Assessment of the degree of non-Markovianity of open quantum systems and the necessary generalization of quantum state distance measures

Abstract

We provide a quantitative evaluation of the degree of non-Markovianity (DNM) for an XX chain of interacting qubits with one end coupled to a reservoir. The DNM is assessed in terms of various quantum state distance (QSD) measures and various cases of non-Markovian spectral densities. Our approach is based on the construction of the density matrix of the open chain, without the necessity of a master equation. For the quantification of the DNM we calculate the dynamics of the QSD measures between the Markovian-damped and various types of non-Markovian-damped cases. Since in the literature several QSD measures, appear in forms that imply trace preserving density matrices, we introduced appropriate modifications so as to render them applicable to open systems with damped traces. Our results produce remarkable consistency between the various QSD measures. They also reveal a subtle and potentially useful interplay between qubit-qubit interaction and non-Markovian damping. Our calculations have also uncovered a surprisingly dramatic slowingdown of dissipation by the squared Lorentzian reservoir.