Nonadditivity of rényi entropy and Dvoretzky's theorem

Guillaume Aubrun, Stanisław Szarek, Elisabeth Werner

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Abstract

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).

Original languageEnglish (US)
Article number046912JMP
JournalJournal of Mathematical Physics
Volume51
Issue number2
DOIs
StatePublished - Feb 1 2010

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