Indirect control of the asymptotic states of a quantum dynamical semigroup

In the dynamics of open quantum systems, the interaction with the external environment usually leads to a contraction of the set of reachable states for the system as time increases, eventually shrinking to a single stationary point. In this contribution we describe to what extent it is possible to modify this asymptotic state by means of indirect control, that is by using an auxiliary system coupled to the target system in order to affect its dynamics, when there is a purely dissipative coupling between the two systems. We prove that, also in this restrictive case, it is possible to modify the asymptotic state of the relevant system, give necessary conditions for that and provide physical examples. Therefore, in indirect control schemes, the environmental action has not only a negative impact on the dynamics of a system, it is rather possible to make use of it for control purposes.