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A minimax approach to one-shot entropy inequalities
File(s)
1906.00333v1.pdf (148.45 KB)
Accepted version
Author(s)
Anshu, Anurag
Berta, Mario
Jain, Rahul
Tomamichel, Marco
Type
Journal Article
Abstract
One-shot information theory entertains a plethora of entropic quantities, such as the smooth max-divergence, hypothesis testing divergence, and information spectrum divergence, that characterize various operational tasks in quantum information theory and are used to analyze their asymptotic behavior. Tight inequalities between these quantities are thus of immediate interest. In this note, we use a minimax approach (appearing previously, for example, in the proofs of the quantum substate theorem), to simplify the quantum problem to a commutative one, which allows us to derive such inequalities. Our derivations are conceptually different from previous arguments and in some cases lead to tighter relations. We hope that the approach discussed here can lead to progress in open problems in quantum Shannon theory and exemplify this by applying it to a simple case of the joint smoothing problem.
Date Issued
2019-12-01
Date Acceptance
2019-10-14
Citation
Journal of Mathematical Physics, 2019, 60 (12), pp.1-7
URI
URL
DOI
ISSN
0022-2488
Publisher
American Institute of Physics
Start Page
1
End Page
7
Journal / Book Title
Journal of Mathematical Physics
Volume
60
Issue
12
Copyright Statement
© 2019 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Math. Phys. 60, 122201 (2019); doi: 10.1063/1.5126723 and may be found at https://doi.org/10.1063/1.5126723
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000550322600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Physical Sciences
Physics, Mathematical
Physics
Publication Status
Published
Article Number
ARTN 122201
Date Publish Online
2019-12-04