Stabilization of stochastic quantum dynamics via open and closed loop control.

In this paper we investigate parametrization free solutions of the problem of quantum pure state preparation and subspace stabilization by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. In particular, we show that whenever suitable dissipative effects are induced either by the unmonitored environment, or by non Hermitian measurements, there is no need for feedback, as open-loop time-invariant control is sufficient to achieve stabilization of the target set in probability. Constructive necessary and sufficient conditions on the form of the control Hamiltonian can be provided in this case. When time-invariant control is not sufficient, state stabilization in expectation can be attained by the addition of filteringbased feedback control.