Recovering complete positivity of non-Markovian quantum dynamics with Choi-proximity regularization

TL;DR

This paper introduces a numerical method to restore complete positivity in non-Markovian quantum dynamics by replacing the Choi operator with its closest physical counterpart, improving the physicality and accuracy of the models.

Contribution

It proposes a Choi-proximity regularization technique to fix complete positivity violations in non-Markovian quantum maps, extending beyond Markovian assumptions.

Findings

Regularized dynamics better reproduces exact dynamics.

Method preserves non-Markovian features.

Improves applicability of master equations in moderate coupling regimes.

Abstract

A relevant problem in the theory of open quantum systems is the lack of complete positivity of dynamical maps obtained after weak-coupling approximations, a famous example being the Redfield master equation. A number of approaches exist to recover well-defined evolutions under additional Markovian assumptions, but much less is known beyond this regime. Here we propose a numerical method to cure the complete-positivity violation issue while preserving the non-Markovian features of an arbitrary original dynamical map. The idea is to replace its unphysical Choi operator with its closest physical one, mimicking recent work on quantum process tomography. We also show that the regularized dynamics is more accurate in terms of reproducing the exact dynamics: this allows to heuristically push the utilization of these master equations in moderate coupling regimes, where the loss of positivity can have relevant impact.