Role of quantum divergences in non-Markovian dynamics

An interesting approach for the description of memory effects in the reduced quantum dynamics of an open system is based on the notion of information exchange between the open system and its environment. This exchange has typically been quantified studying the variation in time of the trace distance between distinct initial system states. We point to the fact that such an information exchange can actually be described by a large class of quantum divergences, including not only distances, but also entropic quantifiers. We consider in particular regularized versions of quantum relative entropy. We derive general upper bounds on the revivals of quantum divergences conditioned and determined by the formation of correlations and changes in the environment.