an important open problem in quantum information concerns with the question whether entanglement between signal states can help in sending classical information over a quantum channel. recently, hastings proved that entanglement does help by finding a counter example for the long standing additivity conjecture that the minimum entropy output of a quantum channel is additive under taking tensor products. in this talk i will show that the minimum entropy output of a quantum channel is locally additive. hastings' counter example 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 a few related open problems.