In the quest of relations between non-Markovianity and quantum optimal control

Abstract

It is widely spread in the literature that non-Markovianity (NM) may be regarded as a resource in quantum mechanics. However, it is still unclear how and when this alleged resource may be exploited. Here, we study the relationship between NM and quantum optimal control in two paradigmatic non-Markovian systems, i.e. the spin star model and the Jaynes Cummings model. In both situations we find that the region of parameters in which both systems were originally more non-Markovian are compatible with the regions where the best control is achieved. Nevertheless, we show that non-Markovian effects are quite sensitive to the control field of the optimization, being able to increase or even decrease due to the latter. As a result, the degree of NM is actively manipulated by the field in order to improve the success of the protocol. Likewise, we finally show that where the system develops the largest degree of NM is at the same time where it becomes more controllable