When do local operations and classical communication suffice for two-qubit state discrimination?

Chitambar, E; Duan, R; Hsieh, MH

When do local operations and classical communication suffice for two-qubit state discrimination?

Chitambar, E Duan, R

Hsieh, MH

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2014, 60 (3), pp. 1549 - 1561
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Chitambar, E	en_US
dc.contributor.author	Duan, R https://orcid.org/0000-0002-4388-7487	en_US
dc.contributor.author	Hsieh, MH https://orcid.org/0000-0002-3396-8427	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2014, 60 (3), pp. 1549 - 1561	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/34579
dc.description.abstract	In this paper, we consider the conditions under which a given ensemble of two-qubit states can be optimally distinguished by local operations and classical communication (LOCC). We begin by completing the perfect distinguishability problem of two-qubit ensembles - both for separable operations and LOCC - by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state. Then, for the well-known task of minimum error discrimination, it is shown that almost all two-qubit ensembles consisting of three pure states cannot be optimally discriminated using LOCC. This is surprising considering that any two pure states can be distinguished optimally by LOCC. Special attention is given to ensembles that lack entanglement, and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by LOCC, thus providing new examples of the phenomenon known as non-locality without entanglement. We next consider an example of N parties who each share the same state but who are ignorant of its identity. The state is drawn from the rotationally invariant trine ensemble, and we establish a tight connection between the N-copy ensemble and Shor's lifted single-copy ensemble. For any finite N, we prove that optimal identification of the states cannot be achieved by LOCC; however, as N → ∞, LOCC can indeed discriminate the states optimally. This is the first result of its kind. Finally, we turn to the task of unambiguous discrimination and derive new lower bounds on the LOCC inconclusive probability for symmetric states. When applied to the double trine ensemble, this leads to a rather different distinguishability character than when the minimum error probability is considered. © 1963-2012 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2013.2295356	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	When do local operations and classical communication suffice for two-qubit state discrimination?	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	60	en_US
utslib.for	0802 Computation Theory and Mathematics	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	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	60	en_US

Abstract:

In this paper, we consider the conditions under which a given ensemble of two-qubit states can be optimally distinguished by local operations and classical communication (LOCC). We begin by completing the perfect distinguishability problem of two-qubit ensembles - both for separable operations and LOCC - by providing necessary and sufficient conditions for the perfect discrimination of one pure and one mixed state. Then, for the well-known task of minimum error discrimination, it is shown that almost all two-qubit ensembles consisting of three pure states cannot be optimally discriminated using LOCC. This is surprising considering that any two pure states can be distinguished optimally by LOCC. Special attention is given to ensembles that lack entanglement, and we prove an easy sufficient condition for when a set of three product states cannot be optimally distinguished by LOCC, thus providing new examples of the phenomenon known as non-locality without entanglement. We next consider an example of N parties who each share the same state but who are ignorant of its identity. The state is drawn from the rotationally invariant trine ensemble, and we establish a tight connection between the N-copy ensemble and Shor's lifted single-copy ensemble. For any finite N, we prove that optimal identification of the states cannot be achieved by LOCC; however, as N → ∞, LOCC can indeed discriminate the states optimally. This is the first result of its kind. Finally, we turn to the task of unambiguous discrimination and derive new lower bounds on the LOCC inconclusive probability for symmetric states. When applied to the double trine ensemble, this leads to a rather different distinguishability character than when the minimum error probability is considered. © 1963-2012 IEEE.

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http://hdl.handle.net/10453/34579