Distinguishability of quantum states by positive operator-valued measures with positive partial transpose

Yu, N; Duan, R; Ying, M

Distinguishability of quantum states by positive operator-valued measures with positive partial transpose

Yu, N

Duan, R

Ying, M

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2014, 60 (4), pp. 2069 - 2079
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Yu, N https://orcid.org/0000-0003-1188-3032	en_US
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.contributor.author	Ying, M https://orcid.org/0000-0003-4847-702X	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2014, 60 (4), pp. 2069 - 2079	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/36388
dc.description.abstract	We study the distinguishability of bipartite quantum states by positive operator-valued measures with positive partial transpose (PPT POVMs). The contributions of this paper include: 1) we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability; 2) we show that a maximally entangled state and its orthogonal complement, no matter how many copies are supplied, cannot be distinguished by the PPT POVMs, even unambiguously. This result is much stronger than the previous known ones; and 3) we study the entanglement cost of distinguishing quantum states. It is proved that √2/3\|00〉 + √1/3\|11〉 is sufficient and necessary for distinguishing three Bell states by the PPT POVMs. An upper bound of entanglement cost of distinguishing a d ⊗ d pure state and its orthogonal complement is obtained for separable operations. Based on this bound, we are able to construct two orthogonal quantum states, which cannot be distinguished unambiguously by separable POVMs, but finite copies would make them perfectly distinguishable by local operations and classical communication. We further observe that a two-qubit maximally entangled state is always enough for distinguishing a d ⊗ d pure state and its orthogonal complement by the PPT POVMs, no matter the value of d. In sharp contrast, an entangled state with Schmidt number at least d is always needed for distinguishing such two states by separable POVMs. As an application, we show that the entanglement cost of distinguishing a d ⊗ d maximally entangled state and its orthogonal complement must be a maximally entangled state for d = 2, which implies that teleportation is optimal, and in general, it could be chosen as O{script} (log d/d). © 1963-2012 IEEE.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP110103473
dc.relation	http://purl.org/au-research/grants/arc/DP120103776
dc.relation	http://purl.org/au-research/grants/arc/FT120100449
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2014.2307575	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Distinguishability of quantum states by positive operator-valued measures with positive partial transpose	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	60	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	1005 Communications Technologies	en_US
pubs.embargo.period	Not known	en_US
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
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	60	en_US

Abstract:

We study the distinguishability of bipartite quantum states by positive operator-valued measures with positive partial transpose (PPT POVMs). The contributions of this paper include: 1) we give a negative answer to an open problem of showing a limitation of a previous known method for detecting nondistinguishability; 2) we show that a maximally entangled state and its orthogonal complement, no matter how many copies are supplied, cannot be distinguished by the PPT POVMs, even unambiguously. This result is much stronger than the previous known ones; and 3) we study the entanglement cost of distinguishing quantum states. It is proved that √2/3|00〉 + √1/3|11〉 is sufficient and necessary for distinguishing three Bell states by the PPT POVMs. An upper bound of entanglement cost of distinguishing a d ⊗ d pure state and its orthogonal complement is obtained for separable operations. Based on this bound, we are able to construct two orthogonal quantum states, which cannot be distinguished unambiguously by separable POVMs, but finite copies would make them perfectly distinguishable by local operations and classical communication. We further observe that a two-qubit maximally entangled state is always enough for distinguishing a d ⊗ d pure state and its orthogonal complement by the PPT POVMs, no matter the value of d. In sharp contrast, an entangled state with Schmidt number at least d is always needed for distinguishing such two states by separable POVMs. As an application, we show that the entanglement cost of distinguishing a d ⊗ d maximally entangled state and its orthogonal complement must be a maximally entangled state for d = 2, which implies that teleportation is optimal, and in general, it could be chosen as O{script} (log d/d). © 1963-2012 IEEE.

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