On the relationship between non-Markovianity and entanglement protection

We test the conjecture that non-Markovian dynamics may help to protect quantum entanglement. To this end, we address an open system whose environment behaves either as a quantal system or as an effective reservoir, depending on the regime chosen to rule the system-environment dynamics. This allows us to study entanglement dynamics within Markovian and non-Markovian regimes. We focus on the recently introduced definition of quantum non-Markovianity that is based on the trace distance between pairs of initial states. The corresponding quantum measure N(φ) for assessing the non-Markovianity of a quantum map φ is submitted to test. We report cases for which N(φ) signals non-Markovianity, even though φ belongs to a purely dissipative regime. We argue that N(φ) is not generally applicable to assess the non-Markovianity of a quantum process, because information is not always encoded in a way that depends on the distinguishability between states. When entanglement is used as the carrier of information, non-Markovianity should be diagnosed in terms of an entanglement measure.We thus compare the dynamics of Wooters concurrence and of trace distance between states, showing that they may behave qualitatively alike but leading to conflicting diagnosis about the backflow of information from the environment to the system. In contrast to other studies, in our case entanglement is transferred only to potential carriers of information, thereby excluding paradoxical situations that involve entangled reservoirs.