Residual quantum correlations and non-Markovian noise

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).

Figures (8)

• Figure 1: Time evolution of Residual Quantum Correlations for a general 2-qubit X state under random telegraph noise (left), in units of $\gamma{}t$ and $a = 4\gamma$, and under the modified Ornstein-Uhlenbeck noise (right), in units of $\gamma{t}$ and $\Gamma=\gamma$.
• Figure 2: Concurrence (solid) and Residual Quantum Correlations (dashed) for Werner states.
• Figure 3: Time evolution of Residual Quantum Correlations (left) and Concurrence (right) for Werner states under random telegraph noise in units of $\gamma{}t$ and $a = 4\gamma$.
• Figure 4: Comparison of the time evolution of Concurrence (dashed) and Residual Quantum Correlations (solid) for $\ket{\psi^-}$ (left) and a Werner state with $z=2/3$ in units of $\gamma{}t$ and $a = 4\gamma$.
• Figure 5: Time evolution of Residual Quantum Correlations (left) and Concurrence (right) for Werner states under the Markovian phase-flip channel (top row) and the modified Ornstein–Uhlenbeck noise in units of $\gamma{}t$ and $\Gamma = \gamma$.