We provide a solution to the problem of determining whether a target pure
state can be asymptotically prepared using dissipative Markovian dynamics under
fixed locality constraints. Beside recovering existing results for a large
class of physically relevant entangled states, our approach has the advantage
of providing an explicit stabilization test solely based on the input state and
constraints of the problem. Connections with the formalism of frustration-free
parent Hamiltonians are discussed, as well as control implementations in terms
of a switching output-feedback law.Comment: 11 pages, no figure
