Reversibility conditions for quantum operations

TL;DR

This paper establishes multiple equivalent conditions for the reversibility of quantum operations, linking it to preservation of various quantum distinguishability measures and properties of quantum derivatives.

Contribution

It provides a comprehensive set of criteria for reversibility of quantum operations, extending known results and connecting it to quantum Fisher information and hi^2-divergences.

Findings

Reversibility characterized by preservation of quantum f-divergences

Conditions involving quantum Radon-Nikodym derivatives

Equivalence with preservation of quantum Fisher information

Abstract

We give a list of equivalent conditions for reversibility of the adjoint of a unital Schwarz map with respect to a set of quantum states. A large class of such conditions is given by preservation of distinguishability measures: f-divergences, L_1 -distance, quantum Chernoff and Hoeffding distances; here we summarize and extend the known results. Moreover, we prove a number of conditions in terms of the properties of a quantum Radon-Nikodym derivative and factorization of states in the given set. Finally, we show that reversibility is equivalent with preservation of a large class of quantum Fisher informations and \chi^2-divergences.