Quantum correlations in mutually unbiased bases and non-Markovian dephasing
Wu et al. introduced a symmetric measure $Q^{s}$ in terms of mutually unbiased bases (MUBs) that quantifies residual quantum correlations (RQC). The definition of this measure involves determining two complementary local bases via an optimization of the quantum mutual information. One defines the first local bases, the optimal computational ones, by maximizing the classical correlations measure. Next, one defines a new set of local bases that are complementary to the first ones. In the latter, one also calculates the corresponding measure of quantum correlations by maximization. Considering alternative optimizations of the mentioned measures, one can define other quantifiers. In particular, Mundarain and Ladrón de Guevara introduced local available quantum correlations (LAQC, $\mathcal{L}$) in terms of the complementary local bases to the ones defining the least classically correlated state. That is, they characterize LAQC by defining the optimal bases as those that minimize the classical correlations measure. This type of quantum correlation is closely related to an entanglement activation protocol proposed by Piani et al. In previous articles, we derived an exact solution for the LAQC measure for 2-qubit X states. Based on these previous results and methodology, we determine the corresponding exact analytical expression for $Q^s$ of 2-qubit X states. We then analyze the behavior of these two measures 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 these measures in X states and illustrate these results with four families of bipartite qubit states: Werner states, Maximally Nonlocal Mixed States (MNMS), Maximally Entangled Mixed States (MEMS), and a mixed symmetric separable state.