Convexity properties of the quantum Rényi divergences, with applications to the quantum Stein's Lemma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis. The proof is based on some simple properties of a new notion of quantum Rényi divergence, recently introduced in [Müller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013)], and [Wilde, Winter, Yang, arXiv:1306.1586].

Original languageEnglish
Title of host publication9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014
EditorsSteven T. Flammia, Aram W. Harrow
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages88-98
Number of pages11
ISBN (Electronic)9783939897736
DOIs
Publication statusPublished - Nov 1 2014
Event9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014 - Singapore, Singapore
Duration: May 21 2014May 23 2014

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume27
ISSN (Print)1868-8969

Other

Other9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014
CountrySingapore
CitySingapore
Period5/21/145/23/14

Keywords

  • Composite null-hypothesis
  • Quantum Rényi divergences
  • Second-order asymptotics
  • Stein's lemma

ASJC Scopus subject areas

  • Software

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  • Cite this

    Mosonyi, M. (2014). Convexity properties of the quantum Rényi divergences, with applications to the quantum Stein's Lemma. In S. T. Flammia, & A. W. Harrow (Eds.), 9th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2014 (pp. 88-98). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 27). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.TQC.2014.88