  We study the spatio-temporal spreading of correlations in an ensemble of
spins due to dissipation characterized by short- and long-range spatial
profiles. We consider systems initially in an uncorrelated state, and find that
correlations widen and contract in a novel pattern intimately related to both
the dissipative nature of the dynamical channel and its spatial profile.
Additionally, we make a methodological contribution by generalizing
non-equilibrium spin-wave theory to the case of dissipative systems and derive
equations of motion for any translationally invariant spin chain whose dynamics
can be described by a combination of Hamiltonian interactions and dissipative
Lindblad channels. Our work aims at extending the study of correlation dynamics
to purely dissipative quantum simulators and compare them with the established
paradigm of correlations spreading in hamiltonian systems.
