On Hastings' counterexamples to the minimum output entropy additivity conjecture

Understand

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.