Optimal Distillation of Non-Markovianity: Bounds, Multi-Copy Gain, and the Weak-to-Essential Transition

TL;DR

This paper develops an algorithm to optimize the distillation of non-Markovianity in quantum channels, enabling enhanced distinguishability recovery in open quantum systems.

Contribution

It introduces a systematic method to determine the maximal distinguishability gain and converts weakly non-Markovian channels into effectively non-Markovian ones.

Findings

Identified the optimal implementation of the distinguishability enhancement protocol.

Demonstrated conversion of weakly non-Markovian channels into essentially non-Markovian channels.

Provided a framework for assessing and optimizing distinguishability recovery.

Abstract

Quantum channels generally reduce the distinguishability of quantum states, limiting information transmission and processing. Previous work introduced a protocol capable of increasing the distinguishability of states after the action of a specific quantum channel. Here we show how to systematically determine the maximal distinguishability gain achievable by this method. We develop an algorithm that identifies the optimal implementation of the protocol and applies to arbitrary quantum channels in a straightforward manner. Using this approach, we demonstrate that a weakly non-Markovian channel can effectively be converted into an essentially non-Markovian one through a distillation-like process. We further analyze the quantitative features of the optimized protocol, characterizing the conditions under which the enhancement is most pronounced. Our results provide a general framework to assess and optimize distinguishability recovery in open quantum systems.