  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.
