The theory of Schrödinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path-space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.
Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space
PAVON, MICHELE;TICOZZI, FRANCESCO
2010
Abstract
The theory of Schrödinger bridges for diffusion processes is extended to classical and quantum discrete-time Markovian evolutions. The solution of the path-space maximum entropy problems is obtained from the a priori model in both cases via a suitable multiplicative functional transformation. In the quantum case, nonequilibrium time reversal of quantum channels is discussed and space-time harmonic processes are introduced.
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