Discrete-time classical and quantum Markovian evolutions: Maximum entropy problems on path space

2008/11/06 by Michele Pavon, Francesco Ticozzi, Pavon, Michele +1 · 2 citations
Computer Science · Physics and Astronomy · #60J10 #81Q99 #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.0811.0933

openalex publication_date 2008/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of Schroedinger 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.

Citations

• Modern Quantum Mechanics
• Completely positive maps and entropy inequalities

Cited by

• A convex approach for Markov chain estimation from aggregate data via inverse optimal transport
• Gradient Flows as Optimal Controlled Evolutions: From Rn to Wasserstein product spaces

Related

• On time-reversal and space-time harmonic processes for Markovian quantum channels
• Markov Chains Approximations of jump-Diffusion Quantum Trajectories
• Dynamics and Quantum Optimal Transport: Three lectures on quantum entropy and quantum Markov semigroups
• Quantum entropy and non-Markovian evolution
• Non-Markovian quantum state diffusion