Role of non-Markovianity and backflow of information in the speed of quantum evolution

We consider a two-level open quantum system undergoing pure dephasing, dissipative, or multiply decohering dynamics and show that whenever the dynamics is non-Markovian, the initial speed of evolution is a monotonic function of the relevant physical parameter driving the transition between the Markovian and non-Markovian behavior of the dynamics. In particular, within the considered models, a speed increase can only be observed in the presence of backflow of information from the environment to the system.