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PERIMETER INSTITUTE RECORDED SEMINAR ARCHIVE

Hasting's counterexamples on the minimum output entropy additivity conjecture by measure concentration
Speaker(s): Fernando Brandao
Abstract: In 2008 Hastings reported a randomized construction of channels violating the minimum output entropy additivity conjecture. In this talk we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. We prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension.
Date: 06/07/2010 - 11:15 am
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