Quantifying irreversibility of channels

In contrast to unitary evolutions which are reversible, generic quantum processes (operations, quantum channels) are often irreversible. However, the degree of irreversibility of different channels are different, and it is desirable to have a quantitative characterization of irreversibility. In this work, by exploiting channel-state duality implemented by the Jamiołkowski–Choi isomorphism, we quantify irreversibility of channels via entropy of the Jamiołkowski–Choi states of the corresponding channels, and compare it with the notions of entanglement fidelity and entropy exchange. General properties of a reasonable measure of irreversibility are discussed from an intuitive perspective, and entropic measures of irreversibility are introduced. Several relations between irreversibility, entanglement fidelity, degree of non-unitality, and decorrelating power are established. Some measures of irreversibility for a variety of prototypical channels are evaluated explicitly, which reveal some information-theoretic aspects of the structure of channels from the perspective of irreversibility.