Non-additivity of Renyi entropy and Dvoretzky's Theorem

Details Non-additivity of Renyi entropy and Dvoretzky's Theorem Non-additivity of Renyi entropy and Dvoretzky's Theorem

2009-10-07

arxiv.org/abs/0910.1189v2

J. Math. Phys. 51, 022102 (2010)

Physics

Quantum Physics

8 pages, LaTeX; v2: added and updated references, minor editorial changes, no content changes

Scientific paper

10.1063/1.3271044

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).

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