Equivalence between non-Markovian dynamics and correlation backflows.

The information encoded into an open quantum system that evolves under a Markovian dynamics is always monotonically decreasing. Nonetheless, given a quantifier for the information contained in the system, in general it is not clear if for any 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 introduce a class of correlation measures and we prove that there exists at least one element from this class that provides a correlation backflow if and only if the dynamics is non-Markovian. 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.