Discrimination of quantum states under locality constraints in the many-copy setting

Cheng, H-C; Winter, A; Yu, N

Discrimination of quantum states under locality constraints in the many-copy setting

Cheng, H-C Winter, A Yu, N

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Publisher:: IEEE
Publication Type:: Conference Proceeding
Citation:: 2021 IEEE International Symposium on Information Theory (ISIT), 2021, 2021-July, pp. 1188-1193
Issue Date:: 2021-09-01

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Field	Value	Language
dc.contributor.author	Cheng, H-C
dc.contributor.author	Winter, A
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.date	2021-07-12
dc.date.accessioned	2022-03-31T04:06:25Z
dc.date.available	2022-03-31T04:06:25Z
dc.date.issued	2021-09-01
dc.identifier.citation	2021 IEEE International Symposium on Information Theory (ISIT), 2021, 2021-July, pp. 1188-1193
dc.identifier.isbn	9781538682098
dc.identifier.issn	2157-8095
dc.identifier.uri	http://hdl.handle.net/10453/155771
dc.description.abstract	We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB.
dc.language	en
dc.publisher	IEEE
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation	http://purl.org/au-research/grants/arc/DP210102449
dc.relation.ispartof	2021 IEEE International Symposium on Information Theory (ISIT)
dc.relation.ispartof	2021 IEEE International Symposium on Information Theory
dc.relation.ispartofseries	IEEE International Symposium on Information Theory
dc.relation.isbasedon	10.1109/isit45174.2021.9518100
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Discrimination of quantum states under locality constraints in the many-copy setting
dc.type	Conference Proceeding
utslib.citation.volume	2021-July
utslib.location.activity	Melbourne, Australia
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	open_access	*
dc.date.updated	2022-03-31T04:06:23Z
pubs.finish-date	2021-07-20
pubs.publication-status	Published
pubs.start-date	2021-07-12
pubs.volume	2021-July

Abstract:

We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB.

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http://hdl.handle.net/10453/155771