Targeting pure quantum states by strong noncommutative dissipation

We propose a solution to the problem of realizing a predefined and arbitrary pure quantum state, based on thesimultaneous presence of coherent and dissipative dynamics, noncommuting on the target state and in the limitof strong dissipation. More precisely, we obtain a necessary and sufficient criterion whereby the nonequilibriumsteady state (NESS) of an open quantum system described by a Lindblad master equation approaches a targetpure state in the Zeno regime, i.e., for infinitely large dissipative coupling. We also provide an explicit formulafor the characteristic dissipative strength beyond which the purity of the NESS becomes effective, thus pavingthe way to an experimental implementation of our criterion. For an illustration, we deal with targeting a Bellstate, an arbitrary pure state ofNqubits, and a spin-helix state ofNqubits