  We investigate the ability of correlation measures to witness non-Markovian
open quantum system dynamics. It is shown that the mutual information and any
entanglement measure between the system and an ancilla do not witness all
non-Markovian dynamics. A correlation measure is introduced, and it is proven
that, in an enlarged setting with two ancillary systems, this measure detects
almost all non-Markovian dynamics, except possibly a zero-measure set of
dynamics that is non-bijective in finite time-intervals. Our proof is
constructive and provides different initial states detecting the non-Markovian
evolutions. These states are all separable and some are arbitrarily close to a
product state.
