  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.
