Quantum Operation Time Reversal

TL;DR

This paper introduces a compact expression for reversing the dynamics of open quantum systems, analogous to classical Markov processes, highlighting the stochastic nature and thermodynamic aspects of quantum evolution.

Contribution

It provides a novel, compact formulation for the time reversal of quantum operations, extending classical concepts to quantum stochastic dynamics.

Findings

Reversal of quantum operations is analogous to classical Markov chain reversal.

Time reversal relates quantum trajectories via exchanged heat with the environment.

Open quantum system dynamics are generally stochastic, not deterministic.

Abstract

The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes towards equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.