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.

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