License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2014.88
URN: urn:nbn:de:0030-drops-48094
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2014/4809/
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Mosonyi, Milán

Convexity Properties of the Quantum Rényi Divergences, with Applications to the Quantum Stein's Lemma

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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 Rènyi divergence, recently introduced in [Müller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013)], and [Wilde, Winter, Yang, arXiv:1306.1586].

BibTeX - Entry

@InProceedings{mosonyi:LIPIcs:2014:4809,
  author =	{Mil{\'a}n Mosonyi},
  title =	{{Convexity Properties of the Quantum R{\'e}nyi Divergences, with Applications to the Quantum Stein's Lemma }},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{88--98},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Steven T. Flammia and Aram W. Harrow},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2014/4809},
  URN =		{urn:nbn:de:0030-drops-48094},
  doi =		{10.4230/LIPIcs.TQC.2014.88},
  annote =	{Keywords: Quantum R{\'e}nyi divergences, Stein's lemma, composite null-hypothesis, second-order asymptotics}
}

Keywords: Quantum Rényi divergences, Stein's lemma, composite null-hypothesis, second-order asymptotics
Collection: 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)
Issue Date: 2014
Date of publication: 11.12.2014

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