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)
aubrun (arrobas) math. univ-lyon1. fr