Non-additivity of Renyi entropy and Dvoretzky's Theorem
Quantum Physics
2010-02-07 v2 Functional Analysis
Abstract
The goal of this note is to show that the analysis of the minimum output p-Renyi 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-Renyi entropy (for p>1).
Keywords
Cite
@article{arxiv.0910.1189,
title = {Non-additivity of Renyi entropy and Dvoretzky's Theorem},
author = {Guillaume Aubrun and Stanislaw Szarek and Elisabeth Werner},
journal= {arXiv preprint arXiv:0910.1189},
year = {2010}
}
Comments
8 pages, LaTeX; v2: added and updated references, minor editorial changes, no content changes