Time-reversal and strong H-theorem for quantum discrete-time Markov channels
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. A strong form of the H-theorem is then established which implies monotonicity of the Belavkin-Staszewski's relative entropy under completely positive, trace-preserving maps.