Nonconvexity of private capacity and classical environment-assisted capacity of a quantum channel

Elkouss, D ; Strelchuk, Sergii (2016-10-17)


The capacity of classical channels is convex. This is not the case for the quantum capacity of a channel: The capacity of a mixture of different quantum channels exceeds the mixture of the individual capacities and thus is nonconvex. Here we show that this effect goes beyond the quantum capacity and holds for the private and classical environment-assisted capacities of quantum channels.