Given a Hilbert space V of dimension k and a sequence of spaces W_n of dimension n, we consider a sequence of random quantum channels obtained by the random inclusion in V W_n of a subspace H_n of dimension approximately tkn (t in (0, 1)). As n tends to infinity, we confine almost surely the singular values of the outputs of all states in H_n. As an application, we obtain new bounds for minimum output entropy entropies and give new examples of random channels violating the additivity of the Renyi entropy (for all parameters p>1). Our techniques rely on free probability type norm estimates for random matrices.

Paper reference: arXiv:0906.1877