  Non-Markovian effects in an open-system dynamics are usually associated to
information backflows from the environment to the system. However, the way
these backflows manifest and how to detect them is unclear. A natural approach
is to study the backflow in terms of the correlations the evolving system
displays with another unperturbed system during the dynamics. In this work, we
study the power of this approach to witness non-Markovian dynamics using
different correlation measures. We identify simple dynamics where the failure
of completely-positive divisibility is in one-to-one correspondence with a
correlation backflow. We then focus on specific correlation measures, such as
those based on entanglement and the mutual information, and identify their
strengths and limitations. We conclude with a study of a recently introduced
correlation measures based on state distinguishability and see how, for these
measures, adding an extra auxiliary system enlarges the set of detectable
non-Markovian dynamics.
