Nonadditivity of rényi entropy and Dvoretzky's theorem

Guillaume Aubrun; Stanisław Szarek; Elisabeth Werner

doi:10.1063/1.3271044

Nonadditivity of rényi entropy and Dvoretzky's theorem

Guillaume Aubrun, Stanisław Szarek, Elisabeth Werner

Institute for Mathematics and its Applications

Research output: Contribution to journal › Article › peer-review

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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 language	English (US)
Article number	046912JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	2
DOIs	https://doi.org/10.1063/1.3271044
State	Published - 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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abstract = "The goal of this note is to show that the analysis of the minimum output p-R{\'e}nyi 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-R{\'e}nyi entropy (for p > 1).",

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Nonadditivity of rényi entropy and Dvoretzky's theorem

Abstract

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