  We demonstrate a new approach to the generation of custom entangled many-body
states through reservoir engineering, using the symmetry properties of bosonic
lattice systems coupled to a local squeezed reservoir. We outline an algorithm
where, beginning with a desired set of squeezing correlations, one uses the
symmetry to constrain the Hamiltonian and find a lattice configuration which
stabilizes a pure steady state realizing these correlations. We demonstrate how
to use this process to stabilize two unique pure states with non-local
correlations that could be useful for quantum information applications. First,
we show how drive a square lattice into a product state of entangled
quadruplets of sites. Second, using a bisected system, we generate a steady
state where local measurements in one half of the lattice herald a pure
delocalized state in the second half.
