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Nonadditivity of Rényi entropy and Dvoretzky's theorem

Source: J. Math. Phys. 51, 022102 (2010); doi:10.1063/1.3271044

Published 1 February 2010

KEYWORDS and PACS
Keywords
PACS
  • 03.67.-a
    Quantum information
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • YEAR: 2010
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Guillaume Aubrun,1 Stanislaw Szarek,2,3 and Elisabeth Werner3,4
1Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France
2Equipe d'Analyse Fonctionnelle, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie-Paris 6, 4 Place Jussieu, 75252 Paris, France
3Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, USA
4UFR de Mathématique, Université de Lille 1, 59655 Villeneuve d'Ascq, France
The goal of this note is to show that the analysis of the minimum output p-Rényi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's theorem about almost Euclidean sections of high-dimensional convex bodies. This conceptually simplifies the (nonconstructive) argument by Hayden–Winter, disproving the additivity conjecture for the minimal output p-Rényi entropy (for p>1). ©2010 American Institute of Physics
History: Received 13 October 2009; accepted 10 November 2009; published 1 February 2010
Permalink: http://link.aip.org/link/?JMAPAQ/51/022102/1

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