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 2010

Bibliographical note

Funding Information:
The research of the first named author was partially supported by the Agence Nationale de la Recherche under Grant No. ANR-08-BLAN-0311-03. The research of the second and third named authors was partially supported by their respective grants from the National Science Foundation (USA) and from the U.S.-Israel Binational Science Foundation. The second named author thanks the organizers and fellow participants (particularly F. Brandao and C. King) of the Workshop on Operator Structures in Quantum Information (Fields Institute, July 2009), which served as a catalyst for this project.

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