Classical capacity of averaged quantum channels

In this paper we extend recent coding results by Datta and Dorlas on classical capacity of averaged quantum channels with finitely many memoryless branches to arbitrary number of branches. Only assumption in our approach is that the channel satisfies some weak measurability properties. Our approach to the direct coding theorem is based on our previous work on compound classical-quantum channels. The weak converse requires an alternative characterization of the essential infimum and the remaining proof proceeds via application of Holevo's bound and Fano's inequality.