Strengthened monotonicity of relative entropy via pinched petz recovery map

Sutter, D; Tomamichel, M; Harrow, AW

Strengthened monotonicity of relative entropy via pinched petz recovery map

Sutter, D Tomamichel, M

Harrow, AW

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2016, 62 (5), pp. 2907 - 2913
Issue Date:: 2016-05-01

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Field	Value	Language
dc.contributor.author	Sutter, D	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.contributor.author	Harrow, AW	en_US
dc.date.issued	2016-05-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2016, 62 (5), pp. 2907 - 2913	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/90335
dc.description.abstract	© 1963-2012 IEEE. The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a recovery map that exactly reverses the effects of the quantum channel on both states. In this paper, we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case, we reproduce recent lower bounds on the conditional mutual information, such as the one proved by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2016.2545680	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Strengthened monotonicity of relative entropy via pinched petz recovery map	en_US
dc.type	Journal Article
utslib.citation.volume	5	en_US
utslib.citation.volume	62	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/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.issue	5	en_US
pubs.publication-status	Published	en_US
pubs.volume	62	en_US

Abstract:

© 1963-2012 IEEE. The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a recovery map that exactly reverses the effects of the quantum channel on both states. In this paper, we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case, we reproduce recent lower bounds on the conditional mutual information, such as the one proved by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm.

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http://hdl.handle.net/10453/90335