Geometrical characterization of non-Markovianity

We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic N-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples.