  The information encoded into an open quantum system that evolves under a
Markovian dynamics is always monotonically non-increasing. Nonetheless, for a
given quantifier of the information contained in the system, it is in general
not clear if for all non-Markovian dynamics it is possible to observe a
non-monotonic evolution of this quantity, namely a backflow. We address this
problem by considering correlations of finite-dimensional bipartite systems.
For this purpose, we consider a class of correlation measures and prove that if
the dynamics is non-Markovian there exists at least one element from this class
that provides a correlation backflow. Moreover, we provide a set of initial
probe states that accomplish this witnessing task. This result provides the
first one-to-one relation between non-Markovian dynamics of finite-dimensional
quantum systems and correlation backflows.
