Approximating Invertible Maps by Recovery Channels: Optimality and an Application to Non-Markovian Dynamics

TL;DR

This paper explores how optimal recovery channels can approximate inverse quantum maps, effectively reversing certain decoherence processes and mitigating non-Markovian effects in quantum dynamics.

Contribution

It introduces a method using optimal Petz recovery maps to approximate inverse quantum channels, including applications to non-Markovian dynamics.

Findings

Recovery maps effectively simulate inverse evolution for typical decoherence channels

The approach attenuates non-Markovian effects like information backflow

Optimal recovery channels improve quantum dynamics control

Abstract

We investigate the problem of reversing quantum dynamics, specifically via optimal Petz recovery maps. We focus on typical decoherence channels, such as dephasing, depolarizing and amplitude damping. We illustrate how well a physically implementable recovery map simulates an inverse evolution. We extend this idea to explore the use of recovery maps as an approximation of inverse maps, and apply it in the context of non-Markovian dynamics. We show how this strategy attenuates non-Markovian effects, such as the backflow of information.