Quantifying Non-Markovianity in Open Quantum Dynamics

TL;DR

This paper introduces two new measures for quantifying non-Markovian behavior in open quantum systems, compatible with the Markovian limit and efficiently computable from multi-time measurements, along with a reconstruction algorithm.

Contribution

It proposes novel non-Markovianity measures and a heuristic reconstruction algorithm, advancing the quantitative analysis of quantum dynamics.

Findings

The measures are consistent with the Markovian limit.

The measures can be efficiently computed from multi-time measurements.

Numerical examples demonstrate the effectiveness of the measures and reconstruction.

Abstract

Characterization of non-Markovian open quantum dynamics is both of theoretical and practical relevance. In a seminal work [Phys. Rev. Lett. 120, 040405 (2018)], a necessary and sufficient quantum Markov condition is proposed, with a clear operational interpretation and correspondence with the classical limit. Here we propose two non-Markovianity measures for general open quantum dynamics, which are fully reconciled with the Markovian limit and can be efficiently calculated based on the multi-time quantum measurements of the system. A heuristic algorithm for reconstructing the underlying open quantum dynamics is proposed, whose complexity is directly related to the proposed non-Markovianity measures. The non-Markovianity measures and the reconstruction algorithm are demonstrated with numerical examples, together with a careful reexamination of the non-Markovianity in quantum dephasing dynamics.