On Hastings' counterexamples to the minimum output entropy additivity conjecture

Details On Hastings' counterexamples to the minimum output entropy additivity conjecture On Hastings' counterexamples to the minimum output entropy additivity conjecture

2009-07-19

arxiv.org/abs/0907.3210v1

Open Syst. Inf. Dyn. 17, 31 (2010)

Physics

Quantum Physics

17 pages + 1 line

Scientific paper

10.1142/S1230161210000047

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here 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. Furthermore, 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. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.

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