On time-reversal and space-time harmonic processes for Markovian quantum channels

TL;DR

This paper introduces a framework for understanding time-reversal in quantum Markov processes using space-time harmonic processes, highlighting their impact on the dynamics of quantum relative entropy.

Contribution

It develops a novel approach to quantum time reversal through adjointness relations and introduces space-time harmonic processes for forward and reverse quantum Markov evolutions.

Findings

Time reversal of quantum Markov processes is characterized via adjointness.

Space-time harmonic processes are defined for quantum transition mechanisms.

The role of these processes in relative entropy dynamics is analyzed.

Abstract

The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition mechanisms, and their role for relative entropy dynamics is discussed.