**Revisiting additivity violation of quantum channels** - Motohisa Fukuda

In this talk we revisit additivity violation of minimum output (von Neumann) entropy of quantum channels, which implies that entangled inputs improve the classical capacity of some quantum channels. After Hastings disproved the additivity several other proofs were made, but recently we found a proof via epsilon-net argument and Levy's lemma. Interestingly, this combination of techniques were already used by Hayden, Leung and Winter to show existence of highly entangled subspaces in a bipartite space of large dimension. Moreover, Hayden and Winter used this result to disprove the additivity of minimum output p-Renyi entropy for p>1, but the estimate was not sharp enough for p=1; von Neumann entropy. We compare the above two methods and discuss what are technical improvements to make such a concise proof on the additivity violation of minimum output entropy.