01218nas a2200121   4500008004100000245008200041210006900123520080800192100002201000700002301022700001501045856003601060       2013                        en  d00aStabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control0 aStabilization of Stochastic Quantum Dynamics via Open and Closed3 aIn 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 can be attained by the addition of filtering-based feedback control1 aAltafini, Claudio1 aTicozzi, Francesco1 aNishio, K.  uhttp://hdl.handle.net/1963/6503