On superactivation of zero-error capacities and reversibility of a quantum channel

We propose examples of low dimensional quantum channels demonstrating different forms of superactivation of one-shot zero-error capacities, in particular, the extreme superactivation (this complements the recent result of T.S.Cubitt and G.Smith). We also describe classes of quantum channels whose zero-error classical and quantum capacities cannot be superactivated. We consider implications of the superactivation of one-shot zero-error capacities to analysis of reversibility of a tensor-product channel with respect to families of pure states. Our approach based on the notions of complementary channel and of transitive subspace of operators makes it possible to study the superactivation effects for infinite-dimensional channels as well.