Some characterizations of reversibility of quantum channels

Abstract: We say that a quantum channel is reversible (or sufficient) with respect to a set of states S if all states in S can be recovered by another channel. This property was studied and characterized by Petz, who proved a number of equivalent conditions. Such conditions can be given in terms of some structural properties of the channel and the states, or by preservation of some information-theoretic quantities such as the relative entropy.

In this talk, we give a review of some of the reversibility conditions. We first note that characterizations of sufficient channels can be obtained from the mean ergodic theorem. We then focus on the conditions given by preservation of sandwiched Rényi relative entropies and the L_1-distance.