Chain rules for smooth min-and max-entropies

Vitanov, A; Dupuis, F; Tomamichel, M; Renner, R

Chain rules for smooth min-and max-entropies

Vitanov, A Dupuis, F Tomamichel, M

Renner, R

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2013, 59 (5), pp. 2603 - 2612
Issue Date:: 2013-05-01

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Field	Value	Language
dc.contributor.author	Vitanov, A	en_US
dc.contributor.author	Dupuis, F	en_US
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329	en_US
dc.contributor.author	Renner, R	en_US
dc.date.issued	2013-05-01	en_US
dc.identifier.citation	IEEE Transactions on Information Theory, 2013, 59 (5), pp. 2603 - 2612	en_US
dc.identifier.issn	0018-9448	en_US
dc.identifier.uri	http://hdl.handle.net/10453/117342
dc.description.abstract	The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min-and max-entropies, used in one-shot information theory. For these entropy measures, the chain rule no longer holds as an equality. However, the standard chain rule for the von Neumann entropy is retrieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states. © 1963-2012 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Information Theory	en_US
dc.relation.isbasedon	10.1109/TIT.2013.2238656	en_US
dc.subject.classification	Networking & Telecommunications	en_US
dc.title	Chain rules for smooth min-and max-entropies	en_US
dc.type	Journal Article
utslib.citation.volume	5	en_US
utslib.citation.volume	59	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	open_access
pubs.issue	5	en_US
pubs.publication-status	Published	en_US
pubs.volume	59	en_US

Abstract:

The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min-and max-entropies, used in one-shot information theory. For these entropy measures, the chain rule no longer holds as an equality. However, the standard chain rule for the von Neumann entropy is retrieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states. © 1963-2012 IEEE.

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http://hdl.handle.net/10453/117342