Non-additivity of Rényi entropy and Dvoretzky's Theorem.


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 counterexample by Hayden--Winter to the additivity conjecture for the minimal output p-Rényi entropy (for p>1).

This paper has a more interesting continuation, dealing with the von Neumann entropy (the limit case p->1)

E-mail :
aubrun (arrobas) math. univ-lyon1. fr

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