The minimum entropy output of a quantum channel is locally additive
  We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of the minimum entropy output is a global effect of quantum channels. 
Gilad Gour, Shmuel Friedland
quant-ph math-ph math.MP