Non-Markovianity in the time evolution of open quantum systems assessed by means of quantum state distance

We provide a quantitative evaluation of non-Markovianity (NM) for an XX chain of interacting qubits with one end coupled to a reservoir. The NM of several non-Markovian spectral densities is assessed in terms of various quantum state distance (QSD) measures. 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 NM 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 the case of decaying traces. The 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 slowing-down of dissipation by the squared Lorentzian reservoir.