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Relating different quantum generalizations of the conditional Rényi entropy

Tomamichel, Marco and Berta, Mario and Hayashi, Masahito (2014) Relating different quantum generalizations of the conditional Rényi entropy. Journal of Mathematical Physics, 55 (8). Art. No. 082206. ISSN 0022-2488. https://resolver.caltech.edu/CaltechAUTHORS:20141110-074713463

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Abstract

Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1311.3887arXivDiscussion Paper
http://scitation.aip.org/content/aip/journal/jmp/55/8/10.1063/1.4892761PublisherArticle
http://dx.doi.org/10.1063/1.4892761DOIArticle
ORCID:
AuthorORCID
Tomamichel, Marco0000-0001-5410-3329
Berta, Mario0000-0002-0428-3429
Additional Information:© 2014 AIP Publishing LLC. Received 26 May 2014; accepted 29 July 2014; published online 14 August 2014. M.T. is funded by the Ministry of Education (MOE) and National Research Foundation Singapore, as well as MOE Tier 3 Grant “Random numbers from quantum processes” (MOE2012-T3-1-009). M.B. thanks the Center for Quantum Technologies, Singapore, for hosting him while this work was done. M.H. is partially supported by a MEXT Grant-in-Aid for Scientific Research (A) No. 23246071 and the National Institute of Information and Communication Technology (NICT), Japan. The Centre for Quantum Technologies is funded by the Singapore Ministry of Education and the National Research Foundation as part of the Research Centres of Excellence programme.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Ministry of Education (Singapore)MOE2012-T3- 1-009
Ministry of Education, Culture, Sports, Science and Technology (MEXT) 23246071
National Institute of Information and Communication Technology (NICT), JapanUNSPECIFIED
National Research Foundation (Singapore)UNSPECIFIED
Issue or Number:8
Record Number:CaltechAUTHORS:20141110-074713463
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141110-074713463
Official Citation:Relating different quantum generalizations of the conditional Rényi entropy Marco Tomamichel, Mario Berta and Masahito Hayashi J. Math. Phys. 55, 082206 (2014); http://dx.doi.org/10.1063/1.4892761
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51477
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Nov 2014 16:54
Last Modified:03 Oct 2019 07:33

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