can	can	AUX
asir-4528	14	4	be	be	AUX
asir-4528	14	5	identified	identify	VERB
asir-4528	14	6	by	by	ADP
asir-4528	14	7	points	point	NOUN
asir-4528	14	8	on	on	ADP
asir-4528	14	9	the	the	DET
asir-4528	14	10	three	three	NUM
asir-4528	14	11	-	-	PUNCT
asir-4528	14	12	sphere	sphere	NOUN
asir-4528	14	13	𝕊3	𝕊3	NOUN
asir-4528	14	14	and	and	CCONJ
asir-4528	14	15	are	be	AUX
asir-4528	14	16	connected	connect	VERB
asir-4528	14	17	,	,	PUNCT
asir-4528	14	18	due	due	ADP
asir-4528	14	19	to	to	ADP
asir-4528	14	20	hedgehog	hedgehog	PROPN
asir-4528	14	21	theorem	theorem	PROPN
asir-4528	14	22	,	,	PUNCT
asir-4528	14	23	by	by	ADP
asir-4528	14	24	clifford	clifford	PROPN
asir-4528	14	25	translations	translation	NOUN
asir-4528	14	26	.	.	PUNCT
asir-4528	15	1	modifying	modify	VERB
asir-4528	15	2	the	the	DET
asir-4528	15	3	operators	operator	NOUN
asir-4528	15	4	due	due	ADP
asir-4528	15	5	to	to	ADP
asir-4528	15	6	clifford	clifford	PROPN
asir-4528	15	7	translation	translation	NOUN
asir-4528	15	8	is	be	AUX
asir-4528	15	9	identified	identify	VERB
asir-4528	15	10	by	by	ADP
asir-4528	15	11	the	the	DET
asir-4528	15	12	generalization	generalization	NOUN
asir-4528	15	13	of	of	ADP
asir-4528	15	14	schrodinger	schrodinger	PROPN
asir-4528	15	15	equation	equation	NOUN
asir-4528	15	16	containing	contain	VERB
asir-4528	15	17	unit	unit	NOUN
asir-4528	15	18	bivectors	bivector	NOUN
asir-4528	15	19	in	in	ADP
asir-4528	15	20	three	three	NUM
asir-4528	15	21	dimensions	dimension	NOUN
asir-4528	15	22	instead	instead	ADV
asir-4528	15	23	of	of	ADP
asir-4528	15	24	formal	formal	ADJ
asir-4528	15	25	imaginary	imaginary	ADJ
asir-4528	15	26	unit	unit	NOUN
asir-4528	15	27	qubits	qubit	NOUN
asir-4528	15	28	,	,	PUNCT
asir-4528	15	29	identifying	identify	VERB
asir-4528	15	30	states	state	NOUN
asir-4528	15	31	in	in	ADP
asir-4528	15	32	conventional	conventional	ADJ
asir-4528	15	33	quantum	quantum	ADJ
asir-4528	15	34	mechanics	mechanic	NOUN
asir-4528	15	35	,	,	PUNCT
asir-4528	15	36	mathematically	mathematically	ADV
asir-4528	15	37	are	be	AUX
asir-4528	15	38	elements	element	NOUN
asir-4528	15	39	of	of	ADP
asir-4528	15	40	two	two	NUM
asir-4528	15	41	-	-	PUNCT
asir-4528	15	42	dimensional	dimensional	ADJ
asir-4528	15	43	complex	complex	ADJ
asir-4528	15	44	spaces	space	NOUN
asir-4528	15	45	:	:	PUNCT
asir-4528	15	46	.𝑥1+𝑖𝑦1	.𝑥1+𝑖𝑦1	SYM
asir-4528	15	47	𝑥2+𝑖𝑦2	𝑥2+𝑖𝑦2	PROPN
asir-4528	15	48	/	/	SYM
asir-4528	15	49	,	,	PUNCT
asir-4528	15	50	‖𝑥1	‖𝑥1	NOUN
asir-4528	16	1	+	+	CCONJ
asir-4528	16	2	𝑖𝑦1‖	𝑖𝑦1‖	ADJ
asir-4528	16	3	2	2	NUM
asir-4528	16	4	+	+	NUM
asir-4528	16	5	‖𝑥2	‖𝑥2	PROPN
asir-4528	17	1	+	+	NUM
asir-4528	17	2	𝑖𝑦2‖	𝑖𝑦2‖	SYM
asir-4528	17	3	2	2	NUM
asir-4528	17	4	=	=	SYM
asir-4528	17	5	1	1	NUM
asir-4528	17	6	,	,	PUNCT
asir-4528	17	7	unit	unit	NOUN
asir-4528	17	8	value	value	NOUN
asir-4528	17	9	element	element	NOUN
asir-4528	17	10	of	of	ADP
asir-4528	17	11	𝐶2	𝐶2	PROPN
asir-4528	17	12	.	.	PUNCT
asir-4528	17	13	imaginary	imaginary	ADJ
asir-4528	17	14	unit	unit	NOUN
asir-4528	17	15	𝑖	𝑖	SYM
asir-4528	17	16	is	be	AUX
asir-4528	17	17	used	use	VERB
asir-4528	17	18	formally	formally	ADV
asir-4528	17	19	,	,	PUNCT
asir-4528	17	20	without	without	ADP
asir-4528	17	21	geometrical	geometrical	ADJ
asir-4528	17	22	identification	identification	NOUN
asir-4528	17	23	in	in	ADP
asir-4528	17	24	three	three	NUM
asir-4528	17	25	dimensions	dimension	NOUN
asir-4528	17	26	.	.	PUNCT
asir-4528	18	1	in	in	ADP
asir-4528	18	2	another	another	DET
asir-4528	18	3	accepted	accept	VERB
asir-4528	18	4	notations	notation	NOUN
asir-4528	18	5	a	a	DET
asir-4528	18	6	qubit	qubit	NOUN
asir-4528	18	7	is	be	AUX
asir-4528	18	8	:	:	PUNCT
asir-4528	18	9	𝐶2	𝐶2	INTJ
asir-4528	18	10	∋	∋	NOUN
asir-4528	18	11	(	(	PUNCT
asir-4528	18	12	𝑧1	𝑧1	PROPN
asir-4528	18	13	𝑧2	𝑧2	PROPN
asir-4528	18	14	)	)	PUNCT
asir-4528	19	1	=	=	SYM
asir-4528	19	2	𝑧1	𝑧1	NOUN
asir-4528	19	3	(	(	PUNCT
asir-4528	19	4	1	1	NUM
asir-4528	19	5	0	0	NUM
asir-4528	19	6	)	)	PUNCT
asir-4528	20	1	+	+	CCONJ
asir-4528	20	2	𝑧2	𝑧2	NOUN
asir-4528	20	3	(	(	PUNCT
asir-4528	20	4	0	0	NUM
asir-4528	20	5	1	1	NUM
asir-4528	20	6	)	)	PUNCT
asir-4528	20	7	=	=	SYM
asir-4528	20	8	𝑧1|0⟩	𝑧1|0⟩	NOUN
asir-4528	20	9	+	+	CCONJ
asir-4528	20	10	𝑧2|1⟩	𝑧2|1⟩	ADJ
asir-4528	20	11	in	in	ADP
asir-4528	20	12	the	the	DET
asir-4528	20	13	suggested	suggest	VERB
asir-4528	20	14	formalism	formalism	NOUN
asir-4528	20	15	complex	complex	ADJ
asir-4528	20	16	numbers	number	NOUN
asir-4528	20	17	𝑥	𝑥	X
asir-4528	21	1	+	+	CCONJ
asir-4528	21	2	𝑖𝑦	𝑖𝑦	PRON
asir-4528	21	3	are	be	AUX
asir-4528	21	4	replaced	replace	VERB
asir-4528	21	5	with	with	ADP
asir-4528	21	6	elements	element	NOUN
asir-4528	21	7	of	of	ADP
asir-4528	21	8	𝐺3	𝐺3	NOUN
asir-4528	21	9	+	+	PROPN
asir-4528	21	10	,	,	PUNCT
asir-4528	21	11	subalgebra	subalgebra	NOUN
asir-4528	21	12	of	of	ADP
asir-4528	21	13	𝐺3	𝐺3	PROPN
asir-4528	21	14	.	.	PUNCT
asir-4528	22	1	the	the	DET
asir-4528	22	2	𝐺3	𝐺3	PROPN
asir-4528	22	3	elements	element	NOUN
asir-4528	22	4	of	of	ADP
asir-4528	22	5	the	the	DET
asir-4528	22	6	form	form	NOUN
asir-4528	22	7	𝑀3	𝑀3	NOUN
asir-4528	22	8	=	=	SYM
asir-4528	22	9	𝛼	𝛼	NOUN
asir-4528	22	10	+	+	X
asir-4528	22	11	𝐼𝑆𝛽	𝐼𝑆𝛽	NOUN
asir-4528	22	12	,	,	PUNCT
asir-4528	22	13	where	where	SCONJ
asir-4528	22	14	𝐼𝑆	𝐼𝑆	PROPN
asir-4528	22	15	is	be	AUX
asir-4528	22	16	some	some	DET
asir-4528	22	17	unit	unit	NOUN
asir-4528	22	18	bivector	bivector	NOUN
asir-4528	22	19	arbitrary	arbitrary	PROPN
asir-4528	22	20	placed	place	VERB
asir-4528	22	21	in	in	ADP
asir-4528	22	22	three	three	NUM
asir-4528	22	23	-	-	PUNCT
asir-4528	22	24	dimensional	dimensional	ADJ
asir-4528	22	25	space	space	NOUN
asir-4528	22	26	,	,	PUNCT
asir-4528	22	27	comprise	comprise	VERB
asir-4528	22	28	so	so	ADV
asir-4528	22	29	called	call	VERB
asir-4528	22	30	even	even	ADV
asir-4528	22	31	subalgebra	subalgebra	NOUN
asir-4528	22	32	of	of	ADP
asir-4528	22	33	algebra	algebra	PROPN
asir-4528	22	34	𝐺3	𝐺3	PROPN
asir-4528	22	35	.	.	PUNCT
asir-4528	23	1	this	this	DET
asir-4528	23	2	subalgebra	subalgebra	NOUN
asir-4528	23	3	is	be	AUX
asir-4528	23	4	denoted	denote	VERB
asir-4528	23	5	by	by	ADP
asir-4528	23	6	𝐺3	𝐺3	NOUN
asir-4528	23	7	+	+	CCONJ
asir-4528	23	8	(	(	PUNCT
asir-4528	23	9	soiguine	soiguine	NOUN
asir-4528	23	10	,	,	PUNCT
asir-4528	23	11	2015	2015	NUM
asir-4528	23	12	,	,	PUNCT
asir-4528	23	13	2020	2020	NUM
asir-4528	23	14	)	)	PUNCT
asir-4528	23	15	.	.	PUNCT
asir-4528	24	1	elements	element	NOUN
asir-4528	24	2	of	of	ADP
asir-4528	24	3	𝐺3	𝐺3	PROPN
asir-4528	24	4	+	+	CCONJ
asir-4528	24	5	can	can	AUX
asir-4528	24	6	be	be	AUX
asir-4528	24	7	depict	depict	ADJ
asir-4528	24	8	as	as	ADP
asir-4528	24	9	in	in	ADP
asir-4528	24	10	figure	figure	NOUN
asir-4528	24	11	1	1	NUM
asir-4528	24	12	.	.	PUNCT
asir-4528	24	13	figure	figure	NOUN
asir-4528	24	14	1	1	NUM
asir-4528	24	15	.	.	PUNCT
asir-4528	25	1	an	an	DET
asir-4528	25	2	element	element	NOUN
asir-4528	25	3	of	of	ADP
asir-4528	25	4	𝑮𝟑	𝑮𝟑	NOUN
asir-4528	25	5	+	+	CCONJ
asir-4528	25	6	unit	unit	NOUN
asir-4528	25	7	value	value	NOUN
asir-4528	25	8	elements	element	NOUN
asir-4528	25	9	of	of	ADP
asir-4528	25	10	𝐺3	𝐺3	PROPN
asir-4528	25	11	+	+	X
asir-4528	25	12	,	,	PUNCT
asir-4528	25	13	𝛼2	𝛼2	PROPN
asir-4528	25	14	+	+	CCONJ
asir-4528	25	15	𝛽2	𝛽2	NOUN
asir-4528	25	16	=	=	SYM
asir-4528	25	17	1	1	NUM
asir-4528	25	18	,	,	PUNCT
asir-4528	25	19	will	will	AUX
asir-4528	25	20	be	be	AUX
asir-4528	25	21	called	call	VERB
asir-4528	25	22	g	g	NOUN
asir-4528	25	23	-	-	PUNCT
asir-4528	25	24	qubits	qubit	NOUN
asir-4528	25	25	.	.	PUNCT
asir-4528	26	1	the	the	DET
asir-4528	26	2	wave	wave	NOUN
asir-4528	26	3	functions	function	NOUN
asir-4528	26	4	(	(	PUNCT
asir-4528	26	5	states	state	NOUN
asir-4528	26	6	)	)	PUNCT
asir-4528	26	7	implemented	implement	VERB
asir-4528	26	8	as	as	SCONJ
asir-4528	26	9	g	g	NOUN
asir-4528	26	10	-	-	PUNCT
asir-4528	26	11	qubits	qubit	NOUN
asir-4528	26	12	store	store	VERB
asir-4528	26	13	much	much	ADV
asir-4528	26	14	more	more	ADJ
asir-4528	26	15	information	information	NOUN
asir-4528	26	16	than	than	ADP
asir-4528	26	17	qubits	qubit	NOUN
asir-4528	26	18	,	,	PUNCT
asir-4528	26	19	see	see	VERB
asir-4528	26	20	figure	figure	NOUN
asir-4528	26	21	2	2	NUM
asir-4528	26	22	.	.	NOUN
asir-4528	26	23	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-4528	26	24	applied	apply	VERB
asir-4528	26	25	science	science	NOUN
asir-4528	26	26	and	and	CCONJ
asir-4528	26	27	innovative	innovative	ADJ
asir-4528	26	28	research	research	NOUN
asir-4528	26	29	vol	vol	NOUN
asir-4528	26	30	.	.	PROPN
asir-4528	27	1	6	6	NUM
asir-4528	27	2	,	,	PUNCT
asir-4528	27	3	no	no	INTJ
asir-4528	27	4	.	.	NOUN
asir-4528	27	5	1	1	NUM
asir-4528	27	6	,	,	PUNCT
asir-4528	27	7	2022	2022	NUM
asir-4528	27	8	48	48	NUM
asir-4528	27	9	published	publish	VERB
asir-4528	27	10	by	by	ADP
asir-4528	27	11	scholink	scholink	PROPN
asir-4528	27	12	inc	inc	PROPN
asir-4528	27	13	.	.	PROPN
asir-4528	27	14	figure	figure	NOUN
asir-4528	27	15	2	2	NUM
asir-4528	27	16	.	.	PUNCT
asir-4528	27	17	geomectrically	geomectrically	ADV
asir-4528	27	18	picted	picte	VERB
asir-4528	27	19	qubits	qubit	NOUN
asir-4528	27	20	and	and	CCONJ
asir-4528	27	21	g	g	NOUN
asir-4528	27	22	-	-	PUNCT
asir-4528	27	23	qubits	qubit	NOUN
asir-4528	27	24	2	2	NUM
asir-4528	27	25	.	.	X
asir-4528	27	26	lift	lift	NOUN
asir-4528	27	27	of	of	ADP
asir-4528	27	28	qubits	qubit	NOUN
asir-4528	27	29	to	to	ADP
asir-4528	27	30	g	g	NOUN
asir-4528	27	31	-	-	PUNCT
asir-4528	27	32	qubits	qubit	NOUN
asir-4528	27	33	,	,	PUNCT
asir-4528	27	34	fiber	fiber	NOUN
asir-4528	27	35	bundles	bundle	NOUN
asir-4528	27	36	and	and	CCONJ
asir-4528	27	37	probabilities	probability	NOUN
asir-4528	27	38	take	take	VERB
asir-4528	27	39	right	right	ADJ
asir-4528	27	40	-	-	PUNCT
asir-4528	27	41	hand	hand	NOUN
asir-4528	27	42	screw	screw	NOUN
asir-4528	27	43	oriented	orient	VERB
asir-4528	27	44	basis	basis	NOUN
asir-4528	27	45	*	*	PUNCT
asir-4528	27	46	𝐵1	𝐵1	PROPN
asir-4528	27	47	,	,	PUNCT
asir-4528	27	48	𝐵2	𝐵2	NOUN
asir-4528	27	49	,	,	PUNCT
asir-4528	27	50	𝐵3	𝐵3	PROPN
asir-4528	27	51	+	+	NUM
asir-4528	27	52	of	of	ADP
asir-4528	27	53	unit	unit	NOUN
asir-4528	27	54	value	value	NOUN
asir-4528	27	55	bivectors	bivector	NOUN
asir-4528	27	56	,	,	PUNCT
asir-4528	27	57	with	with	SCONJ
asir-4528	27	58	the	the	DET
asir-4528	27	59	multiplication	multiplication	NOUN
asir-4528	27	60	rules	rule	VERB
asir-4528	27	61	𝐵1𝐵2	𝐵1𝐵2	NOUN
asir-4528	27	62	=	=	SYM
asir-4528	27	63	−𝐵3	−𝐵3	PROPN
asir-4528	27	64	,	,	PUNCT
asir-4528	27	65	𝐵1𝐵3	𝐵1𝐵3	PROPN
asir-4528	27	66	=	=	PUNCT
asir-4528	27	67	𝐵2	𝐵2	PROPN
asir-4528	27	68	,	,	PUNCT
asir-4528	27	69	𝐵2𝐵3	𝐵2𝐵3	NOUN
asir-4528	27	70	=	=	NUM
asir-4528	27	71	−𝐵1	−𝐵1	PROPN
asir-4528	27	72	,	,	PUNCT
asir-4528	27	73	𝐼3𝐵1𝐼3𝐵2𝐼3𝐵3	𝐼3𝐵1𝐼3𝐵2𝐼3𝐵3	X
asir-4528	28	1	=	=	SYM
asir-4528	28	2	𝐼3	𝐼3	NOUN
asir-4528	28	3	(	(	PUNCT
asir-4528	28	4	or	or	CCONJ
asir-4528	28	5	equivalently	equivalently	ADV
asir-4528	28	6	𝐵1𝐵2𝐵3	𝐵1𝐵2𝐵3	NOUN
asir-4528	28	7	=	=	SYM
asir-4528	28	8	1	1	X
asir-4528	28	9	)	)	PUNCT
asir-4528	28	10	,	,	PUNCT
asir-4528	28	11	where	where	SCONJ
asir-4528	28	12	𝐼3	𝐼3	NOUN
asir-4528	28	13	is	be	AUX
asir-4528	28	14	oriented	orient	VERB
asir-4528	28	15	unit	unit	NOUN
asir-4528	28	16	value	value	NOUN
asir-4528	28	17	volume	volume	NOUN
asir-4528	28	18	in	in	ADP
asir-4528	28	19	three	three	NUM
asir-4528	28	20	dimensions	dimension	NOUN
asir-4528	28	21	named	name	VERB
asir-4528	28	22	also	also	ADV
asir-4528	28	23	pseudoscalar	pseudoscalar	ADJ
asir-4528	28	24	.	.	PUNCT
asir-4528	29	1	quantum	quantum	PROPN
asir-4528	29	2	mechanical	mechanical	ADJ
asir-4528	29	3	qubit	qubit	NOUN
asir-4528	29	4	state	state	PROPN
asir-4528	29	5	,	,	PUNCT
asir-4528	29	6	|𝜓⟩	|𝜓⟩	PROPN
asir-4528	29	7	=	=	SYM
asir-4528	29	8	𝑧1|0⟩	𝑧1|0⟩	PROPN
asir-4528	29	9	+	+	CCONJ
asir-4528	29	10	𝑧2|1⟩	𝑧2|1⟩	ADJ
asir-4528	29	11	,	,	PUNCT
asir-4528	29	12	is	be	AUX
asir-4528	29	13	linear	linear	ADJ
asir-4528	29	14	combination	combination	NOUN
asir-4528	29	15	of	of	ADP
asir-4528	29	16	two	two	NUM
asir-4528	29	17	basis	basis	NOUN
asir-4528	29	18	states	state	NOUN
asir-4528	29	19	|0⟩	|0⟩	VERB
asir-4528	29	20	and	and	CCONJ
asir-4528	29	21	|1⟩.	|1⟩.	VERB
asir-4528	29	22	in	in	ADP
asir-4528	29	23	the	the	DET
asir-4528	29	24	𝐺3	𝐺3	NOUN
asir-4528	29	25	+	+	NUM
asir-4528	29	26	terms	term	NOUN
asir-4528	29	27	these	these	DET
asir-4528	29	28	two	two	NUM
asir-4528	29	29	states	state	NOUN
asir-4528	29	30	correspond	correspond	VERB
asir-4528	29	31	to	to	ADP
asir-4528	29	32	the	the	DET
asir-4528	29	33	following	follow	VERB
asir-4528	29	34	classes	class	NOUN
asir-4528	29	35	of	of	ADP
asir-4528	29	36	equivalence	equivalence	NOUN
asir-4528	29	37	in	in	ADP
asir-4528	29	38	𝐺3	𝐺3	PROPN
asir-4528	30	1	+	+	PROPN
asir-4528	30	2	,	,	PUNCT
asir-4528	30	3	depending	depend	VERB
asir-4528	30	4	on	on	ADP
asir-4528	30	5	which	which	PRON
asir-4528	30	6	basis	basis	NOUN
asir-4528	30	7	bivector	bivector	NOUN
asir-4528	30	8	is	be	AUX
asir-4528	30	9	selected	select	VERB
asir-4528	30	10	as	as	ADP
asir-4528	30	11	complex	complex	ADJ
asir-4528	30	12	plane	plane	NOUN
asir-4528	30	13	:	:	PUNCT
asir-4528	30	14	if	if	SCONJ
asir-4528	30	15	𝐵1	𝐵1	NOUN
asir-4528	30	16	is	be	AUX
asir-4528	30	17	taken	take	VERB
asir-4528	30	18	as	as	ADP
asir-4528	30	19	complex	complex	ADJ
asir-4528	30	20	plane	plane	NOUN
asir-4528	30	21	,	,	PUNCT
asir-4528	30	22	then	then	ADV
asir-4528	30	23	state	state	NOUN
asir-4528	30	24	|0⟩	|0⟩	PROPN
asir-4528	30	25	has	have	VERB
asir-4528	30	26	fiber	fiber	NOUN
asir-4528	30	27	(	(	PUNCT
asir-4528	30	28	level	level	NOUN
asir-4528	30	29	set	set	NOUN
asir-4528	30	30	)	)	PUNCT
asir-4528	30	31	of	of	ADP
asir-4528	30	32	the	the	DET
asir-4528	30	33	𝐺3	𝐺3	NOUN
asir-4528	30	34	+	+	NUM
asir-4528	30	35	elements	element	NOUN
asir-4528	30	36	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	30	37	,	,	PUNCT
asir-4528	30	38	𝛽	𝛽	NOUN
asir-4528	30	39	,	,	PUNCT
asir-4528	30	40	𝑆	𝑆	PROPN
asir-4528	30	41	)	)	PUNCT
asir-4528	30	42	|0⟩	|0⟩	NOUN
asir-4528	30	43	(	(	PUNCT
asir-4528	30	44	0	0	NUM
asir-4528	30	45	-	-	PUNCT
asir-4528	30	46	type	type	NOUN
asir-4528	30	47	𝐺3	𝐺3	NOUN
asir-4528	30	48	+	+	CCONJ
asir-4528	30	49	states	state	NOUN
asir-4528	30	50	):	):	PUNCT
asir-4528	30	51	•	•	ADP
asir-4528	30	52	𝛼	𝛼	NOUN
asir-4528	30	53	+	+	X
asir-4528	30	54	𝛽1𝐵1	𝛽1𝐵1	PROPN
asir-4528	30	55	,	,	PUNCT
asir-4528	30	56	𝛼	𝛼	PROPN
asir-4528	30	57	2	2	NUM
asir-4528	30	58	+	+	NOUN
asir-4528	30	59	𝛽1	𝛽1	NOUN
asir-4528	30	60	2	2	NUM
asir-4528	30	61	=	=	SYM
asir-4528	30	62	1	1	NUM
asir-4528	30	63	state	state	NOUN
asir-4528	30	64	|1⟩	|1⟩	PROPN
asir-4528	30	65	has	have	VERB
asir-4528	30	66	fiber	fiber	NOUN
asir-4528	30	67	of	of	ADP
asir-4528	30	68	the	the	DET
asir-4528	30	69	𝐺3	𝐺3	NOUN
asir-4528	30	70	+	+	NUM
asir-4528	30	71	elements	element	NOUN
asir-4528	30	72	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	30	73	,	,	PUNCT
asir-4528	30	74	𝛽	𝛽	PROPN
asir-4528	30	75	,	,	PUNCT
asir-4528	30	76	𝑆	𝑆	PROPN
asir-4528	30	77	)	)	PUNCT
asir-4528	30	78	|1⟩	|1⟩	PROPN
asir-4528	30	79	(	(	PUNCT
asir-4528	30	80	1	1	NUM
asir-4528	30	81	-	-	PUNCT
asir-4528	30	82	type	type	NOUN
asir-4528	30	83	𝐺3	𝐺3	NOUN
asir-4528	30	84	+	+	CCONJ
asir-4528	30	85	states	state	NOUN
asir-4528	30	86	):	):	PUNCT
asir-4528	30	87	•	•	NUM
asir-4528	30	88	𝛽3	𝛽3	PROPN
asir-4528	30	89	𝐵3	𝐵3	NOUN
asir-4528	30	90	+	+	CCONJ
asir-4528	30	91	𝛽2	𝛽2	ADJ
asir-4528	30	92	𝐵2	𝐵2	NOUN
asir-4528	30	93	=	=	SYM
asir-4528	30	94	(	(	PUNCT
asir-4528	30	95	𝛽3	𝛽3	NOUN
asir-4528	30	96	+	+	CCONJ
asir-4528	30	97	𝛽2𝐵1)𝐵3	𝛽2𝐵1)𝐵3	ADJ
asir-4528	30	98	,	,	PUNCT
asir-4528	30	99	𝛽3	𝛽3	NOUN
asir-4528	30	100	2	2	NUM
asir-4528	30	101	+	+	CCONJ
asir-4528	30	102	𝛽2	𝛽2	ADJ
asir-4528	30	103	2	2	NUM
asir-4528	30	104	=	=	SYM
asir-4528	30	105	1	1	NUM
asir-4528	30	106	if	if	SCONJ
asir-4528	30	107	𝐵2	𝐵2	NOUN
asir-4528	30	108	is	be	AUX
asir-4528	30	109	taken	take	VERB
asir-4528	30	110	as	as	ADP
asir-4528	30	111	complex	complex	ADJ
asir-4528	30	112	plane	plane	NOUN
asir-4528	30	113	,	,	PUNCT
asir-4528	30	114	then	then	ADV
asir-4528	30	115	state	state	NOUN
asir-4528	30	116	|0⟩	|0⟩	PROPN
asir-4528	30	117	has	have	VERB
asir-4528	30	118	fiber	fiber	NOUN
asir-4528	30	119	(	(	PUNCT
asir-4528	30	120	level	level	NOUN
asir-4528	30	121	set	set	NOUN
asir-4528	30	122	)	)	PUNCT
asir-4528	30	123	of	of	ADP
asir-4528	30	124	the	the	DET
asir-4528	30	125	𝐺3	𝐺3	NOUN
asir-4528	30	126	+	+	NUM
asir-4528	30	127	elements	element	NOUN
asir-4528	30	128	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	30	129	,	,	PUNCT
asir-4528	30	130	𝛽	𝛽	NOUN
asir-4528	30	131	,	,	PUNCT
asir-4528	30	132	𝑆	𝑆	PROPN
asir-4528	30	133	)	)	PUNCT
asir-4528	30	134	|0⟩	|0⟩	NOUN
asir-4528	30	135	(	(	PUNCT
asir-4528	30	136	0	0	NUM
asir-4528	30	137	-	-	PUNCT
asir-4528	30	138	type	type	NOUN
asir-4528	30	139	𝐺3	𝐺3	NOUN
asir-4528	30	140	+	+	CCONJ
asir-4528	30	141	states	state	NOUN
asir-4528	30	142	):	):	PUNCT
asir-4528	30	143	•	•	ADP
asir-4528	30	144	𝛼	𝛼	NOUN
asir-4528	30	145	+	+	CCONJ
asir-4528	30	146	𝛽2𝐵2	𝛽2𝐵2	NUM
asir-4528	30	147	,	,	PUNCT
asir-4528	30	148	𝛼	𝛼	PROPN
asir-4528	30	149	2	2	NUM
asir-4528	30	150	+	+	SYM
asir-4528	30	151	𝛽2	𝛽2	ADJ
asir-4528	30	152	2	2	NUM
asir-4528	30	153	=	=	SYM
asir-4528	30	154	1	1	NUM
asir-4528	30	155	state	state	NOUN
asir-4528	30	156	|1⟩	|1⟩	PROPN
asir-4528	30	157	has	have	VERB
asir-4528	30	158	fiber	fiber	NOUN
asir-4528	30	159	of	of	ADP
asir-4528	30	160	the	the	DET
asir-4528	30	161	𝐺3	𝐺3	NOUN
asir-4528	30	162	+	+	NUM
asir-4528	30	163	elements	element	NOUN
asir-4528	30	164	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	30	165	,	,	PUNCT
asir-4528	30	166	𝛽	𝛽	PROPN
asir-4528	30	167	,	,	PUNCT
asir-4528	30	168	𝑆	𝑆	PROPN
asir-4528	30	169	)	)	PUNCT
asir-4528	30	170	|1⟩	|1⟩	PROPN
asir-4528	30	171	(	(	PUNCT
asir-4528	30	172	1	1	NUM
asir-4528	30	173	-	-	PUNCT
asir-4528	30	174	type	type	NOUN
asir-4528	30	175	𝐺3	𝐺3	NOUN
asir-4528	30	176	+	+	CCONJ
asir-4528	30	177	states	state	NOUN
asir-4528	30	178	):	):	PUNCT
asir-4528	30	179	•	•	NUM
asir-4528	30	180	𝛽1	𝛽1	NOUN
asir-4528	30	181	𝐵1	𝐵1	NOUN
asir-4528	30	182	+	+	CCONJ
asir-4528	30	183	𝛽3	𝛽3	NOUN
asir-4528	30	184	𝐵3	𝐵3	NOUN
asir-4528	30	185	=	=	PUNCT
asir-4528	30	186	(	(	PUNCT
asir-4528	30	187	𝛽1	𝛽1	NOUN
asir-4528	30	188	+	+	CCONJ
asir-4528	30	189	𝛽3𝐵2)𝐵1	𝛽3𝐵2)𝐵1	PROPN
asir-4528	30	190	,	,	PUNCT
asir-4528	30	191	𝛽1	𝛽1	NOUN
asir-4528	30	192	2	2	NUM
asir-4528	31	1	+	+	NUM
asir-4528	31	2	𝛽3	𝛽3	NOUN
asir-4528	31	3	2	2	NUM
asir-4528	31	4	=	=	SYM
asir-4528	31	5	1	1	NUM
asir-4528	31	6	if	if	SCONJ
asir-4528	31	7	𝐵3	𝐵3	PROPN
asir-4528	31	8	is	be	AUX
asir-4528	31	9	taken	take	VERB
asir-4528	31	10	as	as	ADP
asir-4528	31	11	complex	complex	ADJ
asir-4528	31	12	plane	plane	NOUN
asir-4528	31	13	,	,	PUNCT
asir-4528	31	14	then	then	ADV
asir-4528	31	15	state	state	NOUN
asir-4528	31	16	|0⟩	|0⟩	PROPN
asir-4528	31	17	has	have	VERB
asir-4528	31	18	fiber	fiber	NOUN
asir-4528	31	19	(	(	PUNCT
asir-4528	31	20	level	level	NOUN
asir-4528	31	21	set	set	NOUN
asir-4528	31	22	)	)	PUNCT
asir-4528	31	23	of	of	ADP
asir-4528	31	24	the	the	DET
asir-4528	31	25	𝐺3	𝐺3	NOUN
asir-4528	31	26	+	+	NUM
asir-4528	31	27	elements	element	NOUN
asir-4528	31	28	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	31	29	,	,	PUNCT
asir-4528	31	30	𝛽	𝛽	NOUN
asir-4528	31	31	,	,	PUNCT
asir-4528	31	32	𝑆	𝑆	PROPN
asir-4528	31	33	)	)	PUNCT
asir-4528	31	34	|0⟩	|0⟩	NOUN
asir-4528	31	35	(	(	PUNCT
asir-4528	31	36	0	0	NUM
asir-4528	31	37	-	-	PUNCT
asir-4528	31	38	type	type	NOUN
asir-4528	31	39	𝐺3	𝐺3	NOUN
asir-4528	31	40	+	+	CCONJ
asir-4528	31	41	states	state	NOUN
asir-4528	31	42	):	):	PUNCT
asir-4528	31	43	•	•	ADP
asir-4528	31	44	𝛼	𝛼	NOUN
asir-4528	31	45	+	+	NOUN
asir-4528	31	46	𝛽3𝐵3	𝛽3𝐵3	PROPN
asir-4528	31	47	,	,	PUNCT
asir-4528	31	48	𝛼	𝛼	PROPN
asir-4528	31	49	2	2	NUM
asir-4528	31	50	+	+	NUM
asir-4528	31	51	𝛽3	𝛽3	NOUN
asir-4528	31	52	2	2	NUM
asir-4528	31	53	=	=	SYM
asir-4528	31	54	1	1	NUM
asir-4528	31	55	state	state	NOUN
asir-4528	31	56	|1⟩	|1⟩	PROPN
asir-4528	31	57	has	have	VERB
asir-4528	31	58	fiber	fiber	NOUN
asir-4528	31	59	of	of	ADP
asir-4528	31	60	the	the	DET
asir-4528	31	61	𝐺3	𝐺3	NOUN
asir-4528	31	62	+	+	NUM
asir-4528	31	63	elements	element	NOUN
asir-4528	31	64	𝑠𝑜(𝛼	𝑠𝑜(𝛼	PUNCT
asir-4528	31	65	,	,	PUNCT
asir-4528	31	66	𝛽	𝛽	PROPN
asir-4528	31	67	,	,	PUNCT
asir-4528	31	68	𝑆	𝑆	PROPN
asir-4528	31	69	)	)	PUNCT
asir-4528	31	70	|1⟩	|1⟩	PROPN
asir-4528	31	71	(	(	PUNCT
asir-4528	31	72	1	1	NUM
asir-4528	31	73	-	-	PUNCT
asir-4528	31	74	type	type	NOUN
asir-4528	31	75	𝐺3	𝐺3	NOUN
asir-4528	31	76	+	+	CCONJ
asir-4528	31	77	states	state	NOUN
asir-4528	31	78	):	):	PUNCT
asir-4528	31	79	•	•	NUM
asir-4528	31	80	𝛽1	𝛽1	NOUN
asir-4528	31	81	𝐵1	𝐵1	NOUN
asir-4528	31	82	+	+	CCONJ
asir-4528	31	83	𝛽2	𝛽2	ADJ
asir-4528	31	84	𝐵2	𝐵2	NOUN
asir-4528	31	85	=	=	PUNCT
asir-4528	31	86	(	(	PUNCT
asir-4528	31	87	𝛽2	𝛽2	PROPN
asir-4528	31	88	+	+	CCONJ
asir-4528	31	89	𝛽1𝐵3)𝐵2	𝛽1𝐵3)𝐵2	PROPN
asir-4528	31	90	,	,	PUNCT
asir-4528	31	91	𝛽2	𝛽2	ADJ
asir-4528	31	92	2	2	NUM
asir-4528	31	93	+	+	CCONJ
asir-4528	31	94	𝛽1	𝛽1	NOUN
asir-4528	31	95	2	2	NUM
asir-4528	31	96	=	=	SYM
asir-4528	31	97	1	1	NUM
asir-4528	31	98	general	general	ADJ
asir-4528	31	99	definition	definition	NOUN
asir-4528	31	100	of	of	ADP
asir-4528	31	101	measurement	measurement	NOUN
asir-4528	31	102	in	in	ADP
asir-4528	31	103	the	the	DET
asir-4528	31	104	suggested	suggested	ADJ
asir-4528	31	105	approach	approach	NOUN
asir-4528	31	106	includes	include	VERB
asir-4528	31	107	:	:	PUNCT
asir-4528	31	108	the	the	DET
asir-4528	31	109	set	set	NOUN
asir-4528	31	110	of	of	ADP
asir-4528	31	111	observables	observable	NOUN
asir-4528	31	112	to	to	PART
asir-4528	31	113	be	be	AUX
asir-4528	31	114	𝐺3	𝐺3	ADJ
asir-4528	32	1	+	+	ADP
asir-4528	32	2	,	,	PUNCT
asir-4528	32	3	the	the	DET
asir-4528	32	4	set	set	NOUN
asir-4528	32	5	of	of	ADP
asir-4528	32	6	states	state	NOUN
asir-4528	32	7	to	to	PART
asir-4528	32	8	be	be	AUX
asir-4528	32	9	elements	element	NOUN
asir-4528	32	10	of	of	ADP
asir-4528	32	11	𝐺3	𝐺3	NOUN
asir-4528	32	12	+	+	CCONJ
asir-4528	32	13	(	(	PUNCT
asir-4528	32	14	g	g	NOUN
asir-4528	32	15	-	-	PUNCT
asir-4528	32	16	qubits	qubit	NOUN
asir-4528	32	17	up	up	ADP
asir-4528	32	18	to	to	ADP
asir-4528	32	19	some	some	DET
asir-4528	32	20	scalar	scalar	ADJ
asir-4528	32	21	factor	factor	NOUN
asir-4528	32	22	)	)	PUNCT
asir-4528	32	23	,	,	PUNCT
asir-4528	32	24	measurement	measurement	NOUN
asir-4528	32	25	of	of	ADP
asir-4528	32	26	an	an	DET
asir-4528	32	27	observable	observable	ADJ
asir-4528	32	28	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-4528	32	29	applied	apply	VERB
asir-4528	32	30	science	science	NOUN
asir-4528	32	31	and	and	CCONJ
asir-4528	32	32	innovative	innovative	ADJ
asir-4528	32	33	research	research	NOUN
asir-4528	32	34	vol	vol	NOUN
asir-4528	32	35	.	.	PROPN
asir-4528	33	1	6	6	NUM
asir-4528	33	2	,	,	PUNCT
asir-4528	33	3	no	no	INTJ
asir-4528	33	4	.	.	NOUN
asir-4528	33	5	1	1	NUM
asir-4528	33	6	,	,	PUNCT
asir-4528	33	7	2022	2022	NUM
asir-4528	33	8	49	49	NUM
asir-4528	33	9	published	publish	VERB
asir-4528	33	10	by	by	ADP
asir-4528	33	11	scholink	scholink	PROPN
asir-4528	33	12	inc	inc	PROPN
asir-4528	33	13	.	.	PUNCT
asir-4528	34	1	𝐶	𝐶	PROPN
asir-4528	34	2	=	=	PUNCT
asir-4528	34	3	𝐶0	𝐶0	PROPN
asir-4528	34	4	+	+	CCONJ
asir-4528	34	5	𝐶1𝐵1	𝐶1𝐵1	PROPN
asir-4528	34	6	+	+	CCONJ
asir-4528	34	7	𝐶2𝐵2	𝐶2𝐵2	X
asir-4528	34	8	+	+	CCONJ
asir-4528	34	9	𝐶3𝐵3	𝐶3𝐵3	NOUN
asir-4528	34	10	by	by	ADP
asir-4528	34	11	g	g	NOUN
asir-4528	34	12	-	-	PUNCT
asir-4528	34	13	qubit	qubit	NOUN
asir-4528	34	14	(	(	PUNCT
asir-4528	34	15	wave	wave	NOUN
asir-4528	34	16	function	function	NOUN
asir-4528	34	17	)	)	PUNCT
asir-4528	34	18	𝛼	𝛼	PROPN
asir-4528	35	1	+	+	NUM
asir-4528	35	2	𝐼𝑆𝛽	𝐼𝑆𝛽	X
asir-4528	35	3	=	=	SYM
asir-4528	35	4	𝛼	𝛼	NOUN
asir-4528	35	5	+	+	CCONJ
asir-4528	35	6	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	35	7	+	+	CCONJ
asir-4528	35	8	𝛽2𝐵2	𝛽2𝐵2	PUNCT
asir-4528	35	9	+	+	CCONJ
asir-4528	35	10	𝛽3𝐵3	𝛽3𝐵3	NUM
asir-4528	35	11	is	be	AUX
asir-4528	35	12	defined	define	VERB
asir-4528	35	13	as	as	ADP
asir-4528	35	14	(	(	PUNCT
asir-4528	35	15	𝛼	𝛼	NOUN
asir-4528	35	16	−	−	PROPN
asir-4528	35	17	𝐼𝑆𝛽)𝐶(𝛼	𝐼𝑆𝛽)𝐶(𝛼	X
asir-4528	35	18	+	+	NUM
asir-4528	35	19	𝐼𝑆𝛽	𝐼𝑆𝛽	NOUN
asir-4528	35	20	)	)	PUNCT
asir-4528	35	21	with	with	ADP
asir-4528	35	22	the	the	DET
asir-4528	35	23	result	result	NOUN
asir-4528	35	24	:	:	PUNCT
asir-4528	35	25	𝐶0	𝐶0	PROPN
asir-4528	35	26	+	+	CCONJ
asir-4528	35	27	𝐶1𝐵1	𝐶1𝐵1	PROPN
asir-4528	35	28	+	+	CCONJ
asir-4528	35	29	𝐶2𝐵2	𝐶2𝐵2	X
asir-4528	35	30	+	+	CCONJ
asir-4528	35	31	𝐶3𝐵3	𝐶3𝐵3	NOUN
asir-4528	35	32	𝛼+𝛽1𝐵1+𝛽2𝐵2+𝛽3𝐵3	𝛼+𝛽1𝐵1+𝛽2𝐵2+𝛽3𝐵3	NOUN
asir-4528	35	33	→	→	PUNCT
asir-4528	35	34	𝐶0	𝐶0	PROPN
asir-4528	35	35	+	+	CCONJ
asir-4528	35	36	(	(	PUNCT
asir-4528	35	37	𝐶1,(𝛼	𝐶1,(𝛼	PROPN
asir-4528	35	38	2	2	NUM
asir-4528	35	39	+	+	NOUN
asir-4528	35	40	𝛽1	𝛽1	NOUN
asir-4528	35	41	2	2	NUM
asir-4528	35	42	)	)	PUNCT
asir-4528	35	43	−	−	PROPN
asir-4528	36	1	(	(	PUNCT
asir-4528	36	2	𝛽2	𝛽2	PROPN
asir-4528	36	3	2	2	NUM
asir-4528	36	4	+	+	NUM
asir-4528	36	5	𝛽3	𝛽3	NOUN
asir-4528	36	6	2)+	2)+	NUM
asir-4528	36	7	2𝐶2(𝛽1𝛽2	2𝐶2(𝛽1𝛽2	NUM
asir-4528	36	8	−	−	NOUN
asir-4528	36	9	𝛼𝛽3	𝛼𝛽3	ADV
asir-4528	36	10	)	)	PUNCT
asir-4528	37	1	+	+	CCONJ
asir-4528	37	2	2𝐶3(𝛼𝛽2	2𝐶3(𝛼𝛽2	NUM
asir-4528	37	3	+	+	CCONJ
asir-4528	37	4	𝛽1𝛽3))𝐵1	𝛽1𝛽3))𝐵1	NOUN
asir-4528	37	5	+	+	CCONJ
asir-4528	37	6	(	(	PUNCT
asir-4528	37	7	2𝐶1(𝛼𝛽3	2𝐶1(𝛼𝛽3	NUM
asir-4528	37	8	+	+	NUM
asir-4528	37	9	𝛽1𝛽2	𝛽1𝛽2	X
asir-4528	37	10	)	)	PUNCT
asir-4528	38	1	+	+	CCONJ
asir-4528	38	2	𝐶2,(𝛼	𝐶2,(𝛼	PROPN
asir-4528	38	3	2	2	NUM
asir-4528	38	4	+	+	SYM
asir-4528	38	5	𝛽2	𝛽2	PROPN
asir-4528	38	6	2	2	NUM
asir-4528	38	7	)	)	PUNCT
asir-4528	38	8	−	−	PROPN
asir-4528	38	9	(	(	PUNCT
asir-4528	38	10	𝛽1	𝛽1	NOUN
asir-4528	38	11	2	2	NUM
asir-4528	38	12	+	+	NUM
asir-4528	38	13	𝛽3	𝛽3	NOUN
asir-4528	38	14	2)+	2)+	NUM
asir-4528	38	15	2𝐶3(𝛽2𝛽3	2𝐶3(𝛽2𝛽3	NUM
asir-4528	38	16	−	−	PROPN
asir-4528	38	17	𝛼𝛽1))𝐵2	𝛼𝛽1))𝐵2	PROPN
asir-4528	38	18	+	+	CCONJ
asir-4528	38	19	(	(	PUNCT
asir-4528	38	20	2𝐶1(𝛽1𝛽3	2𝐶1(𝛽1𝛽3	NUM
asir-4528	38	21	−	−	NOUN
asir-4528	38	22	𝛼𝛽2	𝛼𝛽2	NOUN
asir-4528	38	23	)	)	PUNCT
asir-4528	39	1	+	+	CCONJ
asir-4528	39	2	2𝐶2(𝛼𝛽1	2𝐶2(𝛼𝛽1	NUM
asir-4528	39	3	+	+	CCONJ
asir-4528	39	4	𝛽2𝛽3	𝛽2𝛽3	NOUN
asir-4528	39	5	)	)	PUNCT
asir-4528	40	1	+	+	CCONJ
asir-4528	40	2	𝐶3,(𝛼	𝐶3,(𝛼	VERB
asir-4528	40	3	2	2	NUM
asir-4528	40	4	+	+	NUM
asir-4528	40	5	𝛽3	𝛽3	NOUN
asir-4528	40	6	2	2	NUM
asir-4528	40	7	)	)	PUNCT
asir-4528	40	8	−	−	PROPN
asir-4528	40	9	(	(	PUNCT
asir-4528	40	10	𝛽1	𝛽1	NOUN
asir-4528	40	11	2	2	NUM
asir-4528	40	12	+	+	CCONJ
asir-4528	40	13	𝛽2	𝛽2	NOUN
asir-4528	40	14	2)-)𝐵3	2)-)𝐵3	NUM
asir-4528	40	15	probabilities	probability	NOUN
asir-4528	40	16	of	of	ADP
asir-4528	40	17	observed	observed	ADJ
asir-4528	40	18	values	value	NOUN
asir-4528	40	19	are	be	AUX
asir-4528	40	20	relative	relative	ADJ
asir-4528	40	21	measures	measure	NOUN
asir-4528	40	22	of	of	ADP
asir-4528	40	23	the	the	DET
asir-4528	40	24	g	g	NOUN
asir-4528	40	25	-	-	PUNCT
asir-4528	40	26	qubit	qubit	NOUN
asir-4528	40	27	fibers	fiber	NOUN
asir-4528	40	28	for	for	ADP
asir-4528	40	29	each	each	DET
asir-4528	40	30	observable	observable	ADJ
asir-4528	40	31	value	value	NOUN
asir-4528	40	32	received	receive	VERB
asir-4528	40	33	by	by	ADP
asir-4528	40	34	the	the	DET
asir-4528	40	35	action	action	NOUN
asir-4528	40	36	of	of	ADP
asir-4528	40	37	the	the	DET
asir-4528	40	38	states	state	NOUN
asir-4528	40	39	on	on	ADP
asir-4528	40	40	observable	observable	ADJ
asir-4528	40	41	.	.	PUNCT
asir-4528	41	1	the	the	DET
asir-4528	41	2	lift	lift	NOUN
asir-4528	41	3	from	from	ADP
asir-4528	41	4	𝐶2	𝐶2	PROPN
asir-4528	41	5	to	to	PART
asir-4528	41	6	𝐺3	𝐺3	VERB
asir-4528	41	7	+	+	CCONJ
asir-4528	41	8	needs	need	VERB
asir-4528	41	9	some	some	DET
asir-4528	41	10	*	*	ADJ
asir-4528	41	11	𝐵1	𝐵1	PROPN
asir-4528	41	12	,	,	PUNCT
asir-4528	41	13	𝐵2	𝐵2	NOUN
asir-4528	41	14	,	,	PUNCT
asir-4528	41	15	𝐵3	𝐵3	PROPN
asir-4528	41	16	+	+	PROPN
asir-4528	41	17	reference	reference	NOUN
asir-4528	41	18	frame	frame	NOUN
asir-4528	41	19	of	of	ADP
asir-4528	41	20	unit	unit	NOUN
asir-4528	41	21	value	value	NOUN
asir-4528	41	22	bivectors	bivector	NOUN
asir-4528	41	23	.	.	PUNCT
asir-4528	42	1	this	this	DET
asir-4528	42	2	frame	frame	NOUN
asir-4528	42	3	,	,	PUNCT
asir-4528	42	4	as	as	ADP
asir-4528	42	5	a	a	DET
asir-4528	42	6	solid	solid	ADJ
asir-4528	42	7	,	,	PUNCT
asir-4528	42	8	can	can	AUX
asir-4528	42	9	be	be	AUX
asir-4528	42	10	arbitrary	arbitrary	ADJ
asir-4528	42	11	rotated	rotate	VERB
asir-4528	42	12	in	in	ADP
asir-4528	42	13	three	three	NUM
asir-4528	42	14	dimensions	dimension	NOUN
asir-4528	42	15	.	.	PUNCT
asir-4528	43	1	in	in	ADP
asir-4528	43	2	that	that	DET
asir-4528	43	3	sense	sense	NOUN
asir-4528	43	4	we	we	PRON
asir-4528	43	5	have	have	VERB
asir-4528	43	6	principal	principal	ADJ
asir-4528	43	7	fiber	fiber	NOUN
asir-4528	43	8	bundle	bundle	NOUN
asir-4528	43	9	𝐺3	𝐺3	NOUN
asir-4528	44	1	+	+	X
asir-4528	44	2	→	→	SYM
asir-4528	44	3	𝐶2	𝐶2	X
asir-4528	44	4	with	with	ADP
asir-4528	44	5	the	the	DET
asir-4528	44	6	standard	standard	ADJ
asir-4528	44	7	fiber	fiber	NOUN
asir-4528	44	8	as	as	ADP
asir-4528	44	9	group	group	NOUN
asir-4528	44	10	of	of	ADP
asir-4528	44	11	rotations	rotation	NOUN
asir-4528	44	12	which	which	PRON
asir-4528	44	13	is	be	AUX
asir-4528	44	14	also	also	ADV
asir-4528	44	15	effectively	effectively	ADV
asir-4528	44	16	identified	identify	VERB
asir-4528	44	17	by	by	ADP
asir-4528	44	18	elements	element	NOUN
asir-4528	44	19	of	of	ADP
asir-4528	44	20	𝐺3	𝐺3	NOUN
asir-4528	44	21	+	+	PROPN
asir-4528	44	22	.	.	PUNCT
asir-4528	44	23	suppose	suppose	VERB
asir-4528	44	24	we	we	PRON
asir-4528	44	25	are	be	AUX
asir-4528	44	26	interested	interested	ADJ
asir-4528	44	27	in	in	ADP
asir-4528	44	28	the	the	DET
asir-4528	44	29	probability	probability	NOUN
asir-4528	44	30	of	of	ADP
asir-4528	44	31	the	the	DET
asir-4528	44	32	result	result	NOUN
asir-4528	44	33	of	of	ADP
asir-4528	44	34	measurement	measurement	NOUN
asir-4528	44	35	in	in	ADP
asir-4528	44	36	which	which	PRON
asir-4528	44	37	the	the	DET
asir-4528	44	38	observable	observable	ADJ
asir-4528	44	39	component	component	NOUN
asir-4528	44	40	𝐶1𝐵1	𝐶1𝐵1	PROPN
asir-4528	44	41	does	do	AUX
asir-4528	44	42	not	not	PART
asir-4528	44	43	change	change	VERB
asir-4528	44	44	.	.	PUNCT
asir-4528	45	1	this	this	PRON
asir-4528	45	2	is	be	AUX
asir-4528	45	3	relative	relative	ADJ
asir-4528	45	4	measure	measure	NOUN
asir-4528	45	5	of	of	ADP
asir-4528	45	6	states	state	NOUN
asir-4528	45	7	√𝛼2	√𝛼2	PROPN
asir-4528	45	8	+	+	NUM
asir-4528	45	9	𝛽1	𝛽1	NOUN
asir-4528	45	10	2	2	NUM
asir-4528	45	11	(	(	PUNCT
asir-4528	45	12	𝛼	𝛼	NOUN
asir-4528	45	13	√𝛼2+𝛽1	√𝛼2+𝛽1	PROPN
asir-4528	45	14	2	2	NUM
asir-4528	45	15	+	+	CCONJ
asir-4528	45	16	𝛽1	𝛽1	NOUN
asir-4528	45	17	√𝛼2+𝛽1	√𝛼2+𝛽1	NUM
asir-4528	45	18	2	2	NUM
asir-4528	45	19	𝐵1	𝐵1	NOUN
asir-4528	45	20	)	)	PUNCT
asir-4528	45	21	in	in	ADP
asir-4528	45	22	the	the	DET
asir-4528	45	23	measurements	measurement	NOUN
asir-4528	45	24	:	:	PUNCT
asir-4528	45	25	√𝛼2	√𝛼2	PROPN
asir-4528	45	26	+	+	NUM
asir-4528	45	27	𝛽1	𝛽1	NOUN
asir-4528	45	28	2	2	NUM
asir-4528	45	29	(	(	PUNCT
asir-4528	45	30	𝛼	𝛼	PROPN
asir-4528	45	31	√𝛼2	√𝛼2	PROPN
asir-4528	45	32	+	+	ADJ
asir-4528	45	33	𝛽1	𝛽1	NOUN
asir-4528	45	34	2	2	NUM
asir-4528	45	35	−	−	PROPN
asir-4528	45	36	𝛽1	𝛽1	NOUN
asir-4528	45	37	√𝛼2	√𝛼2	PROPN
asir-4528	45	38	+	+	NUM
asir-4528	45	39	𝛽1	𝛽1	NOUN
asir-4528	45	40	2	2	NUM
asir-4528	45	41	𝐵1)𝐶√𝛼	𝐵1)𝐶√𝛼	PROPN
asir-4528	45	42	2	2	NUM
asir-4528	45	43	+	+	CCONJ
asir-4528	45	44	𝛽1	𝛽1	NOUN
asir-4528	45	45	2	2	NUM
asir-4528	45	46	(	(	PUNCT
asir-4528	45	47	𝛼	𝛼	PROPN
asir-4528	45	48	√𝛼2	√𝛼2	PROPN
asir-4528	45	49	+	+	ADJ
asir-4528	45	50	𝛽1	𝛽1	NOUN
asir-4528	45	51	2	2	NUM
asir-4528	45	52	+	+	CCONJ
asir-4528	45	53	𝛽1	𝛽1	NOUN
asir-4528	45	54	√𝛼2	√𝛼2	PROPN
asir-4528	45	55	+	+	NUM
asir-4528	45	56	𝛽1	𝛽1	ADJ
asir-4528	45	57	2	2	NUM
asir-4528	45	58	𝐵1	𝐵1	NOUN
asir-4528	45	59	)	)	PUNCT
asir-4528	45	60	that	that	PRON
asir-4528	45	61	measure	measure	NOUN
asir-4528	45	62	is	be	AUX
asir-4528	45	63	equal	equal	ADJ
asir-4528	45	64	to	to	PART
asir-4528	45	65	𝛼2	𝛼2	VERB
asir-4528	45	66	+	+	CCONJ
asir-4528	45	67	𝛽1	𝛽1	NOUN
asir-4528	45	68	2	2	NUM
asir-4528	45	69	,	,	PUNCT
asir-4528	45	70	that	that	PRON
asir-4528	45	71	is	be	AUX
asir-4528	45	72	equal	equal	ADJ
asir-4528	45	73	to	to	ADP
asir-4528	45	74	𝑧1	𝑧1	NOUN
asir-4528	45	75	2	2	NUM
asir-4528	45	76	in	in	ADP
asir-4528	45	77	the	the	DET
asir-4528	45	78	down	down	ADJ
asir-4528	45	79	mapping	mapping	NOUN
asir-4528	45	80	from	from	ADP
asir-4528	45	81	𝐺3	𝐺3	NOUN
asir-4528	45	82	+	+	CCONJ
asir-4528	45	83	to	to	ADP
asir-4528	45	84	𝑧1|0⟩	𝑧1|0⟩	NOUN
asir-4528	45	85	+	+	CCONJ
asir-4528	45	86	𝑧2	𝑧2	PROPN
asir-4528	45	87	|1⟩.	|1⟩.	NOUN
asir-4528	45	88	thus	thus	ADV
asir-4528	45	89	,	,	PUNCT
asir-4528	45	90	we	we	PRON
asir-4528	45	91	have	have	VERB
asir-4528	45	92	clear	clear	ADJ
asir-4528	45	93	explanation	explanation	NOUN
asir-4528	45	94	of	of	ADP
asir-4528	45	95	common	common	ADJ
asir-4528	45	96	quantum	quantum	ADJ
asir-4528	45	97	mechanics	mechanic	NOUN
asir-4528	45	98	wisdom	wisdom	NOUN
asir-4528	45	99	on	on	ADP
asir-4528	45	100	“	"	PUNCT
asir-4528	45	101	probability	probability	NOUN
asir-4528	45	102	of	of	ADP
asir-4528	45	103	finding	find	VERB
asir-4528	45	104	system	system	NOUN
asir-4528	45	105	in	in	ADP
asir-4528	45	106	state	state	NOUN
asir-4528	45	107	|0⟩	|0⟩	NOUN
asir-4528	45	108	”	"	PUNCT
asir-4528	45	109	.	.	PUNCT
asir-4528	46	1	similar	similar	ADJ
asir-4528	46	2	calculations	calculation	NOUN
asir-4528	46	3	explain	explain	VERB
asir-4528	46	4	correspondence	correspondence	NOUN
asir-4528	46	5	of	of	ADP
asir-4528	46	6	𝛽3	𝛽3	PROPN
asir-4528	46	7	2	2	NUM
asir-4528	46	8	+	+	CCONJ
asir-4528	46	9	𝛽2	𝛽2	NOUN
asir-4528	46	10	2	2	NUM
asir-4528	46	11	to	to	ADP
asir-4528	46	12	𝑧2	𝑧2	PROPN
asir-4528	46	13	2	2	NUM
asir-4528	46	14	in	in	ADP
asir-4528	46	15	𝑧1|0⟩	𝑧1|0⟩	NOUN
asir-4528	46	16	+	+	CCONJ
asir-4528	46	17	𝑧2	𝑧2	PROPN
asir-4528	46	18	|1⟩	|1⟩	PROPN
asir-4528	46	19	when	when	SCONJ
asir-4528	46	20	the	the	DET
asir-4528	46	21	component	component	NOUN
asir-4528	46	22	𝐶1𝐵1	𝐶1𝐵1	PROPN
asir-4528	46	23	in	in	ADP
asir-4528	46	24	measurement	measurement	NOUN
asir-4528	46	25	just	just	ADV
asir-4528	46	26	got	get	AUX
asir-4528	46	27	flipped	flip	VERB
asir-4528	46	28	.	.	PUNCT
asir-4528	47	1	any	any	DET
asir-4528	47	2	arbitrary	arbitrary	ADJ
asir-4528	47	3	𝐺3	𝐺3	NOUN
asir-4528	47	4	+	+	CCONJ
asir-4528	47	5	state	state	NOUN
asir-4528	47	6	𝑠𝑜(𝛼	𝑠𝑜(𝛼	NOUN
asir-4528	47	7	,	,	PUNCT
asir-4528	47	8	𝛽	𝛽	PROPN
asir-4528	47	9	,	,	PUNCT
asir-4528	47	10	𝑆	𝑆	PROPN
asir-4528	47	11	)	)	PUNCT
asir-4528	47	12	=	=	SYM
asir-4528	47	13	𝛼	𝛼	PROPN
asir-4528	47	14	+	+	CCONJ
asir-4528	47	15	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	47	16	+	+	CCONJ
asir-4528	47	17	𝛽2𝐵2	𝛽2𝐵2	PUNCT
asir-4528	47	18	+	+	CCONJ
asir-4528	47	19	𝛽3𝐵3	𝛽3𝐵3	PROPN
asir-4528	47	20	can	can	AUX
asir-4528	47	21	be	be	AUX
asir-4528	47	22	rewritten	rewrite	VERB
asir-4528	47	23	either	either	CCONJ
asir-4528	47	24	as	as	ADP
asir-4528	47	25	0	0	NUM
asir-4528	47	26	-	-	PUNCT
asir-4528	47	27	type	type	NOUN
asir-4528	47	28	state	state	NOUN
asir-4528	47	29	or	or	CCONJ
asir-4528	47	30	1	1	NUM
asir-4528	47	31	-	-	PUNCT
asir-4528	47	32	type	type	NOUN
asir-4528	47	33	state	state	NOUN
asir-4528	47	34	:	:	PUNCT
asir-4528	47	35	𝛼	𝛼	X
asir-4528	48	1	+	+	CCONJ
asir-4528	48	2	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	48	3	+	+	CCONJ
asir-4528	48	4	𝛽2𝐵2	𝛽2𝐵2	PRON
asir-4528	48	5	+	+	CCONJ
asir-4528	48	6	𝛽3𝐵3	𝛽3𝐵3	PROPN
asir-4528	48	7	=	=	SYM
asir-4528	48	8	𝛼	𝛼	X
asir-4528	48	9	+	+	NOUN
asir-4528	48	10	𝐼𝑆(𝛽1,𝛽2,𝛽3)√𝛽1	𝐼𝑆(𝛽1,𝛽2,𝛽3)√𝛽1	PROPN
asir-4528	48	11	2	2	NUM
asir-4528	48	12	+	+	SYM
asir-4528	48	13	𝛽2	𝛽2	ADJ
asir-4528	48	14	2	2	NUM
asir-4528	48	15	+	+	NUM
asir-4528	48	16	𝛽3	𝛽3	PROPN
asir-4528	48	17	2	2	NUM
asir-4528	48	18	,	,	PUNCT
asir-4528	48	19	where	where	SCONJ
asir-4528	48	20	𝐼𝑆(𝛽1,𝛽2,𝛽3	𝐼𝑆(𝛽1,𝛽2,𝛽3	NOUN
asir-4528	48	21	)	)	PUNCT
asir-4528	48	22	=	=	PUNCT
asir-4528	49	1	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	49	2	+	+	NOUN
asir-4528	49	3	𝛽2𝐵2	𝛽2𝐵2	NUM
asir-4528	49	4	+	+	ADJ
asir-4528	49	5	𝛽3𝐵3	𝛽3𝐵3	NUM
asir-4528	49	6	√𝛽1	√𝛽1	ADP
asir-4528	49	7	2+𝛽2	2+𝛽2	NUM
asir-4528	49	8	2+𝛽3	2+𝛽3	NUM
asir-4528	49	9	2	2	NUM
asir-4528	49	10	,	,	PUNCT
asir-4528	49	11	0	0	NUM
asir-4528	49	12	-	-	PUNCT
asir-4528	49	13	type	type	NOUN
asir-4528	49	14	,	,	PUNCT
asir-4528	49	15	or	or	CCONJ
asir-4528	49	16	𝛼	𝛼	PRON
asir-4528	49	17	+	+	ADJ
asir-4528	49	18	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	49	19	+	+	CCONJ
asir-4528	49	20	𝛽2𝐵2	𝛽2𝐵2	PRON
asir-4528	49	21	+	+	CCONJ
asir-4528	49	22	𝛽3𝐵3	𝛽3𝐵3	PROPN
asir-4528	49	23	=	=	SYM
asir-4528	49	24	(	(	PUNCT
asir-4528	49	25	𝛽3	𝛽3	PROPN
asir-4528	49	26	+	+	CCONJ
asir-4528	49	27	𝛽2𝐵1	𝛽2𝐵1	PROPN
asir-4528	49	28	−	−	PROPN
asir-4528	49	29	𝛽1𝐵2	𝛽1𝐵2	PROPN
asir-4528	49	30	−	−	ADP
asir-4528	49	31	𝛼𝐵3)𝐵3	𝛼𝐵3)𝐵3	ADV
asir-4528	49	32	=	=	SYM
asir-4528	49	33	.𝛽3	.𝛽3	PUNCT
asir-4528	50	1	+	+	CCONJ
asir-4528	50	2	𝐼𝑆(𝛽2,−𝛽1,−𝛼	𝐼𝑆(𝛽2,−𝛽1,−𝛼	NUM
asir-4528	50	3	)	)	PUNCT
asir-4528	50	4	√𝛼	√𝛼	CCONJ
asir-4528	50	5	2	2	NUM
asir-4528	51	1	+	+	CCONJ
asir-4528	51	2	𝛽1	𝛽1	NOUN
asir-4528	51	3	2	2	NUM
asir-4528	51	4	+	+	CCONJ
asir-4528	51	5	𝛽2	𝛽2	PROPN
asir-4528	51	6	2/𝐵3	2/𝐵3	PROPN
asir-4528	51	7	,	,	PUNCT
asir-4528	51	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-4528	51	9	applied	apply	VERB
asir-4528	51	10	science	science	NOUN
asir-4528	51	11	and	and	CCONJ
asir-4528	51	12	innovative	innovative	ADJ
asir-4528	51	13	research	research	NOUN
asir-4528	51	14	vol	vol	NOUN
asir-4528	51	15	.	.	PROPN
asir-4528	52	1	6	6	NUM
asir-4528	52	2	,	,	PUNCT
asir-4528	52	3	no	no	INTJ
asir-4528	52	4	.	.	NOUN
asir-4528	52	5	1	1	NUM
asir-4528	52	6	,	,	PUNCT
asir-4528	52	7	2022	2022	NUM
asir-4528	52	8	50	50	NUM
asir-4528	52	9	published	publish	VERB
asir-4528	52	10	by	by	ADP
asir-4528	52	11	scholink	scholink	PROPN
asir-4528	52	12	inc	inc	PROPN
asir-4528	52	13	.	.	PROPN
asir-4528	53	1	where	where	SCONJ
asir-4528	53	2	𝐼𝑆(𝛽2,−𝛽1,−𝛼	𝐼𝑆(𝛽2,−𝛽1,−𝛼	PUNCT
asir-4528	53	3	)	)	PUNCT
asir-4528	53	4	=	=	PUNCT
asir-4528	53	5	𝛽2𝐵1−𝛽1𝐵2−𝛼𝐵3	𝛽2𝐵1−𝛽1𝐵2−𝛼𝐵3	NOUN
asir-4528	53	6	√𝛼2+𝛽1	√𝛼2+𝛽1	NUM
asir-4528	53	7	2+𝛽2	2+𝛽2	NUM
asir-4528	53	8	2	2	NUM
asir-4528	53	9	,	,	PUNCT
asir-4528	53	10	1	1	NUM
asir-4528	53	11	-	-	PUNCT
asir-4528	53	12	type	type	NOUN
asir-4528	53	13	.	.	PUNCT
asir-4528	54	1	all	all	DET
asir-4528	54	2	that	that	PRON
asir-4528	54	3	means	mean	VERB
asir-4528	54	4	that	that	SCONJ
asir-4528	54	5	any	any	DET
asir-4528	54	6	𝐺3	𝐺3	NOUN
asir-4528	54	7	+	+	CCONJ
asir-4528	54	8	state	state	NOUN
asir-4528	54	9	𝛼	𝛼	NOUN
asir-4528	54	10	+	+	NOUN
asir-4528	54	11	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	54	12	+	+	CCONJ
asir-4528	54	13	𝛽2𝐵2	𝛽2𝐵2	PRON
asir-4528	54	14	+	+	CCONJ
asir-4528	54	15	𝛽3𝐵3	𝛽3𝐵3	VERB
asir-4528	54	16	measuring	measure	VERB
asir-4528	54	17	arbitrary	arbitrary	ADJ
asir-4528	54	18	observable	observable	ADJ
asir-4528	54	19	𝐶1𝐵1	𝐶1𝐵1	NOUN
asir-4528	54	20	+	+	CCONJ
asir-4528	54	21	𝐶2𝐵2	𝐶2𝐵2	X
asir-4528	54	22	+	+	CCONJ
asir-4528	54	23	𝐶3𝐵3	𝐶3𝐵3	NOUN
asir-4528	54	24	does	do	AUX
asir-4528	54	25	not	not	PART
asir-4528	54	26	change	change	VERB
asir-4528	54	27	the	the	DET
asir-4528	54	28	observable	observable	ADJ
asir-4528	54	29	projection	projection	NOUN
asir-4528	54	30	onto	onto	ADP
asir-4528	54	31	plane	plane	NOUN
asir-4528	54	32	of	of	ADP
asir-4528	54	33	𝐼𝑆(𝛽1,𝛽2,𝛽3	𝐼𝑆(𝛽1,𝛽2,𝛽3	NOUN
asir-4528	54	34	)	)	PUNCT
asir-4528	54	35	=	=	PUNCT
asir-4528	54	36	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	54	37	+	+	NOUN
asir-4528	54	38	𝛽2𝐵2	𝛽2𝐵2	NUM
asir-4528	54	39	+	+	ADJ
asir-4528	54	40	𝛽3𝐵3	𝛽3𝐵3	NUM
asir-4528	54	41	√𝛽1	√𝛽1	ADP
asir-4528	54	42	2+𝛽2	2+𝛽2	NUM
asir-4528	54	43	2+𝛽3	2+𝛽3	NUM
asir-4528	54	44	2	2	NUM
asir-4528	54	45	and	and	CCONJ
asir-4528	54	46	just	just	ADV
asir-4528	54	47	flips	flip	VERB
asir-4528	54	48	the	the	DET
asir-4528	54	49	observable	observable	ADJ
asir-4528	54	50	projection	projection	NOUN
asir-4528	54	51	onto	onto	ADP
asir-4528	54	52	plane	plane	NOUN
asir-4528	54	53	𝐼𝑆(𝛽2,−𝛽1,−𝛼	𝐼𝑆(𝛽2,−𝛽1,−𝛼	NUM
asir-4528	54	54	)	)	PUNCT
asir-4528	55	1	=	=	PUNCT
asir-4528	55	2	𝛽2𝐵1−𝛽1𝐵2−𝛼𝐵3	𝛽2𝐵1−𝛽1𝐵2−𝛼𝐵3	NOUN
asir-4528	55	3	√𝛼2+𝛽1	√𝛼2+𝛽1	NUM
asir-4528	55	4	2+𝛽2	2+𝛽2	NUM
asir-4528	55	5	2	2	NUM
asir-4528	55	6	.	.	PUNCT
asir-4528	56	1	3	3	X
asir-4528	56	2	.	.	X
asir-4528	56	3	double	double	ADJ
asir-4528	56	4	slit	slit	NOUN
asir-4528	56	5	experiment	experiment	NOUN
asir-4528	56	6	taking	take	VERB
asir-4528	56	7	the	the	DET
asir-4528	56	8	set	set	NOUN
asir-4528	56	9	of	of	ADP
asir-4528	56	10	g	g	NOUN
asir-4528	56	11	-	-	PUNCT
asir-4528	56	12	qubits	qubit	NOUN
asir-4528	56	13	and	and	CCONJ
asir-4528	56	14	projection	projection	NOUN
asir-4528	56	15	of	of	ADP
asir-4528	56	16	them	they	PRON
asir-4528	56	17	onto	onto	ADP
asir-4528	56	18	𝐶2	𝐶2	ADJ
asir-4528	56	19	:	:	PUNCT
asir-4528	56	20	𝜋	𝜋	NOUN
asir-4528	56	21	:	:	PUNCT
asir-4528	56	22	𝐺3	𝐺3	NOUN
asir-4528	57	1	+	+	X
asir-4528	57	2	→	→	SYM
asir-4528	57	3	𝐶2	𝐶2	X
asir-4528	57	4	,	,	PUNCT
asir-4528	57	5	we	we	PRON
asir-4528	57	6	get	get	VERB
asir-4528	57	7	fiber	fiber	NOUN
asir-4528	57	8	bundle	bundle	NOUN
asir-4528	57	9	.	.	PUNCT
asir-4528	58	1	the	the	DET
asir-4528	58	2	projection	projection	NOUN
asir-4528	58	3	depends	depend	VERB
asir-4528	58	4	on	on	ADP
asir-4528	58	5	which	which	PRON
asir-4528	58	6	basis	basis	NOUN
asir-4528	58	7	bivector	bivector	NOUN
asir-4528	58	8	plane	plane	NOUN
asir-4528	58	9	is	be	AUX
asir-4528	58	10	selected	select	VERB
asir-4528	58	11	as	as	ADP
asir-4528	58	12	corresponding	correspond	VERB
asir-4528	58	13	to	to	ADP
asir-4528	58	14	formal	formal	ADJ
asir-4528	58	15	imaginary	imaginary	ADJ
asir-4528	58	16	unit	unit	NOUN
asir-4528	58	17	plane	plane	NOUN
asir-4528	58	18	.	.	PUNCT
asir-4528	59	1	if	if	SCONJ
asir-4528	59	2	we	we	PRON
asir-4528	59	3	take	take	VERB
asir-4528	59	4	,	,	PUNCT
asir-4528	59	5	for	for	ADP
asir-4528	59	6	example	example	NOUN
asir-4528	59	7	𝐵3	𝐵3	PROPN
asir-4528	59	8	,	,	PUNCT
asir-4528	59	9	the	the	DET
asir-4528	59	10	projection	projection	NOUN
asir-4528	59	11	is	be	AUX
asir-4528	59	12	:	:	PUNCT
asir-4528	59	13	𝜋	𝜋	X
asir-4528	59	14	:	:	PUNCT
asir-4528	59	15	𝑠𝑜(𝛼	𝑠𝑜(𝛼	NOUN
asir-4528	59	16	,	,	PUNCT
asir-4528	59	17	𝛽	𝛽	NOUN
asir-4528	59	18	,	,	PUNCT
asir-4528	59	19	𝑆	𝑆	PROPN
asir-4528	59	20	)	)	PUNCT
asir-4528	59	21	=	=	SYM
asir-4528	59	22	𝛼	𝛼	PROPN
asir-4528	60	1	+	+	CCONJ
asir-4528	60	2	𝛽1𝐵1	𝛽1𝐵1	NUM
asir-4528	60	3	+	+	CCONJ
asir-4528	60	4	𝛽2𝐵2	𝛽2𝐵2	PRON
asir-4528	60	5	+	+	CCONJ
asir-4528	60	6	𝛽3𝐵3	𝛽3𝐵3	PROPN
asir-4528	60	7	→	→	SYM
asir-4528	60	8	(	(	PUNCT
asir-4528	60	9	𝛼	𝛼	X
asir-4528	60	10	+	+	NOUN
asir-4528	60	11	𝑖𝛽3	𝑖𝛽3	NOUN
asir-4528	60	12	𝛽2	𝛽2	PROPN
asir-4528	60	13	+	+	CCONJ
asir-4528	60	14	𝑖𝛽1	𝑖𝛽1	PROPN
asir-4528	60	15	)	)	PUNCT
asir-4528	60	16	then	then	ADV
asir-4528	60	17	for	for	ADP
asir-4528	60	18	any	any	DET
asir-4528	60	19	𝑧	𝑧	PRON
asir-4528	60	20	=	=	X
asir-4528	60	21	.𝑥1+𝑖𝑦1	.𝑥1+𝑖𝑦1	ADJ
asir-4528	60	22	𝑥2+𝑖𝑦2	𝑥2+𝑖𝑦2	PROPN
asir-4528	60	23	/	/	SYM
asir-4528	60	24	∈	∈	PROPN
asir-4528	60	25	𝐶2	𝐶2	INTJ
asir-4528	60	26	the	the	DET
asir-4528	60	27	fiber	fiber	NOUN
asir-4528	60	28	in	in	ADP
asir-4528	60	29	𝐺3	𝐺3	NOUN
asir-4528	60	30	+	+	CCONJ
asir-4528	60	31	consists	consist	VERB
asir-4528	60	32	of	of	ADP
asir-4528	60	33	all	all	DET
asir-4528	60	34	elements	element	NOUN
asir-4528	60	35	𝐹𝑧	𝐹𝑧	PROPN
asir-4528	60	36	=	=	SYM
asir-4528	60	37	𝑥1	𝑥1	PROPN
asir-4528	60	38	+	+	CCONJ
asir-4528	60	39	𝑦2𝐵1	𝑦2𝐵1	PROPN
asir-4528	60	40	+	+	CCONJ
asir-4528	60	41	𝑥2𝐵2	𝑥2𝐵2	PROPN
asir-4528	60	42	+	+	CCONJ
asir-4528	60	43	𝑦1𝐵3	𝑦1𝐵3	PROPN
asir-4528	60	44	with	with	ADP
asir-4528	60	45	an	an	DET
asir-4528	60	46	arbitrary	arbitrary	ADJ
asir-4528	60	47	triple	triple	NOUN
asir-4528	60	48	of	of	ADP
asir-4528	60	49	orthonormal	orthonormal	ADJ
asir-4528	60	50	bivectors	bivector	NOUN
asir-4528	60	51	*	*	NOUN
asir-4528	60	52	𝐵1	𝐵1	PROPN
asir-4528	60	53	,	,	PUNCT
asir-4528	60	54	𝐵2	𝐵2	NOUN
asir-4528	60	55	,	,	PUNCT
asir-4528	60	56	𝐵3	𝐵3	PROPN
asir-4528	60	57	+	+	X
asir-4528	60	58	satisfying	satisfy	VERB
asir-4528	60	59	multiplication	multiplication	NOUN
asir-4528	60	60	rules	rule	NOUN
asir-4528	60	61	.	.	PUNCT
asir-4528	61	1	that	that	PRON
asir-4528	61	2	particularly	particularly	ADV
asir-4528	61	3	means	mean	VERB
asir-4528	61	4	that	that	SCONJ
asir-4528	61	5	the	the	DET
asir-4528	61	6	standard	standard	ADJ
asir-4528	61	7	fiber	fiber	NOUN
asir-4528	61	8	is	be	AUX
asir-4528	61	9	group	group	NOUN
asir-4528	61	10	of	of	ADP
asir-4528	61	11	rotations	rotation	NOUN
asir-4528	61	12	of	of	ADP
asir-4528	61	13	basis	basis	NOUN
asir-4528	61	14	bivectors	bivector	NOUN
asir-4528	61	15	in	in	ADP
asir-4528	61	16	the	the	DET
asir-4528	61	17	standard	standard	ADJ
asir-4528	61	18	fiber	fiber	NOUN
asir-4528	61	19	𝐹𝑧.	𝐹𝑧.	PROPN
asir-4528	62	1	thus	thus	ADV
asir-4528	62	2	,	,	PUNCT
asir-4528	62	3	the	the	DET
asir-4528	62	4	fiber	fiber	NOUN
asir-4528	62	5	bundle	bundle	NOUN
asir-4528	62	6	is	be	AUX
asir-4528	62	7	principal	principal	ADJ
asir-4528	62	8	fiber	fiber	NOUN
asir-4528	62	9	bundle	bundle	NOUN
asir-4528	62	10	.	.	PUNCT
asir-4528	63	1	let	let	VERB
asir-4528	63	2	one	one	NUM
asir-4528	63	3	first	first	ADJ
asir-4528	63	4	slit	slit	NOUN
asir-4528	63	5	is	be	AUX
asir-4528	63	6	only	only	ADV
asir-4528	63	7	open	open	ADJ
asir-4528	63	8	,	,	PUNCT
asir-4528	63	9	and	and	CCONJ
asir-4528	63	10	the	the	DET
asir-4528	63	11	fiber	fiber	NOUN
asir-4528	63	12	,	,	PUNCT
asir-4528	63	13	wave	wave	NOUN
asir-4528	63	14	function	function	NOUN
asir-4528	63	15	,	,	PUNCT
asir-4528	63	16	is	be	AUX
asir-4528	63	17	some	some	DET
asir-4528	63	18	𝐹1	𝐹1	NOUN
asir-4528	63	19	=	=	SYM
asir-4528	63	20	𝑥1	𝑥1	NOUN
asir-4528	63	21	1	1	NUM
asir-4528	63	22	+	+	NUM
asir-4528	63	23	𝑦2	𝑦2	PROPN
asir-4528	63	24	1𝐵1	1𝐵1	NUM
asir-4528	64	1	+	+	CCONJ
asir-4528	64	2	𝑥2	𝑥2	NOUN
asir-4528	64	3	1𝐵2	1𝐵2	NUM
asir-4528	65	1	+	+	CCONJ
asir-4528	65	2	𝑦1	𝑦1	PROPN
asir-4528	65	3	1𝐵3	1𝐵3	NUM
asir-4528	65	4	.	.	PUNCT
asir-4528	66	1	for	for	ADP
asir-4528	66	2	the	the	DET
asir-4528	66	3	only	only	ADJ
asir-4528	66	4	open	open	ADJ
asir-4528	66	5	second	second	ADJ
asir-4528	66	6	slit	slit	NOUN
asir-4528	66	7	the	the	DET
asir-4528	66	8	fiber	fiber	NOUN
asir-4528	66	9	is	be	AUX
asir-4528	66	10	different	different	ADJ
asir-4528	66	11	:	:	PUNCT
asir-4528	66	12	𝐹2	𝐹2	PROPN
asir-4528	66	13	=	=	SYM
asir-4528	66	14	𝑥1	𝑥1	PROPN
asir-4528	66	15	2	2	NUM
asir-4528	66	16	+	+	CCONJ
asir-4528	66	17	𝑦2	𝑦2	PROPN
asir-4528	66	18	2𝐵1	2𝐵1	NUM
asir-4528	66	19	+	+	CCONJ
asir-4528	66	20	𝑥2	𝑥2	NOUN
asir-4528	66	21	2𝐵2	2𝐵2	NUM
asir-4528	66	22	+	+	PUNCT
asir-4528	66	23	𝑦1	𝑦1	PROPN
asir-4528	66	24	2𝐵3	2𝐵3	NUM
asir-4528	66	25	.	.	PUNCT
asir-4528	67	1	when	when	SCONJ
asir-4528	67	2	both	both	DET
asir-4528	67	3	slits	slit	NOUN
asir-4528	67	4	are	be	AUX
asir-4528	67	5	open	open	ADJ
asir-4528	67	6	the	the	DET
asir-4528	67	7	corresponding	corresponding	ADJ
asir-4528	67	8	fiber	fiber	NOUN
asir-4528	67	9	is	be	AUX
asir-4528	67	10	defined	define	VERB
asir-4528	67	11	by	by	ADP
asir-4528	67	12	connection	connection	NOUN
asir-4528	67	13	,	,	PUNCT
asir-4528	67	14	parallel	parallel	ADJ
asir-4528	67	15	transport	transport	NOUN
asir-4528	67	16	anywhere	anywhere	ADV
asir-4528	67	17	between	between	ADP
asir-4528	67	18	fibers	fiber	NOUN
asir-4528	67	19	𝐹1	𝐹1	PROPN
asir-4528	67	20	and	and	CCONJ
asir-4528	67	21	𝐹2	𝐹2	PROPN
asir-4528	67	22	.	.	PUNCT
asir-4528	68	1	let	let	VERB
asir-4528	68	2	we	we	PRON
asir-4528	68	3	have	have	VERB
asir-4528	68	4	a	a	DET
asir-4528	68	5	smooth	smooth	ADJ
asir-4528	68	6	curve	curve	NOUN
asir-4528	68	7	𝛾(𝑡	𝛾(𝑡	PROPN
asir-4528	68	8	,	,	PUNCT
asir-4528	68	9	𝑃1	𝑃1	NOUN
asir-4528	68	10	,	,	PUNCT
asir-4528	68	11	𝑃2	𝑃2	NOUN
asir-4528	68	12	)	)	PUNCT
asir-4528	68	13	,	,	PUNCT
asir-4528	68	14	0	0	NUM
asir-4528	68	15	≤	≤	NUM
asir-4528	68	16	𝑡	𝑡	VERB
asir-4528	68	17	≤	≤	ADV
asir-4528	68	18	1	1	NUM
asir-4528	68	19	,	,	PUNCT
asir-4528	68	20	connecting	connect	VERB
asir-4528	68	21	points	point	NOUN
asir-4528	68	22	𝑃1	𝑃1	NOUN
asir-4528	68	23	=	=	SYM
asir-4528	68	24	(	(	PUNCT
asir-4528	68	25	𝑥1	𝑥1	NOUN
asir-4528	68	26	1	1	NUM
asir-4528	68	27	,	,	PUNCT
asir-4528	68	28	𝑦2	𝑦2	PROPN
asir-4528	68	29	1	1	NUM
asir-4528	68	30	,	,	PUNCT
asir-4528	68	31	𝑥2	𝑥2	NOUN
asir-4528	68	32	1	1	NUM
asir-4528	68	33	,	,	PUNCT
asir-4528	68	34	𝑦1	𝑦1	PROPN
asir-4528	68	35	1	1	NUM
asir-4528	68	36	)	)	PUNCT
asir-4528	68	37	and	and	CCONJ
asir-4528	68	38	𝑃2	𝑃2	NOUN
asir-4528	68	39	=	=	SYM
asir-4528	68	40	(	(	PUNCT
asir-4528	68	41	𝑥1	𝑥1	NOUN
asir-4528	68	42	2	2	NUM
asir-4528	68	43	,	,	PUNCT
asir-4528	68	44	𝑦2	𝑦2	PROPN
asir-4528	68	45	2	2	NUM
asir-4528	68	46	,	,	PUNCT
asir-4528	68	47	𝑥2	𝑥2	NOUN
asir-4528	68	48	2	2	NUM
asir-4528	68	49	,	,	PUNCT
asir-4528	68	50	𝑦1	𝑦1	NOUN
asir-4528	68	51	2	2	NUM
asir-4528	68	52	)	)	PUNCT
asir-4528	68	53	,	,	PUNCT
asir-4528	68	54	on	on	ADP
asir-4528	68	55	three	three	NUM
asir-4528	68	56	-	-	PUNCT
asir-4528	68	57	dimensional	dimensional	ADJ
asir-4528	68	58	sphere	sphere	NOUN
asir-4528	68	59	𝕊3	𝕊3	NOUN
asir-4528	68	60	such	such	ADJ
asir-4528	68	61	that	that	SCONJ
asir-4528	68	62	𝛾(0	𝛾(0	PROPN
asir-4528	68	63	,	,	PUNCT
asir-4528	68	64	𝑃1	𝑃1	NOUN
asir-4528	68	65	,	,	PUNCT
asir-4528	68	66	𝑃2	𝑃2	NOUN
asir-4528	68	67	)	)	PUNCT
asir-4528	68	68	=	=	NOUN
asir-4528	68	69	𝑃1	𝑃1	NOUN
asir-4528	68	70	and	and	CCONJ
asir-4528	68	71	𝛾(1	𝛾(1	PROPN
asir-4528	68	72	,	,	PUNCT
asir-4528	68	73	𝑃1	𝑃1	NOUN
asir-4528	68	74	,	,	PUNCT
asir-4528	68	75	𝑃2	𝑃2	NOUN
asir-4528	68	76	)	)	PUNCT
asir-4528	68	77	=	=	SYM
asir-4528	68	78	𝑃2	𝑃2	PROPN
asir-4528	68	79	.	.	PUNCT
asir-4528	69	1	the	the	DET
asir-4528	69	2	easiest	easy	ADJ
asir-4528	69	3	way	way	NOUN
asir-4528	69	4	to	to	PART
asir-4528	69	5	define	define	VERB
asir-4528	69	6	parallel	parallel	ADJ
asir-4528	69	7	transport	transport	NOUN
asir-4528	69	8	is	be	AUX
asir-4528	69	9	𝛾(𝑡	𝛾(𝑡	PROPN
asir-4528	69	10	,	,	PUNCT
asir-4528	69	11	𝑃1	𝑃1	NOUN
asir-4528	69	12	,	,	PUNCT
asir-4528	69	13	𝑃2	𝑃2	NOUN
asir-4528	69	14	)	)	PUNCT
asir-4528	69	15	=	=	PUNCT
asir-4528	70	1	(	(	PUNCT
asir-4528	70	2	1	1	NUM
asir-4528	70	3	−	−	NOUN
asir-4528	70	4	𝑡)𝑃1	𝑡)𝑃1	NOUN
asir-4528	70	5	+	+	CCONJ
asir-4528	70	6	𝑡𝑃2	𝑡𝑃2	PROPN
asir-4528	70	7	.	.	PROPN
asir-4528	71	1	for	for	ADP
asir-4528	71	2	convenience	convenience	NOUN
asir-4528	71	3	purposes	purpose	NOUN
asir-4528	71	4	let	let	VERB
asir-4528	71	5	us	we	PRON
asir-4528	71	6	write	write	VERB
asir-4528	71	7	𝐹1	𝐹1	PROPN
asir-4528	71	8	and	and	CCONJ
asir-4528	71	9	𝐹2	𝐹2	NOUN
asir-4528	71	10	as	as	ADP
asir-4528	71	11	exponents	exponent	NOUN
asir-4528	71	12	:	:	PUNCT
asir-4528	71	13	𝐹1	𝐹1	PROPN
asir-4528	71	14	=	=	PROPN
asir-4528	71	15	𝑥1	𝑥1	PROPN
asir-4528	71	16	1	1	NUM
asir-4528	71	17	+	+	NUM
asir-4528	71	18	𝑦2	𝑦2	PROPN
asir-4528	71	19	1𝐵1	1𝐵1	NUM
asir-4528	71	20	+	+	CCONJ
asir-4528	71	21	𝑥2	𝑥2	NOUN
asir-4528	71	22	1𝐵2	1𝐵2	NUM
asir-4528	72	1	+	+	CCONJ
asir-4528	72	2	𝑦1	𝑦1	PROPN
asir-4528	72	3	1𝐵3	1𝐵3	NUM
asir-4528	72	4	=	=	SYM
asir-4528	72	5	𝑥1	𝑥1	NOUN
asir-4528	72	6	1	1	NUM
asir-4528	73	1	+	+	NOUN
asir-4528	73	2	√(𝑦2	√(𝑦2	PROPN
asir-4528	73	3	1)2	1)2	NUM
asir-4528	73	4	+	+	CCONJ
asir-4528	73	5	(	(	PUNCT
asir-4528	73	6	𝑥2	𝑥2	NOUN
asir-4528	73	7	1)2	1)2	NUM
asir-4528	73	8	+	+	CCONJ
asir-4528	73	9	(	(	PUNCT
asir-4528	73	10	𝑦1	𝑦1	PROPN
asir-4528	73	11	1)2	1)2	NUM
asir-4528	73	12	(	(	PUNCT
asir-4528	73	13	𝑦2	𝑦2	PROPN
asir-4528	73	14	1	1	NUM
asir-4528	73	15	√(𝑦2	√(𝑦2	PROPN
asir-4528	73	16	1	1	NUM
asir-4528	73	17	)	)	PUNCT
asir-4528	73	18	2	2	NUM
asir-4528	74	1	+	+	NOUN
asir-4528	74	2	(	(	PUNCT
asir-4528	74	3	𝑥2	𝑥2	NOUN
asir-4528	74	4	1	1	NUM
asir-4528	74	5	)	)	PUNCT
asir-4528	74	6	2	2	NUM
asir-4528	74	7	+	+	NOUN
asir-4528	74	8	(	(	PUNCT
asir-4528	74	9	𝑦1	𝑦1	NOUN
asir-4528	74	10	1	1	NUM
asir-4528	74	11	)	)	PUNCT
asir-4528	74	12	2	2	NUM
asir-4528	74	13	𝐵1	𝐵1	NOUN
asir-4528	74	14	+	+	CCONJ
asir-4528	74	15	𝑥2	𝑥2	NOUN
asir-4528	74	16	1	1	NUM
asir-4528	74	17	√(𝑦2	√(𝑦2	PROPN
asir-4528	74	18	1	1	NUM
asir-4528	74	19	)	)	PUNCT
asir-4528	74	20	2	2	NUM
asir-4528	74	21	+	+	NOUN
asir-4528	74	22	(	(	PUNCT
asir-4528	74	23	𝑥2	𝑥2	NOUN
asir-4528	74	24	1	1	NUM
asir-4528	74	25	)	)	PUNCT
asir-4528	74	26	2	2	NUM
asir-4528	74	27	+	+	NOUN
asir-4528	74	28	(	(	PUNCT
asir-4528	74	29	𝑦1	𝑦1	NOUN
asir-4528	74	30	1	1	NUM
asir-4528	74	31	)	)	PUNCT
asir-4528	74	32	2	2	NUM
asir-4528	74	33	𝐵2	𝐵2	NOUN
asir-4528	74	34	+	+	X
asir-4528	74	35	𝑦1	𝑦1	NOUN
asir-4528	74	36	1	1	NUM
asir-4528	74	37	√(𝑦2	√(𝑦2	PROPN
asir-4528	74	38	1	1	NUM
asir-4528	74	39	)	)	PUNCT
asir-4528	74	40	2	2	NUM
asir-4528	74	41	+	+	NOUN
asir-4528	74	42	(	(	PUNCT
asir-4528	74	43	𝑥2	𝑥2	NOUN
asir-4528	74	44	1	1	NUM
asir-4528	74	45	)	)	PUNCT
asir-4528	74	46	2	2	NUM
asir-4528	74	47	+	+	NOUN
asir-4528	74	48	(	(	PUNCT
asir-4528	74	49	𝑦1	𝑦1	NOUN
asir-4528	74	50	1	1	NUM
asir-4528	74	51	)	)	PUNCT
asir-4528	74	52	2	2	NUM
asir-4528	74	53	𝐵3	𝐵3	NOUN
asir-4528	74	54	)	)	PUNCT
asir-4528	74	55	=	=	PUNCT
asir-4528	74	56	𝑒	𝑒	PRON
asir-4528	74	57	𝐼𝑆1𝜑1	𝐼𝑆1𝜑1	NOUN
asir-4528	74	58	,	,	PUNCT
asir-4528	74	59	where	where	SCONJ
asir-4528	74	60	𝜑1	𝜑1	NOUN
asir-4528	74	61	=	=	SYM
asir-4528	74	62	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
asir-4528	74	63	−1	−1	PROPN
asir-4528	74	64	𝑥1	𝑥1	PROPN
asir-4528	74	65	1	1	NUM
asir-4528	74	66	,	,	PUNCT
asir-4528	74	67	𝐼𝑆1	𝐼𝑆1	PROPN
asir-4528	74	68	=	=	PUNCT
asir-4528	74	69	𝑦2	𝑦2	PROPN
asir-4528	74	70	1	1	NUM
asir-4528	74	71	√(𝑦2	√(𝑦2	PROPN
asir-4528	74	72	1	1	NUM
asir-4528	74	73	)	)	PUNCT
asir-4528	74	74	2	2	NUM
asir-4528	74	75	+	+	NOUN
asir-4528	74	76	(	(	PUNCT
asir-4528	74	77	𝑥2	𝑥2	NOUN
asir-4528	74	78	1	1	NUM
asir-4528	74	79	)	)	PUNCT
asir-4528	74	80	2	2	NUM
asir-4528	74	81	+	+	NOUN
asir-4528	74	82	(	(	PUNCT
asir-4528	74	83	𝑦1	𝑦1	NOUN
asir-4528	74	84	1	1	NUM
asir-4528	74	85	)	)	PUNCT
asir-4528	74	86	2	2	NUM
asir-4528	74	87	𝐵1	𝐵1	NOUN
asir-4528	74	88	+	+	CCONJ
asir-4528	74	89	𝑥2	𝑥2	NOUN
asir-4528	74	90	1	1	NUM
asir-4528	74	91	√(𝑦2	√(𝑦2	PROPN
asir-4528	74	92	1	1	NUM
asir-4528	74	93	)	)	PUNCT
asir-4528	74	94	2	2	NUM
asir-4528	74	95	+	+	NOUN
asir-4528	74	96	(	(	PUNCT
asir-4528	74	97	𝑥2	𝑥2	NOUN
asir-4528	74	98	1	1	NUM
asir-4528	74	99	)	)	PUNCT
asir-4528	74	100	2	2	NUM
asir-4528	74	101	+	+	NOUN
asir-4528	74	102	(	(	PUNCT
asir-4528	74	103	𝑦1	𝑦1	NOUN
asir-4528	74	104	1	1	NUM
asir-4528	74	105	)	)	PUNCT
asir-4528	74	106	2	2	NUM
asir-4528	74	107	𝐵2	𝐵2	NOUN
asir-4528	74	108	+	+	X
asir-4528	74	109	𝑦1	𝑦1	NOUN
asir-4528	74	110	1	1	NUM
asir-4528	74	111	√(𝑦2	√(𝑦2	PROPN
asir-4528	74	112	1	1	NUM
asir-4528	74	113	)	)	PUNCT
asir-4528	74	114	2	2	NUM
asir-4528	74	115	+	+	NOUN
asir-4528	74	116	(	(	PUNCT
asir-4528	74	117	𝑥2	𝑥2	NOUN
asir-4528	74	118	1	1	NUM
asir-4528	74	119	)	)	PUNCT
asir-4528	74	120	2	2	NUM
asir-4528	74	121	+	+	NOUN
asir-4528	74	122	(	(	PUNCT
asir-4528	74	123	𝑦1	𝑦1	NOUN
asir-4528	74	124	1	1	NUM
asir-4528	74	125	)	)	PUNCT
asir-4528	74	126	2	2	NUM
asir-4528	74	127	𝐵3	𝐵3	PROPN
asir-4528	74	128	.	.	PUNCT
asir-4528	75	1	angle	angle	NOUN
asir-4528	75	2	𝜑1	𝜑1	PROPN
asir-4528	75	3	is	be	AUX
asir-4528	75	4	not	not	PART
asir-4528	75	5	uniquely	uniquely	ADV
asir-4528	75	6	defined	define	VERB
asir-4528	75	7	since	since	SCONJ
asir-4528	75	8	it	it	PRON
asir-4528	75	9	can	can	AUX
asir-4528	75	10	be	be	AUX
asir-4528	75	11	any	any	PRON
asir-4528	75	12	of	of	ADP
asir-4528	75	13	cos−1	cos−1	PROPN
asir-4528	75	14	𝑥1	𝑥1	PROPN
asir-4528	75	15	1	1	NUM
asir-4528	75	16	±	±	NUM
asir-4528	75	17	2𝜋𝑘1	2𝜋𝑘1	NUM
asir-4528	75	18	,	,	PUNCT
asir-4528	75	19	𝑘1	𝑘1	PROPN
asir-4528	75	20	=	=	SYM
asir-4528	75	21	0,1,2	0,1,2	NUM
asir-4528	75	22	,	,	PUNCT
asir-4528	75	23	…	…	PUNCT
asir-4528	75	24	,	,	PUNCT
asir-4528	75	25	where	where	SCONJ
asir-4528	75	26	cos−1	cos−1	PROPN
asir-4528	75	27	𝑥1	𝑥1	NOUN
asir-4528	75	28	1	1	NUM
asir-4528	75	29	is	be	AUX
asir-4528	75	30	,	,	PUNCT
asir-4528	75	31	by	by	ADP
asir-4528	75	32	definition	definition	NOUN
asir-4528	75	33	,	,	PUNCT
asir-4528	75	34	taken	take	VERB
asir-4528	75	35	from	from	ADP
asir-4528	75	36	interval	interval	NOUN
asir-4528	75	37	,	,	PUNCT
asir-4528	75	38	0	0	NUM
asir-4528	75	39	,	,	PUNCT
asir-4528	75	40	𝜋-	𝜋-	X
asir-4528	75	41	.	.	PUNCT
asir-4528	76	1	the	the	DET
asir-4528	76	2	angle	angle	NOUN
asir-4528	76	3	cos−1	cos−1	PROPN
asir-4528	76	4	𝑥1	𝑥1	PROPN
asir-4528	76	5	1	1	NUM
asir-4528	76	6	will	will	AUX
asir-4528	76	7	be	be	AUX
asir-4528	76	8	denoted	denote	VERB
asir-4528	76	9	as	as	ADP
asir-4528	76	10	𝜑1(0	𝜑1(0	PROPN
asir-4528	76	11	)	)	PUNCT
asir-4528	76	12	.	.	PUNCT
asir-4528	77	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-4528	77	2	applied	apply	VERB
asir-4528	77	3	science	science	NOUN
asir-4528	77	4	and	and	CCONJ
asir-4528	77	5	innovative	innovative	ADJ
asir-4528	77	6	research	research	NOUN
asir-4528	77	7	vol	vol	NOUN
asir-4528	77	8	.	.	PROPN
asir-4528	78	1	6	6	NUM
asir-4528	78	2	,	,	PUNCT
asir-4528	78	3	no	no	INTJ
asir-4528	78	4	.	.	NOUN
asir-4528	78	5	1	1	NUM
asir-4528	78	6	,	,	PUNCT
asir-4528	78	7	2022	2022	NUM
asir-4528	78	8	51	51	NUM
asir-4528	78	9	published	publish	VERB
asir-4528	78	10	by	by	ADP
asir-4528	78	11	scholink	scholink	PROPN
asir-4528	78	12	inc	inc	PROPN
asir-4528	78	13	.	.	PROPN
asir-4528	78	14	𝐹2	𝐹2	PROPN
asir-4528	78	15	=	=	SYM
asir-4528	78	16	𝑥1	𝑥1	PROPN
asir-4528	78	17	2	2	NUM
asir-4528	78	18	+	+	CCONJ
asir-4528	78	19	𝑦2	𝑦2	PROPN
asir-4528	78	20	2𝐵1	2𝐵1	NUM
asir-4528	79	1	+	+	CCONJ
asir-4528	79	2	𝑥2	𝑥2	NOUN
asir-4528	79	3	2𝐵2	2𝐵2	NUM
asir-4528	79	4	+	+	CCONJ
asir-4528	79	5	𝑦1	𝑦1	PROPN
asir-4528	79	6	2𝐵3	2𝐵3	NUM
asir-4528	79	7	=	=	SYM
asir-4528	79	8	𝑥1	𝑥1	NOUN
asir-4528	79	9	2	2	NUM
asir-4528	79	10	+	+	NOUN
asir-4528	79	11	√(𝑦2	√(𝑦2	PROPN
asir-4528	79	12	2)2	2)2	NUM
asir-4528	79	13	+	+	CCONJ
asir-4528	79	14	(	(	PUNCT
asir-4528	79	15	𝑥2	𝑥2	NOUN
asir-4528	79	16	2)2	2)2	NUM
asir-4528	79	17	+	+	CCONJ
asir-4528	79	18	(	(	PUNCT
asir-4528	79	19	𝑦1	𝑦1	PROPN
asir-4528	79	20	2)2	2)2	NUM
asir-4528	79	21	(	(	PUNCT
asir-4528	79	22	𝑦2	𝑦2	PROPN
asir-4528	79	23	2	2	NUM
asir-4528	79	24	√(𝑦2	√(𝑦2	PROPN
asir-4528	79	25	2	2	NUM
asir-4528	79	26	)	)	PUNCT
asir-4528	79	27	2	2	NUM
asir-4528	80	1	+	+	NOUN
asir-4528	80	2	(	(	PUNCT
asir-4528	80	3	𝑥2	𝑥2	NOUN
asir-4528	80	4	2	2	NUM
asir-4528	80	5	)	)	PUNCT
asir-4528	80	6	2	2	NUM
asir-4528	80	7	+	+	NOUN
asir-4528	80	8	(	(	PUNCT
asir-4528	80	9	𝑦1	𝑦1	NOUN
asir-4528	80	10	2	2	NUM
asir-4528	80	11	)	)	PUNCT
asir-4528	80	12	2	2	NUM
asir-4528	80	13	𝐵1	𝐵1	NOUN
asir-4528	80	14	+	+	CCONJ
asir-4528	80	15	𝑥2	𝑥2	NOUN
asir-4528	80	16	2	2	NUM
asir-4528	80	17	√(𝑦2	√(𝑦2	PROPN
asir-4528	80	18	2	2	NUM
asir-4528	80	19	)	)	PUNCT
asir-4528	80	20	2	2	NUM
asir-4528	80	21	+	+	NOUN
asir-4528	80	22	(	(	PUNCT
asir-4528	80	23	𝑥2	𝑥2	NOUN
asir-4528	80	24	2	2	NUM
asir-4528	80	25	)	)	PUNCT
asir-4528	80	26	2	2	NUM
asir-4528	80	27	+	+	NOUN
asir-4528	80	28	(	(	PUNCT
asir-4528	80	29	𝑦1	𝑦1	NOUN
asir-4528	80	30	2	2	NUM
asir-4528	80	31	)	)	PUNCT
asir-4528	80	32	2	2	NUM
asir-4528	80	33	𝐵2	𝐵2	NOUN
asir-4528	80	34	+	+	X
asir-4528	80	35	𝑦1	𝑦1	NOUN
asir-4528	80	36	2	2	NUM
asir-4528	80	37	√(𝑦2	√(𝑦2	PROPN
asir-4528	80	38	2	2	NUM
asir-4528	80	39	)	)	PUNCT
asir-4528	80	40	2	2	NUM
asir-4528	80	41	+	+	NOUN
asir-4528	80	42	(	(	PUNCT
asir-4528	80	43	𝑥2	𝑥2	NOUN
asir-4528	80	44	2	2	NUM
asir-4528	80	45	)	)	PUNCT
asir-4528	80	46	2	2	NUM
asir-4528	80	47	+	+	NOUN
asir-4528	80	48	(	(	PUNCT
asir-4528	80	49	𝑦1	𝑦1	NOUN
asir-4528	80	50	2	2	NUM
asir-4528	80	51	)	)	PUNCT
asir-4528	80	52	2	2	NUM
asir-4528	80	53	𝐵3	𝐵3	NOUN
asir-4528	80	54	)	)	PUNCT
asir-4528	80	55	=	=	PUNCT
asir-4528	80	56	𝑒	𝑒	PROPN
asir-4528	80	57	𝐼𝑆2𝜑2	𝐼𝑆2𝜑2	PROPN
asir-4528	80	58	,	,	PUNCT
asir-4528	80	59	where	where	SCONJ
asir-4528	80	60	𝜑2	𝜑2	NOUN
asir-4528	80	61	=	=	PUNCT
asir-4528	80	62	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
asir-4528	80	63	−1	−1	PROPN
asir-4528	80	64	𝑥1	𝑥1	PROPN
asir-4528	80	65	2	2	NUM
asir-4528	80	66	,	,	PUNCT
asir-4528	80	67	𝐼𝑆2	𝐼𝑆2	PROPN
asir-4528	80	68	=	=	PROPN
asir-4528	80	69	𝑦2	𝑦2	PROPN
asir-4528	80	70	2	2	NUM
asir-4528	80	71	√(𝑦2	√(𝑦2	PROPN
asir-4528	80	72	2	2	NUM
asir-4528	80	73	)	)	PUNCT
asir-4528	80	74	2	2	NUM
asir-4528	80	75	+	+	NOUN
asir-4528	80	76	(	(	PUNCT
asir-4528	80	77	𝑥2	𝑥2	NOUN
asir-4528	80	78	2	2	NUM
asir-4528	80	79	)	)	PUNCT
asir-4528	80	80	2	2	NUM
asir-4528	80	81	+	+	NOUN
asir-4528	80	82	(	(	PUNCT
asir-4528	80	83	𝑦1	𝑦1	NOUN
asir-4528	80	84	2	2	NUM
asir-4528	80	85	)	)	PUNCT
asir-4528	80	86	2	2	NUM
asir-4528	80	87	𝐵1	𝐵1	NOUN
asir-4528	80	88	+	+	CCONJ
asir-4528	80	89	𝑥2	𝑥2	NOUN
asir-4528	80	90	2	2	NUM
asir-4528	80	91	√(𝑦2	√(𝑦2	PROPN
asir-4528	80	92	2	2	NUM
asir-4528	80	93	)	)	PUNCT
asir-4528	80	94	2	2	NUM
asir-4528	80	95	+	+	NOUN
asir-4528	80	96	(	(	PUNCT
asir-4528	80	97	𝑥2	𝑥2	NOUN
asir-4528	80	98	2	2	NUM
asir-4528	80	99	)	)	PUNCT
asir-4528	80	100	2	2	NUM
asir-4528	80	101	+	+	NOUN
asir-4528	80	102	(	(	PUNCT
asir-4528	80	103	𝑦1	𝑦1	NOUN
asir-4528	80	104	2	2	NUM
asir-4528	80	105	)	)	PUNCT
asir-4528	80	106	2	2	NUM
asir-4528	80	107	𝐵2	𝐵2	NOUN
asir-4528	80	108	+	+	X
asir-4528	80	109	𝑦1	𝑦1	NOUN
asir-4528	80	110	2	2	NUM
asir-4528	80	111	√(𝑦2	√(𝑦2	PROPN
asir-4528	80	112	2	2	NUM
asir-4528	80	113	)	)	PUNCT
asir-4528	80	114	2	2	NUM
asir-4528	80	115	+	+	NOUN
asir-4528	80	116	(	(	PUNCT
asir-4528	80	117	𝑥2	𝑥2	NOUN
asir-4528	80	118	2	2	NUM
asir-4528	80	119	)	)	PUNCT
asir-4528	80	120	2	2	NUM
asir-4528	80	121	+	+	NOUN
asir-4528	80	122	(	(	PUNCT
asir-4528	80	123	𝑦1	𝑦1	NOUN
asir-4528	80	124	2	2	NUM
asir-4528	80	125	)	)	PUNCT
asir-4528	80	126	2	2	NUM
asir-4528	80	127	𝐵3	𝐵3	NOUN
asir-4528	80	128	.	.	PUNCT
asir-4528	81	1	as	as	ADP
asir-4528	81	2	above	above	ADV
asir-4528	81	3	,	,	PUNCT
asir-4528	81	4	𝜑2	𝜑2	NOUN
asir-4528	81	5	=	=	SYM
asir-4528	81	6	cos	cos	PROPN
asir-4528	81	7	−1	−1	PROPN
asir-4528	81	8	𝑥1	𝑥1	PROPN
asir-4528	81	9	2	2	NUM
asir-4528	81	10	±	±	NUM
asir-4528	81	11	2𝜋	2𝜋	NOUN
asir-4528	81	12	𝑘2	𝑘2	PROPN
asir-4528	81	13	,	,	PUNCT
asir-4528	81	14	𝑘2	𝑘2	PROPN
asir-4528	81	15	=	=	PUNCT
asir-4528	81	16	0,1,2	0,1,2	NUM
asir-4528	81	17	,	,	PUNCT
asir-4528	81	18	…	…	PUNCT
asir-4528	81	19	the	the	DET
asir-4528	81	20	angle	angle	NOUN
asir-4528	81	21	cos−1	cos−1	PROPN
asir-4528	81	22	𝑥1	𝑥1	PROPN
asir-4528	81	23	2	2	NUM
asir-4528	81	24	will	will	AUX
asir-4528	81	25	be	be	AUX
asir-4528	81	26	denoted	denote	VERB
asir-4528	81	27	as	as	ADP
asir-4528	81	28	𝜑2(0	𝜑2(0	PROPN
asir-4528	81	29	)	)	PUNCT
asir-4528	81	30	.	.	PUNCT
asir-4528	82	1	measurement	measurement	NOUN
asir-4528	82	2	of	of	ADP
asir-4528	82	3	an	an	DET
asir-4528	82	4	observable	observable	ADJ
asir-4528	82	5	𝐶	𝐶	NOUN
asir-4528	82	6	=	=	PROPN
asir-4528	82	7	𝐶0	𝐶0	PROPN
asir-4528	82	8	+	+	CCONJ
asir-4528	82	9	𝐶1𝐵1	𝐶1𝐵1	PROPN
asir-4528	82	10	+	+	CCONJ
asir-4528	82	11	𝐶2𝐵2	𝐶2𝐵2	X
asir-4528	82	12	+	+	CCONJ
asir-4528	82	13	𝐶3𝐵3	𝐶3𝐵3	NOUN
asir-4528	82	14	=	=	SYM
asir-4528	82	15	|𝐶|	|𝐶|	NOUN
asir-4528	82	16	(	(	PUNCT
asir-4528	82	17	𝐶0	𝐶0	X
asir-4528	82	18	|𝐶|	|𝐶|	NOUN
asir-4528	82	19	+	+	CCONJ
asir-4528	82	20	𝐶1	𝐶1	PRON
asir-4528	82	21	|𝐶|	|𝐶|	NOUN
asir-4528	82	22	𝐵1	𝐵1	NOUN
asir-4528	82	23	+	+	CCONJ
asir-4528	82	24	𝐶2	𝐶2	ADJ
asir-4528	82	25	|𝐶|	|𝐶|	X
asir-4528	82	26	𝐵2	𝐵2	NOUN
asir-4528	82	27	+	+	CCONJ
asir-4528	82	28	𝐶3	𝐶3	PROPN
asir-4528	82	29	|𝐶|	|𝐶|	X
asir-4528	82	30	𝐵3	𝐵3	PROPN
asir-4528	82	31	)	)	PUNCT
asir-4528	83	1	=	=	PRON
asir-4528	83	2	|𝐶|	|𝐶|	NOUN
asir-4528	83	3	(	(	PUNCT
asir-4528	83	4	𝐶0	𝐶0	X
asir-4528	83	5	|𝐶|	|𝐶|	VERB
asir-4528	83	6	+	+	PROPN
asir-4528	83	7	√1	√1	ADV
asir-4528	83	8	−	−	PROPN
asir-4528	83	9	𝐶0	𝐶0	NOUN
asir-4528	83	10	2	2	NUM
asir-4528	83	11	|𝐶|2	|𝐶|2	X
asir-4528	83	12	(	(	PUNCT
asir-4528	83	13	𝐶1	𝐶1	PROPN
asir-4528	83	14	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	83	15	𝐶0	𝐶0	NOUN
asir-4528	83	16	2	2	NUM
asir-4528	83	17	|𝐶|2	|𝐶|2	PUNCT
asir-4528	83	18	𝐵1	𝐵1	NOUN
asir-4528	83	19	+	+	CCONJ
asir-4528	83	20	𝐶2	𝐶2	PROPN
asir-4528	83	21	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	83	22	𝐶0	𝐶0	NOUN
asir-4528	83	23	2	2	NUM
asir-4528	83	24	|𝐶|2	|𝐶|2	PUNCT
asir-4528	83	25	𝐵2	𝐵2	NOUN
asir-4528	83	26	+	+	CCONJ
asir-4528	83	27	𝐶3	𝐶3	PROPN
asir-4528	83	28	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	83	29	𝐶0	𝐶0	NOUN
asir-4528	83	30	2	2	NUM
asir-4528	83	31	|𝐶|2	|𝐶|2	ADJ
asir-4528	83	32	𝐵3	𝐵3	NOUN
asir-4528	83	33	)	)	PUNCT
asir-4528	83	34	)	)	PUNCT
asir-4528	84	1	=	=	SYM
asir-4528	84	2	|𝐶|𝑒𝐼𝑆𝜑	|𝐶|𝑒𝐼𝑆𝜑	PROPN
asir-4528	84	3	,	,	PUNCT
asir-4528	84	4	where	where	SCONJ
asir-4528	84	5	|𝐶|	|𝐶|	NOUN
asir-4528	84	6	=	=	SYM
asir-4528	84	7	√𝐶0	√𝐶0	VERB
asir-4528	84	8	2	2	NUM
asir-4528	84	9	+	+	CCONJ
asir-4528	84	10	𝐶1	𝐶1	NUM
asir-4528	84	11	2	2	NUM
asir-4528	84	12	+	+	CCONJ
asir-4528	84	13	𝐶2	𝐶2	X
asir-4528	84	14	2	2	NUM
asir-4528	84	15	+	+	CCONJ
asir-4528	84	16	𝐶3	𝐶3	PROPN
asir-4528	84	17	2	2	NUM
asir-4528	84	18	,	,	PUNCT
asir-4528	84	19	𝜑	𝜑	X
asir-4528	84	20	=	=	SYM
asir-4528	84	21	cos−1	cos−1	NUM
asir-4528	84	22	𝐶0	𝐶0	NOUN
asir-4528	84	23	|𝐶|	|𝐶|	PROPN
asir-4528	84	24	,	,	PUNCT
asir-4528	84	25	𝐼𝑆	𝐼𝑆	PROPN
asir-4528	84	26	=	=	SYM
asir-4528	84	27	𝐶1	𝐶1	PROPN
asir-4528	84	28	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	84	29	𝐶0	𝐶0	NOUN
asir-4528	84	30	2	2	NUM
asir-4528	84	31	|𝐶|2	|𝐶|2	PUNCT
asir-4528	84	32	𝐵1	𝐵1	NOUN
asir-4528	84	33	+	+	CCONJ
asir-4528	84	34	𝐶2	𝐶2	PROPN
asir-4528	84	35	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	84	36	𝐶0	𝐶0	NOUN
asir-4528	84	37	2	2	NUM
asir-4528	84	38	|𝐶|2	|𝐶|2	PUNCT
asir-4528	84	39	𝐵2	𝐵2	NOUN
asir-4528	84	40	+	+	CCONJ
asir-4528	84	41	𝐶3	𝐶3	PROPN
asir-4528	84	42	|𝐶|√1−	|𝐶|√1−	ADJ
asir-4528	84	43	𝐶0	𝐶0	NOUN
asir-4528	84	44	2	2	NUM
asir-4528	84	45	|𝐶|2	|𝐶|2	NOUN
asir-4528	84	46	𝐵3	𝐵3	PROPN
asir-4528	84	47	,	,	PUNCT
asir-4528	84	48	by	by	ADP
asir-4528	84	49	the	the	DET
asir-4528	84	50	wave	wave	NOUN
asir-4528	84	51	function	function	NOUN
asir-4528	84	52	𝑒𝐼𝑆1𝜑1	𝑒𝐼𝑆1𝜑1	PROPN
asir-4528	84	53	is	be	AUX
asir-4528	84	54	:	:	PUNCT
asir-4528	84	55	𝑀1	𝑀1	PROPN
asir-4528	84	56	=	=	SYM
asir-4528	84	57	𝑒	𝑒	PROPN
asir-4528	84	58	−𝐼𝑆1𝜑1	−𝐼𝑆1𝜑1	PUNCT
asir-4528	84	59	|𝐶|𝑒𝐼𝑆𝜑	|𝐶|𝑒𝐼𝑆𝜑	PROPN
asir-4528	84	60	𝑒𝐼𝑆1𝜑1	𝑒𝐼𝑆1𝜑1	PROPN
asir-4528	84	61	measurement	measurement	NOUN
asir-4528	84	62	by	by	ADP
asir-4528	84	63	𝑒𝐼𝑆2𝜑2	𝑒𝐼𝑆2𝜑2	PROPN
asir-4528	84	64	is	be	AUX
asir-4528	84	65	:	:	PUNCT
asir-4528	85	1	𝑀2	𝑀2	PROPN
asir-4528	85	2	=	=	PUNCT
asir-4528	85	3	𝑒	𝑒	PART
asir-4528	85	4	−𝐼𝑆2𝜑2	−𝐼𝑆2𝜑2	PUNCT
asir-4528	86	1	|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	ADP
asir-4528	86	2	measurement	measurement	NOUN
asir-4528	86	3	by	by	ADP
asir-4528	86	4	any	any	DET
asir-4528	86	5	intermediate	intermediate	ADJ
asir-4528	86	6	parallel	parallel	ADJ
asir-4528	86	7	transport	transport	NOUN
asir-4528	86	8	wave	wave	NOUN
asir-4528	86	9	function	function	NOUN
asir-4528	86	10	(	(	PUNCT
asir-4528	86	11	1	1	NUM
asir-4528	86	12	−	−	NOUN
asir-4528	86	13	𝑡)𝑒𝐼𝑆1𝜑1	𝑡)𝑒𝐼𝑆1𝜑1	X
asir-4528	86	14	+	+	CCONJ
asir-4528	86	15	𝑡𝑒𝐼𝑆2𝜑2	𝑡𝑒𝐼𝑆2𝜑2	NOUN
asir-4528	86	16	then	then	ADV
asir-4528	86	17	reads	read	VERB
asir-4528	86	18	:	:	PUNCT
asir-4528	86	19	(	(	PUNCT
asir-4528	86	20	1	1	NUM
asir-4528	86	21	−	−	NOUN
asir-4528	86	22	𝑡)2𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑	𝑡)2𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑	ADJ
asir-4528	86	23	𝑒𝐼𝑆1𝜑1	𝑒𝐼𝑆1𝜑1	PROPN
asir-4528	86	24	+	+	CCONJ
asir-4528	86	25	𝑡2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	𝑡2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	ADP
asir-4528	86	26	+	+	NOUN
asir-4528	86	27	|𝐶|𝑡(1	|𝐶|𝑡(1	PUNCT
asir-4528	86	28	−	−	NOUN
asir-4528	86	29	𝑡)(𝑒−𝐼𝑆1𝜑1𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	𝑡)(𝑒−𝐼𝑆1𝜑1𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	NOUN
asir-4528	86	30	+	+	CCONJ
asir-4528	86	31	𝑒−𝐼𝑆2𝜑2𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	𝑒−𝐼𝑆2𝜑2𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	NOUN
asir-4528	86	32	)	)	PUNCT
asir-4528	86	33	=	=	PUNCT
asir-4528	86	34	(	(	PUNCT
asir-4528	86	35	1	1	NUM
asir-4528	86	36	−	−	PRON
asir-4528	86	37	𝑡)2𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	𝑡)2𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	PROPN
asir-4528	86	38	+	+	CCONJ
asir-4528	86	39	𝑡2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	𝑡2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	ADP
asir-4528	86	40	+	+	NOUN
asir-4528	86	41	𝑡(1	𝑡(1	PROPN
asir-4528	86	42	−	−	PROPN
asir-4528	87	1	𝑡)(𝑒−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	𝑡)(𝑒−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑒−𝐼𝑆2𝜑2|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆2𝜑2	PROPN
asir-4528	87	2	+	+	CCONJ
asir-4528	87	3	𝑒−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	𝑒−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑒−𝐼𝑆1𝜑1|𝐶|𝑒𝐼𝑆𝜑𝑒𝐼𝑆1𝜑1	NOUN
asir-4528	87	4	)	)	PUNCT
asir-4528	87	5	=	=	PUNCT
asir-4528	87	6	(	(	PUNCT
asir-4528	87	7	1	1	NUM
asir-4528	87	8	−	−	NOUN
asir-4528	87	9	𝑡)2𝑀1	𝑡)2𝑀1	PROPN
asir-4528	87	10	+	+	CCONJ
asir-4528	87	11	𝑡	𝑡	PROPN
asir-4528	87	12	2𝑀2	2𝑀2	NUM
asir-4528	87	13	+	+	CCONJ
asir-4528	87	14	𝑡(1	𝑡(1	PROPN
asir-4528	87	15	−	−	PROPN
asir-4528	87	16	𝑡)(𝑒	𝑡)(𝑒	PROPN
asir-4528	87	17	−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑀1	−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑀1	NOUN
asir-4528	87	18	+	+	CCONJ
asir-4528	87	19	𝑒	𝑒	PROPN
asir-4528	87	20	−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑀2	−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑀2	NOUN
asir-4528	87	21	)	)	PUNCT
asir-4528	87	22	let	let	VERB
asir-4528	87	23	us	we	PRON
asir-4528	87	24	make	make	VERB
asir-4528	87	25	natural	natural	ADJ
asir-4528	87	26	for	for	ADP
asir-4528	87	27	double	double	ADJ
asir-4528	87	28	split	split	ADJ
asir-4528	87	29	experiment	experiment	NOUN
asir-4528	87	30	assumption	assumption	NOUN
asir-4528	87	31	𝑆1	𝑆1	NOUN
asir-4528	87	32	=	=	SYM
asir-4528	87	33	𝑆2	𝑆2	NOUN
asir-4528	87	34	=	=	PUNCT
asir-4528	87	35	𝑆0	𝑆0	PROPN
asir-4528	87	36	(	(	PUNCT
asir-4528	87	37	that	that	PRON
asir-4528	87	38	is	be	AUX
asir-4528	87	39	the	the	DET
asir-4528	87	40	two	two	NUM
asir-4528	87	41	wave	wave	NOUN
asir-4528	87	42	functions	function	NOUN
asir-4528	87	43	,	,	PUNCT
asir-4528	87	44	measuring	measure	VERB
asir-4528	87	45	states	state	NOUN
asir-4528	87	46	,	,	PUNCT
asir-4528	87	47	are	be	AUX
asir-4528	87	48	of	of	ADP
asir-4528	87	49	0	0	NUM
asir-4528	87	50	-	-	PUNCT
asir-4528	87	51	type	type	NOUN
asir-4528	87	52	with	with	ADP
asir-4528	87	53	identical	identical	ADJ
asir-4528	87	54	bivector	bivector	NOUN
asir-4528	87	55	planes	plane	NOUN
asir-4528	87	56	.	.	PUNCT
asir-4528	87	57	)	)	PUNCT
asir-4528	88	1	then	then	ADV
asir-4528	88	2	we	we	PRON
asir-4528	88	3	get	get	VERB
asir-4528	88	4	the	the	DET
asir-4528	88	5	measurement	measurement	NOUN
asir-4528	88	6	result	result	NOUN
asir-4528	88	7	by	by	ADP
asir-4528	88	8	the	the	DET
asir-4528	88	9	intermediate	intermediate	ADJ
asir-4528	88	10	parallel	parallel	ADJ
asir-4528	88	11	transport	transport	NOUN
asir-4528	88	12	wave	wave	NOUN
asir-4528	88	13	function	function	NOUN
asir-4528	88	14	:	:	PUNCT
asir-4528	88	15	(	(	PUNCT
asir-4528	88	16	1	1	NUM
asir-4528	88	17	−	−	NOUN
asir-4528	88	18	𝑡)2𝑀1	𝑡)2𝑀1	PROPN
asir-4528	88	19	+	+	CCONJ
asir-4528	88	20	𝑡	𝑡	PROPN
asir-4528	88	21	2𝑀2	2𝑀2	NUM
asir-4528	88	22	+	+	CCONJ
asir-4528	88	23	𝑡(1	𝑡(1	PROPN
asir-4528	88	24	−	−	PROPN
asir-4528	88	25	𝑡)(𝑒	𝑡)(𝑒	PROPN
asir-4528	88	26	−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑀1	−𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1𝑀1	NOUN
asir-4528	88	27	+	+	CCONJ
asir-4528	88	28	𝑒	𝑒	PROPN
asir-4528	88	29	−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑀2	−𝐼𝑆1𝜑1𝑒𝐼𝑆2𝜑2𝑀2	NOUN
asir-4528	88	30	)	)	PUNCT
asir-4528	88	31	=	=	PUNCT
asir-4528	89	1	(	(	PUNCT
asir-4528	89	2	1	1	NUM
asir-4528	89	3	−	−	NOUN
asir-4528	89	4	𝑡)2𝑀1	𝑡)2𝑀1	PROPN
asir-4528	89	5	+	+	CCONJ
asir-4528	89	6	𝑡	𝑡	PROPN
asir-4528	89	7	2𝑀2	2𝑀2	NUM
asir-4528	89	8	+	+	CCONJ
asir-4528	89	9	𝑡(1	𝑡(1	PROPN
asir-4528	89	10	−	−	NOUN
asir-4528	89	11	𝑡)(𝑒	𝑡)(𝑒	PROPN
asir-4528	89	12	𝐼𝑆0(𝜑1−𝜑2)𝑀1	𝐼𝑆0(𝜑1−𝜑2)𝑀1	PROPN
asir-4528	89	13	+	+	CCONJ
asir-4528	89	14	𝑒	𝑒	PROPN
asir-4528	89	15	𝐼𝑆0(𝜑2−𝜑1)𝑀2	𝐼𝑆0(𝜑2−𝜑1)𝑀2	PROPN
asir-4528	89	16	)	)	PUNCT
asir-4528	89	17	it	it	PRON
asir-4528	89	18	is	be	AUX
asir-4528	89	19	easily	easily	ADV
asir-4528	89	20	seen	see	VERB
asir-4528	89	21	that	that	SCONJ
asir-4528	89	22	the	the	DET
asir-4528	89	23	result	result	NOUN
asir-4528	89	24	of	of	ADP
asir-4528	89	25	measurement	measurement	NOUN
asir-4528	89	26	is	be	AUX
asir-4528	89	27	𝑀1	𝑀1	ADV
asir-4528	89	28	when	when	SCONJ
asir-4528	89	29	𝑡	𝑡	X
asir-4528	89	30	=	=	NOUN
asir-4528	89	31	0	0	NUM
asir-4528	89	32	and	and	CCONJ
asir-4528	89	33	𝑀2	𝑀2	PROPN
asir-4528	89	34	when	when	SCONJ
asir-4528	89	35	𝑡	𝑡	X
asir-4528	89	36	=	=	NOUN
asir-4528	89	37	1	1	X
asir-4528	89	38	.	.	PUNCT
asir-4528	89	39	consider	consider	VERB
asir-4528	89	40	the	the	DET
asir-4528	89	41	following	following	ADJ
asir-4528	89	42	simplified	simplified	ADJ
asir-4528	89	43	scenario	scenario	NOUN
asir-4528	89	44	.	.	PUNCT
asir-4528	90	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-4528	90	2	applied	apply	VERB
asir-4528	90	3	science	science	NOUN
asir-4528	90	4	and	and	CCONJ
asir-4528	90	5	innovative	innovative	ADJ
asir-4528	90	6	research	research	NOUN
asir-4528	90	7	vol	vol	NOUN
asir-4528	90	8	.	.	PROPN
asir-4528	91	1	6	6	NUM
asir-4528	91	2	,	,	PUNCT
asir-4528	91	3	no	no	INTJ
asir-4528	91	4	.	.	NOUN
asir-4528	91	5	1	1	NUM
asir-4528	91	6	,	,	PUNCT
asir-4528	91	7	2022	2022	NUM
asir-4528	91	8	52	52	NUM
asir-4528	91	9	published	publish	VERB
asir-4528	91	10	by	by	ADP
asir-4528	91	11	scholink	scholink	PROPN
asir-4528	91	12	inc	inc	PROPN
asir-4528	91	13	.	.	PROPN
asir-4528	91	14	assume	assume	VERB
asir-4528	91	15	we	we	PRON
asir-4528	91	16	are	be	AUX
asir-4528	91	17	only	only	ADV
asir-4528	91	18	interested	interested	ADJ
asir-4528	91	19	in	in	ADP
asir-4528	91	20	the	the	DET
asir-4528	91	21	projections	projection	NOUN
asir-4528	91	22	of	of	ADP
asir-4528	91	23	𝑀1	𝑀1	PROPN
asir-4528	91	24	and	and	CCONJ
asir-4528	91	25	𝑀2	𝑀2	PROPN
asir-4528	91	26	onto	onto	ADP
asir-4528	91	27	the	the	DET
asir-4528	91	28	plane	plane	NOUN
asir-4528	91	29	of	of	ADP
asir-4528	91	30	their	their	PRON
asir-4528	91	31	rotations	rotation	NOUN
asir-4528	91	32	,	,	PUNCT
asir-4528	91	33	𝑆0	𝑆0	NOUN
asir-4528	91	34	,	,	PUNCT
asir-4528	91	35	𝑀1(𝑆0	𝑀1(𝑆0	NOUN
asir-4528	91	36	)	)	PUNCT
asir-4528	91	37	and	and	CCONJ
asir-4528	91	38	𝑀2(𝑆0	𝑀2(𝑆0	PROPN
asir-4528	91	39	)	)	PUNCT
asir-4528	91	40	.	.	PUNCT
asir-4528	92	1	then	then	ADV
asir-4528	92	2	from	from	ADP
asir-4528	92	3	the	the	DET
asir-4528	92	4	general	general	ADJ
asir-4528	92	5	formula	formula	NOUN
asir-4528	92	6	𝑒𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1	𝑒𝐼𝑆2𝜑2𝑒𝐼𝑆1𝜑1	PUNCT
asir-4528	92	7	=	=	SYM
asir-4528	92	8	cosφ1	cosφ1	PROPN
asir-4528	92	9	cosφ2	cosφ2	NOUN
asir-4528	92	10	−	−	PROPN
asir-4528	93	1	(	(	PUNCT
asir-4528	93	2	𝑠1	𝑠1	PROPN
asir-4528	93	3	⋅	⋅	PROPN
asir-4528	93	4	𝑠2	𝑠2	PROPN
asir-4528	93	5	)	)	PUNCT
asir-4528	93	6	sinφ1	sinφ1	ADJ
asir-4528	93	7	sinφ2	sinφ2	PROPN
asir-4528	94	1	+	+	CCONJ
asir-4528	94	2	𝐼3𝑠2	𝐼3𝑠2	PROPN
asir-4528	94	3	cosφ1	cosφ1	X
asir-4528	94	4	sinφ2	sinφ2	PROPN
asir-4528	94	5	+	+	CCONJ
asir-4528	94	6	𝐼3𝑠1	𝐼3𝑠1	PROPN
asir-4528	94	7	cosφ2	cosφ2	NOUN
asir-4528	94	8	sinφ1	sinφ1	ADJ
asir-4528	94	9	−	−	ADP
asir-4528	94	10	𝐼3(𝑠2	𝐼3(𝑠2	PROPN
asir-4528	94	11	×	×	PROPN
asir-4528	94	12	𝑠1	𝑠1	PROPN
asir-4528	94	13	)	)	PUNCT
asir-4528	95	1	sinφ1	sinφ1	ADJ
asir-4528	95	2	sinφ2	sinφ2	PROPN
asir-4528	95	3	we	we	PRON
asir-4528	95	4	get	get	VERB
asir-4528	95	5	that	that	PRON
asir-4528	95	6	up	up	ADP
asir-4528	95	7	to	to	ADP
asir-4528	95	8	some	some	DET
asir-4528	95	9	factors	factor	NOUN
asir-4528	95	10	𝑒𝐼𝑆0(𝜑1−𝜑2)𝑀1(𝑆0	𝑒𝐼𝑆0(𝜑1−𝜑2)𝑀1(𝑆0	NOUN
asir-4528	95	11	)	)	PUNCT
asir-4528	95	12	is	be	AUX
asir-4528	95	13	𝑀1(𝑆0	𝑀1(𝑆0	PROPN
asir-4528	95	14	)	)	PUNCT
asir-4528	95	15	rotated	rotate	VERB
asir-4528	95	16	in	in	ADP
asir-4528	95	17	𝑆0	𝑆0	NOUN
asir-4528	95	18	by	by	ADP
asir-4528	95	19	angle	angle	NOUN
asir-4528	95	20	𝜑1	𝜑1	PROPN
asir-4528	95	21	−	−	ADP
asir-4528	95	22	𝜑2	𝜑2	NOUN
asir-4528	95	23	and	and	CCONJ
asir-4528	95	24	𝑒𝐼𝑆0(𝜑2−𝜑1)𝑀2(𝑆0	𝑒𝐼𝑆0(𝜑2−𝜑1)𝑀2(𝑆0	NUM
asir-4528	95	25	)	)	PUNCT
asir-4528	95	26	is	be	AUX
asir-4528	95	27	𝑀2(𝑆0	𝑀2(𝑆0	PROPN
asir-4528	95	28	)	)	PUNCT
asir-4528	95	29	rotated	rotate	VERB
asir-4528	95	30	in	in	ADP
asir-4528	95	31	𝑆0	𝑆0	NOUN
asir-4528	95	32	by	by	ADP
asir-4528	95	33	angle	angle	NOUN
asir-4528	95	34	𝜑2	𝜑2	NOUN
asir-4528	95	35	−	−	PROPN
asir-4528	95	36	𝜑1	𝜑1	PROPN
asir-4528	95	37	.	.	PUNCT
asir-4528	96	1	without	without	ADP
asir-4528	96	2	loss	loss	NOUN
asir-4528	96	3	of	of	ADP
asir-4528	96	4	generality	generality	NOUN
asir-4528	96	5	suppose	suppose	VERB
asir-4528	96	6	that	that	SCONJ
asir-4528	96	7	the	the	DET
asir-4528	96	8	angles	angles	NOUN
asir-4528	96	9	𝜑1(0	𝜑1(0	NOUN
asir-4528	96	10	)	)	PUNCT
asir-4528	96	11	and	and	CCONJ
asir-4528	96	12	𝜑2(0)are	𝜑2(0)are	ADV
asir-4528	96	13	equal	equal	ADJ
asir-4528	96	14	by	by	ADP
asir-4528	96	15	values	value	NOUN
asir-4528	96	16	but	but	CCONJ
asir-4528	96	17	opposite	opposite	ADJ
asir-4528	96	18	in	in	ADP
asir-4528	96	19	sign	sign	NOUN
asir-4528	96	20	:	:	PUNCT
asir-4528	96	21	𝜑1(0	𝜑1(0	NOUN
asir-4528	96	22	)	)	PUNCT
asir-4528	96	23	=	=	PUNCT
asir-4528	96	24	−𝜑0	−𝜑0	PROPN
asir-4528	96	25	,	,	PUNCT
asir-4528	96	26	𝜑2(0	𝜑2(0	PROPN
asir-4528	96	27	)	)	PUNCT
asir-4528	96	28	=	=	SYM
asir-4528	96	29	𝜑0	𝜑0	NOUN
asir-4528	96	30	,	,	PUNCT
asir-4528	96	31	𝜑1(0	𝜑1(0	PROPN
asir-4528	96	32	)	)	PUNCT
asir-4528	96	33	−	−	PROPN
asir-4528	96	34	𝜑2(0	𝜑2(0	PROPN
asir-4528	96	35	)	)	PUNCT
asir-4528	96	36	=	=	SYM
asir-4528	96	37	−2𝜑0	−2𝜑0	NUM
asir-4528	96	38	𝜑2(0	𝜑2(0	PROPN
asir-4528	96	39	)	)	PUNCT
asir-4528	97	1	−	−	PROPN
asir-4528	97	2	𝜑1(0	𝜑1(0	NOUN
asir-4528	97	3	)	)	PUNCT
asir-4528	98	1	=	=	PUNCT
asir-4528	99	1	2𝜑0	2𝜑0	NUM
asir-4528	99	2	then	then	ADV
asir-4528	99	3	it	it	PRON
asir-4528	99	4	follows	follow	VERB
asir-4528	99	5	that	that	SCONJ
asir-4528	99	6	in	in	ADP
asir-4528	99	7	clifford	clifford	PROPN
asir-4528	99	8	translations	translation	NOUN
asir-4528	99	9	the	the	DET
asir-4528	99	10	projection	projection	NOUN
asir-4528	99	11	𝑀1(𝑆0	𝑀1(𝑆0	PROPN
asir-4528	99	12	)	)	PUNCT
asir-4528	99	13	rotates	rotate	NOUN
asir-4528	99	14	in	in	ADP
asir-4528	99	15	𝑆0	𝑆0	NOUN
asir-4528	99	16	additionally	additionally	ADV
asir-4528	99	17	by	by	ADP
asir-4528	99	18	−2(𝜑0	−2(𝜑0	PROPN
asir-4528	99	19	±	±	PROPN
asir-4528	99	20	𝜋(𝑘1	𝜋(𝑘1	PROPN
asir-4528	99	21	−	−	PROPN
asir-4528	99	22	𝑘2	𝑘2	PROPN
asir-4528	99	23	)	)	PUNCT
asir-4528	99	24	)	)	PUNCT
asir-4528	99	25	,	,	PUNCT
asir-4528	99	26	𝑘1	𝑘1	NOUN
asir-4528	99	27	=	=	SYM
asir-4528	99	28	0,1,2	0,1,2	NUM
asir-4528	99	29	,	,	PUNCT
asir-4528	99	30	…	…	PUNCT
asir-4528	99	31	,	,	PUNCT
asir-4528	99	32	𝑘2	𝑘2	PROPN
asir-4528	99	33	=	=	PUNCT
asir-4528	99	34	0,1,2	0,1,2	NUM
asir-4528	99	35	,	,	PUNCT
asir-4528	99	36	…	…	PUNCT
asir-4528	99	37	,	,	PUNCT
asir-4528	99	38	and	and	CCONJ
asir-4528	99	39	projection	projection	PROPN
asir-4528	99	40	𝑀2(𝑆0	𝑀2(𝑆0	PROPN
asir-4528	99	41	)	)	PUNCT
asir-4528	99	42	rotates	rotate	NOUN
asir-4528	99	43	in	in	ADP
asir-4528	99	44	𝑆0	𝑆0	NOUN
asir-4528	99	45	additionally	additionally	ADV
asir-4528	99	46	by	by	ADP
asir-4528	99	47	2(𝜑0	2(𝜑0	NUM
asir-4528	99	48	±	±	NOUN
asir-4528	99	49	𝜋(𝑘1	𝜋(𝑘1	NOUN
asir-4528	99	50	−	−	PROPN
asir-4528	99	51	𝑘2	𝑘2	PROPN
asir-4528	99	52	)	)	PUNCT
asir-4528	99	53	)	)	PUNCT
asir-4528	99	54	,	,	PUNCT
asir-4528	99	55	𝑘1	𝑘1	NOUN
asir-4528	99	56	=	=	SYM
asir-4528	99	57	0,1,2	0,1,2	NUM
asir-4528	99	58	,	,	PUNCT
asir-4528	99	59	…	…	PUNCT
asir-4528	99	60	,	,	PUNCT
asir-4528	99	61	𝑘2	𝑘2	PROPN
asir-4528	99	62	=	=	PUNCT
asir-4528	99	63	0,1,2	0,1,2	NUM
asir-4528	99	64	,	,	PUNCT
asir-4528	99	65	…	…	PUNCT
asir-4528	99	66	.	.	PUNCT
asir-4528	100	1	thus	thus	ADV
asir-4528	100	2	,	,	PUNCT
asir-4528	100	3	we	we	PRON
asir-4528	100	4	get	get	VERB
asir-4528	100	5	infinite	infinite	ADJ
asir-4528	100	6	number	number	NOUN
asir-4528	100	7	of	of	ADP
asir-4528	100	8	copies	copy	NOUN
asir-4528	100	9	of	of	ADP
asir-4528	100	10	𝑀1(𝑆0	𝑀1(𝑆0	NOUN
asir-4528	100	11	)	)	PUNCT
asir-4528	100	12	and	and	CCONJ
asir-4528	100	13	𝑀2(𝑆0	𝑀2(𝑆0	PROPN
asir-4528	100	14	)	)	PUNCT
asir-4528	100	15	with	with	ADP
asir-4528	100	16	varying	vary	VERB
asir-4528	100	17	values	value	NOUN
asir-4528	100	18	depending	depend	VERB
asir-4528	100	19	every	every	DET
asir-4528	100	20	time	time	NOUN
asir-4528	100	21	on	on	ADP
asir-4528	100	22	uniformly	uniformly	ADV
asir-4528	100	23	distributed	distribute	VERB
asir-4528	100	24	,	,	PUNCT
asir-4528	100	25	by	by	ADP
asir-4528	100	26	assumption	assumption	NOUN
asir-4528	100	27	,	,	PUNCT
asir-4528	100	28	value	value	NOUN
asir-4528	100	29	of	of	ADP
asir-4528	100	30	𝑡	𝑡	PROPN
asir-4528	100	31	,	,	PUNCT
asir-4528	100	32	0	0	NUM
asir-4528	100	33	≤	≤	NUM
asir-4528	100	34	𝑡	𝑡	VERB
asir-4528	100	35	≤	≤	ADV
asir-4528	100	36	1	1	NUM
asir-4528	100	37	,	,	PUNCT
asir-4528	100	38	and	and	CCONJ
asir-4528	100	39	separated	separate	VERB
asir-4528	100	40	by	by	ADP
asir-4528	100	41	±𝜋	±𝜋	PROPN
asir-4528	100	42	along	along	ADP
asir-4528	100	43	the	the	DET
asir-4528	100	44	big	big	ADJ
asir-4528	100	45	circle	circle	NOUN
asir-4528	100	46	of	of	ADP
asir-4528	100	47	intersection	intersection	NOUN
asir-4528	100	48	of	of	ADP
asir-4528	100	49	plane	plane	NOUN
asir-4528	100	50	𝑆0	𝑆0	NOUN
asir-4528	100	51	with	with	ADP
asir-4528	100	52	the	the	DET
asir-4528	100	53	sphere	sphere	NOUN
asir-4528	100	54	𝕊3	𝕊3	NOUN
asir-4528	100	55	.	.	PUNCT
asir-4528	101	1	4	4	NUM
asir-4528	101	2	.	.	X
asir-4528	101	3	conclusions	conclusion	NOUN
asir-4528	101	4	it	it	PRON
asir-4528	101	5	was	be	AUX
asir-4528	101	6	demonstrated	demonstrate	VERB
asir-4528	101	7	that	that	SCONJ
asir-4528	101	8	the	the	DET
asir-4528	101	9	geometric	geometric	ADJ
asir-4528	101	10	algebra	algebra	NOUN
asir-4528	101	11	formalism	formalism	NOUN
asir-4528	101	12	along	along	ADP
asir-4528	101	13	with	with	ADP
asir-4528	101	14	generalization	generalization	NOUN
asir-4528	101	15	of	of	ADP
asir-4528	101	16	complex	complex	ADJ
asir-4528	101	17	numbers	number	NOUN
asir-4528	101	18	and	and	CCONJ
asir-4528	101	19	subsequent	subsequent	ADJ
asir-4528	101	20	lift	lift	NOUN
asir-4528	101	21	of	of	ADP
asir-4528	101	22	the	the	DET
asir-4528	101	23	two	two	NUM
asir-4528	101	24	-	-	PUNCT
asir-4528	101	25	dimensional	dimensional	ADJ
asir-4528	101	26	hilbert	hilbert	NOUN
asir-4528	101	27	space	space	NOUN
asir-4528	101	28	valued	value	VERB
asir-4528	101	29	qubits	qubit	NOUN
asir-4528	101	30	to	to	ADP
asir-4528	101	31	geometrically	geometrically	ADV
asir-4528	101	32	feasible	feasible	ADJ
asir-4528	101	33	elements	element	NOUN
asir-4528	101	34	of	of	ADP
asir-4528	101	35	even	even	ADJ
asir-4528	101	36	subalgebra	subalgebra	NOUN
asir-4528	101	37	of	of	ADP
asir-4528	101	38	geometric	geometric	ADJ
asir-4528	101	39	algebra	algebra	NOUN
asir-4528	101	40	in	in	ADP
asir-4528	101	41	three	three	NUM
asir-4528	101	42	dimensions	dimension	NOUN
asir-4528	101	43	allows	allow	VERB
asir-4528	101	44	,	,	PUNCT
asir-4528	101	45	particularly	particularly	ADV
asir-4528	101	46	,	,	PUNCT
asir-4528	101	47	to	to	PART
asir-4528	101	48	resolve	resolve	VERB
asir-4528	101	49	the	the	DET
asir-4528	101	50	double	double	ADJ
asir-4528	101	51	split	split	NOUN
asir-4528	101	52	experiment	experiment	NOUN
asir-4528	101	53	results	result	NOUN
asir-4528	101	54	with	with	ADP
asir-4528	101	55	diffraction	diffraction	NOUN
asir-4528	101	56	patterns	pattern	NOUN
asir-4528	101	57	inherent	inherent	ADJ
asir-4528	101	58	to	to	PART
asir-4528	101	59	wave	wave	VERB
asir-4528	101	60	diffraction	diffraction	NOUN
asir-4528	101	61	.	.	PUNCT
asir-4528	102	1	this	this	DET
asir-4528	102	2	weirdness	weirdness	NOUN
asir-4528	102	3	of	of	ADP
asir-4528	102	4	the	the	DET
asir-4528	102	5	double	double	ADJ
asir-4528	102	6	split	split	NOUN
asir-4528	102	7	experiment	experiment	NOUN
asir-4528	102	8	is	be	AUX
asir-4528	102	9	milestone	milestone	NOUN
asir-4528	102	10	of	of	ADP
asir-4528	102	11	all	all	DET
asir-4528	102	12	further	further	ADJ
asir-4528	102	13	difficulties	difficulty	NOUN
asir-4528	102	14	in	in	ADP
asir-4528	102	15	interpretation	interpretation	NOUN
asir-4528	102	16	of	of	ADP
asir-4528	102	17	conventional	conventional	ADJ
asir-4528	102	18	quantum	quantum	ADJ
asir-4528	102	19	mechanics	mechanic	NOUN
asir-4528	102	20	.	.	PUNCT
asir-4528	103	1	references	reference	NOUN
asir-4528	103	2	soiguine	soiguine	PROPN
asir-4528	103	3	,	,	PUNCT
asir-4528	103	4	a.	a.	NOUN
asir-4528	103	5	(	(	PUNCT
asir-4528	103	6	2014	2014	NUM
asir-4528	103	7	)	)	PUNCT
asir-4528	103	8	.	.	PUNCT
asir-4528	104	1	what	what	PRON
asir-4528	104	2	quantum	quantum	ADJ
asir-4528	104	3	“	"	PUNCT
asir-4528	104	4	state	state	NOUN
asir-4528	104	5	”	"	PUNCT
asir-4528	104	6	really	really	ADV
asir-4528	104	7	is	be	AUX
asir-4528	104	8	?	?	PUNCT
asir-4528	105	1	retrieved	retrieve	VERB
asir-4528	105	2	from	from	ADP
asir-4528	105	3	http://arxiv.org/abs/1406.3751	http://arxiv.org/abs/1406.3751	PROPN
asir-4528	105	4	soiguine	soiguine	NOUN
asir-4528	105	5	,	,	PUNCT
asir-4528	105	6	a.	a.	NOUN
asir-4528	105	7	(	(	PUNCT
asir-4528	105	8	2015	2015	NUM
asir-4528	105	9	)	)	PUNCT
asir-4528	105	10	.	.	PUNCT
asir-4528	106	1	geometric	geometric	ADJ
asir-4528	106	2	algebra	algebra	NOUN
asir-4528	106	3	,	,	PUNCT
asir-4528	106	4	qubits	qubit	NOUN
asir-4528	106	5	,	,	PUNCT
asir-4528	106	6	geometric	geometric	ADJ
asir-4528	106	7	evolution	evolution	NOUN
asir-4528	106	8	,	,	PUNCT
asir-4528	106	9	and	and	CCONJ
asir-4528	106	10	all	all	DET
asir-4528	106	11	that	that	PRON
asir-4528	106	12	.	.	PUNCT
asir-4528	107	1	retrieved	retrieve	VERB
asir-4528	107	2	from	from	ADP
asir-4528	107	3	http://arxiv.org/abs/1502.02169	http://arxiv.org/abs/1502.02169	PROPN
asir-4528	107	4	soiguine	soiguine	NOUN
asir-4528	107	5	,	,	PUNCT
asir-4528	107	6	a.	a.	NOUN
asir-4528	107	7	(	(	PUNCT
asir-4528	107	8	2020	2020	NUM
asir-4528	107	9	)	)	PUNCT
asir-4528	107	10	.	.	PUNCT
asir-4528	108	1	the	the	DET
asir-4528	108	2	geometric	geometric	ADJ
asir-4528	108	3	algebra	algebra	NOUN
asir-4528	108	4	lift	lift	NOUN
asir-4528	108	5	of	of	ADP
asir-4528	108	6	qubits	qubit	NOUN
asir-4528	108	7	and	and	CCONJ
asir-4528	108	8	beyond	beyond	ADP
asir-4528	108	9	.	.	PUNCT
asir-4528	109	1	s.l.:lambert	s.l.:lambert	VERB
asir-4528	109	2	academic	academic	ADJ
asir-4528	109	3	publishing	publishing	NOUN
asir-4528	109	4	.	.	PUNCT
asir-4528	110	1	soiguine	soiguine	NOUN
asir-4528	110	2	,	,	PUNCT
asir-4528	110	3	a.	a.	NOUN
asir-4528	110	4	m.	m.	NOUN
asir-4528	110	5	(	(	PUNCT
asir-4528	110	6	1996	1996	NUM
asir-4528	110	7	)	)	PUNCT
asir-4528	110	8	.	.	PUNCT
asir-4528	111	1	complex	complex	ADJ
asir-4528	111	2	conjugation	conjugation	NOUN
asir-4528	111	3	relative	relative	ADJ
asir-4528	111	4	to	to	ADP
asir-4528	111	5	what	what	PRON
asir-4528	111	6	?	?	PUNCT
asir-4528	112	1	in	in	ADP
asir-4528	112	2	clifford	clifford	PROPN
asir-4528	112	3	algebras	algebras	PROPN
asir-4528	112	4	with	with	ADP
asir-4528	112	5	numeric	numeric	ADJ
asir-4528	112	6	and	and	CCONJ
asir-4528	112	7	symbolic	symbolic	ADJ
asir-4528	112	8	computations	computation	NOUN
asir-4528	112	9	(	(	PUNCT
asir-4528	112	10	pp	pp	ADJ
asir-4528	112	11	.	.	PUNCT
asir-4528	112	12	284	284	NUM
asir-4528	112	13	-	-	NUM
asir-4528	112	14	294	294	NUM
asir-4528	112	15	)	)	PUNCT
asir-4528	112	16	.	.	PUNCT
asir-4528	113	1	boston	boston	PROPN
asir-4528	113	2	:	:	PUNCT
asir-4528	113	3	birkhauser	birkhauser	VERB
asir-4528	113	4	.	.	PUNCT