Partially smoothed information measures

Anshu, A; Berta, M; Jain, R; Tomamichel, M

Partially smoothed information measures

Anshu, A Berta, M Jain, R Tomamichel, M

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Information Theory, 2018, 66 (8), pp 5022-5036
Issue Date:: 2020-08

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Field	Value	Language
dc.contributor.author	Anshu, A
dc.contributor.author	Berta, M
dc.contributor.author	Jain, R
dc.contributor.author	Tomamichel, M https://orcid.org/0000-0001-5410-3329
dc.date.accessioned	2021-06-17T00:42:42Z
dc.date.available	2021-06-17T00:42:42Z
dc.date.issued	2020-08
dc.identifier.citation	IEEE Transactions on Information Theory, 2018, 66 (8), pp 5022-5036
dc.identifier.uri	http://hdl.handle.net/10453/149569
dc.description.abstract	Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well. However, for quantum systems we can so far only give the asymptotic first-order expansion of these quantities.
dc.language	en
dc.relation	http://purl.org/au-research/grants/arc/DE160100821
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies
dc.subject.classification	Networking & Telecommunications
dc.title	Partially smoothed information measures
dc.type	Journal Article
utslib.for	0801 Artificial Intelligence and Image Processing
utslib.for	0906 Electrical and Electronic Engineering
utslib.for	1005 Communications Technologies
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access	*
dc.date.updated	2021-06-17T00:42:40Z

Abstract:

Smooth entropies are a tool for quantifying resource trade-offs in (quantum) information theory and cryptography. In typical bi- and multi-partite problems, however, some of the sub-systems are often left unchanged and this is not reflected by the standard smoothing of information measures over a ball of close states. We propose to smooth instead only over a ball of close states which also have some of the reduced states on the relevant sub-systems fixed. This partial smoothing of information measures naturally allows to give more refined characterizations of various information-theoretic problems in the one-shot setting. In particular, we immediately get asymptotic second-order characterizations for tasks such as privacy amplification against classical side information or classical state splitting. For quantum problems like state merging the general resource trade-off is tightly characterized by partially smoothed information measures as well. However, for quantum systems we can so far only give the asymptotic first-order expansion of these quantities.

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