Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

We consider the model of random quantum channels where the Stinespring isometries are chosen uniformly at random. We show that under a suitable choice of parameters for the dimensions of the input, output and ancilla, the output space is almost deterministic and conveniently described with a new free probability tool, the free compression norm. Then we study the problem of maximizing the Lp norm on this output space. Surprisingly, the output maximizing the Lp norm does not depend on p and has a very simple form. As a consequence we obtain the best bounds known so far for the violation of the additivity of the minimum output entropy. This talk is based on two joint works with Belinschi and Nechita.