Residual quantum correlations and non-Markovian noise

TL;DR

This paper investigates residual quantum correlations in two-qubit states under non-Markovian noise, deriving conditions for their sudden death and revival, and analyzing specific state families.

Contribution

It provides an analytical solution for residual quantum correlations in X states and explores their dynamics under non-Markovian dephasing channels.

Findings

Conditions for sudden death and revival of RQC are derived.

Residual quantum correlations exhibit non-trivial dynamics under non-Markovian noise.

Analysis includes Werner states, MNMS, and MEMS.

Abstract

Wu et al. introduced residual quantum correlations (RQC) in 2015 and defined them in terms of two complementary bases. Given a measure for classical correlations, its optimization defines a local basis. Relative to this local basis, one defines a new one that is mutually unbiased to the first one. In the latter, the corresponding measure for quantum correlations is calculated. Local available quantum correlations (LAQC) define a measure for maximal RQC and were introduced by Mundarain and Ladron de Guevara. In previous articles, we derived an analytical exact solution for this measure for 2-qubit X states. Using those results and deriving an expression for the RQC measure introduced by Wu et al., we analyze their behavior for two non-Markovian quantum dephasing channels: Random Telegraph (RT) and Modified Ornstein-Uhlenbeck (MOU) noises. We derive general conditions for sudden death and revival of RQC in X states and illustrate these results with three families of bipartite qubit states: Werner states, Maximally Nonlocal Mixed States (MNMS), and Maximally Entangled Mixed States (MEMS).