Quantum discord and non-Markovianity of quantum dynamics

TL;DR

This paper explores how quantum discord relates to non-Markovianity in quantum dynamics, proposing criteria and measures for identifying Markovian and non-Markovian behavior using quantum correlations and state tomography.

Contribution

It establishes that vanishing quantum discord characterizes Markovianity and introduces a practical, less demanding measure of non-Markovianity based on quantum correlation monogamy and ancilla-assisted tomography.

Findings

Quantum discord's vanishing is necessary and sufficient for Markovianity.

A new measure of non-Markovianity using quantum correlation monogamy.

A simplified method for detecting non-Markovianity via state tomography.

Abstract

The problem of recognizing (non-)Markovianity of a quantum dynamics is revisited through analyzing quantum correlations. We argue that instantaneously-vanishing quantum discord provides a necessary and sufficient condition for Markovianity of a quantum map. This is used to introduce a measure of non-Markovianity. This measure, however, requires demanding knowledge about the system and the environment. By using a quantum correlation monogamy property and an ancillary system, we propose a simplified measure with less requirements. Non-Markovianity is thereby decided by quantum state tomography of the system and the ancilla.