  A measure of quantum non-Markovianity for an open system dynamics, based on
revivals of the distinguishability between system states, has been introduced
in the literature using the trace distance as quantifier for
distinguishability. Recently it has been suggested to use as measure for the
distinguishability of quantum states the trace norm of Helstrom matrices, given
by weighted differences of statistical operators. Here we show that this new
approach, which generalizes the original one, is consistent with the
interpretation of information flow between the system and its environment
associated to the original definition. To this aim we prove a bound on the
growth of the external information, that is information which cannot be
accessed by performing measurements on the system only, as quantified by means
of the Helstrom matrix. We further demonstrate by means of example that it is
of relevance in generalizing schemes for the local detection of initial
correlations based on the increase of internal information. Finally we exploit
this viewpoint to show the optimality of a previously introduced strategy for
the local detection of quantum correlations.
