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 slowing-down of dissipation by the
squared Lorentzian reservoir.Comment: 13 pages, 5 figure