  We consider a bipartite open quantum system constituted by two interacting
qubits $A$ and $B$, assuming that the former is coupled to the environment and
is directly affected by coherent control, while the latter does not interact
directly with the environment and the control fields. We are interested in the
controllability properties of the subsystem $B$.
  In this paper, we give a first analysis of the problem and provide some
negative answers.
