Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

Yu, N; Duan, R; Xu, Q

Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels

Yu, N

Duan, R

Xu, Q

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2017, 63 (2), pp. 1299 - 1310
Issue Date:: 2017-02-01

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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	Xu, Q	en_US
dc.date.issued	2017-02-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2017, 63 (2), pp. 1299 - 1310	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114758
dc.description.abstract	© 2016 IEEE. Motivated by the recent resolution of asymptotic quantum birkhoff conjecture (AQBC), we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels. We provide two lower bounds on this distance by employing techniques from quantum information and operator algebras, respectively. We then show how to apply these results to construct some explicit counterexamples to AQBC. We also point out an interesting connection between the Grothendieck's inequality and AQBC.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2016.2641447	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	63	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	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	63	en_US

Abstract:

© 2016 IEEE. Motivated by the recent resolution of asymptotic quantum birkhoff conjecture (AQBC), we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels. We provide two lower bounds on this distance by employing techniques from quantum information and operator algebras, respectively. We then show how to apply these results to construct some explicit counterexamples to AQBC. We also point out an interesting connection between the Grothendieck's inequality and AQBC.

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http://hdl.handle.net/10453/114758