  We study the time evolution of four distance measures in the presence of
initial systemenvironment correlations. It is well-known that the trace
distance between two quantum states of an open system may increase due to
initial correlations which leads to a breakdown of the contractivity of the
reduced dynamics. Here we compare and analyze, for two different models, the
time evolution of the trace distance, the Bures metric, the Hellinger distance
and the Jensen-Shannon divergence regarding an increase above their initial
values, witnessing initial correlations. This work generalizes, deepens and
corrects the study performed by Dajka et al. [Phys. Rev. A 84 032120 (2011)]
and thereby reveals generic features of the considered distance measures with
respect to the capability of detecting initial system-environment correlations.
