**Local additivity of the minimum entropy output of a quantum channel**

One of the major open problems in quantum information concerns
with the question whether entanglement between signal states can help to
send classical information on quantum channels. Recently, Hasting proved
that entanglement does help by finding a counter-example for the long
standing additivity conjecture that the minimum von-Neumann entropy
output of a quantum channel is additive under taking tensor products.
In this talk I will show that the minimum von-Neumann entropy output of
a quantum channel is locally additive. Hasting's counterexample for the
global additivity conjecture, makes this result somewhat surprising. In
particular, it indicates that the non-additivity of the minimum entropy
output is related to a global effect of quantum channels. I will end
with few related open problems.