  Standard quantum state preparation methods work by preparing a required state
locally and then distributing it to a distant location by a free-space
propagation. We instead study procedures of preparing a target state at a
remote location in the presence of an interacting background medium on which no
control is required, manipulating only local dissipation. In mathematical
terms, we characterize a set of reduced steady states stabilizable by local
dissipation. An explicit local method is proposed by which one can construct a
wanted one-site reduced steady state at an arbitrary remote site in a lattice
of any size and geometry. In the chain geometry we also prove uniqueness of
such a steady state. We demonstrate that the convergence time to fixed
precision is smaller than the inverse gap, and we study robustness of the
scheme in different medium interactions.
