Markovianity criteria for quantum evolution

Abstract

We characterize a class of Markovian dynamics using the concept of a divisible dynamical map. Moreover, we provide a family of criteria which can distinguish Markovian and non-Markovian dynamics. These Markovianity criteria are based on a simple observation that Markovian dynamics implies monotonic behaviour of several well-known quantities such as distinguishability of states, fidelity, relative entropy and genuine entanglement measures.