Discrimination of Quantum States Under Locality Constraints in the Many-Copy Setting

Cheng, HC; Winter, A; Yu, N

Discrimination of Quantum States Under Locality Constraints in the Many-Copy Setting

Cheng, HC Winter, A Yu, N

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Publisher:: Springer Nature
Publication Type:: Journal Article
Citation:: Communications in Mathematical Physics, 2023, 404, (1), pp. 151-183
Issue Date:: 2023-11-01

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Field	Value	Language
dc.contributor.author	Cheng, HC
dc.contributor.author	Winter, A
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032
dc.date.accessioned	2024-02-26T05:27:48Z
dc.date.available	2024-02-26T05:27:48Z
dc.date.issued	2023-11-01
dc.identifier.citation	Communications in Mathematical Physics, 2023, 404, (1), pp. 151-183
dc.identifier.issn	0010-3616
dc.identifier.issn	1432-0916
dc.identifier.uri	http://hdl.handle.net/10453/175892
dc.description.abstract	We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local operation and classical communication (LOCC) operation, we prove that the optimal average error probability always decays exponentially in the number of copies. Second, we provide a sufficient condition for the LOCC operations to achieve the same performance as the positive-partial-transpose (PPT) operations. We further show that testing a maximally entangled state against its orthogonal complement and testing extremal Werner states both fulfill the above-mentioned condition. Hence, we determine the explicit expressions for the optimal average error probability, the optimal trade-off between the type-I and type-II errors, and the associated Chernoff, Stein, Hoeffding, and strong converse exponents. Then, we show an infinite asymptotic separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB). The quantum states can be distinguished perfectly by PPT operations, while the optimal error probability, with SEP operations, 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 a UPB.
dc.language	en
dc.publisher	Springer Nature
dc.relation	http://purl.org/au-research/grants/arc/DE180100156
dc.relation	http://purl.org/au-research/grants/arc/DP210102449
dc.relation.ispartof	Communications in Mathematical Physics
dc.relation.isbasedon	10.1007/s00220-023-04836-0
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0101 Pure Mathematics, 0105 Mathematical Physics, 0206 Quantum Physics
dc.subject.classification	Mathematical Physics
dc.subject.classification	4902 Mathematical physics
dc.subject.classification	4904 Pure mathematics
dc.subject.classification	5107 Particle and high energy physics
dc.title	Discrimination of Quantum States Under Locality Constraints in the Many-Copy Setting
dc.type	Journal Article
utslib.citation.volume	404
utslib.for	0101 Pure Mathematics
utslib.for	0105 Mathematical Physics
utslib.for	0206 Quantum Physics
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	closed_access	*
dc.date.updated	2024-02-26T05:27:47Z
pubs.issue	1
pubs.publication-status	Published
pubs.volume	404
utslib.citation.issue	1

Abstract:

We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local operation and classical communication (LOCC) operation, we prove that the optimal average error probability always decays exponentially in the number of copies. Second, we provide a sufficient condition for the LOCC operations to achieve the same performance as the positive-partial-transpose (PPT) operations. We further show that testing a maximally entangled state against its orthogonal complement and testing extremal Werner states both fulfill the above-mentioned condition. Hence, we determine the explicit expressions for the optimal average error probability, the optimal trade-off between the type-I and type-II errors, and the associated Chernoff, Stein, Hoeffding, and strong converse exponents. Then, we show an infinite asymptotic separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB). The quantum states can be distinguished perfectly by PPT operations, while the optimal error probability, with SEP operations, 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 a UPB.

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http://hdl.handle.net/10453/175892