This is an announcement for the paper "Non-additivity of Renyi entropy and Dvoretzky's Theorem" by Guillaume Aubrun, Stanislaw Szarek, and Elisabeth Werner. 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 counterexample by Hayden-Winter to the additivity conjecture for the minimal output p-Renyi entropy (for p>1). Archive classification: quant-ph math.FA Remarks: 7 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: szarek@cwru.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0910.1189 or http://arXiv.org/abs/0910.1189 or by email in unzipped form by transmitting an empty message with subject line uget 0910.1189 or in gzipped form by using subject line get 0910.1189 to: math@arXiv.org.