  We study ensembles of phase-covariant channels. We show that such ensembles
arise naturally from familiar spin-chain models (e.g., XXZ) with a special
class of initial states, and that the disorder-averaged map of disordered spin
chains is phase-covariant under a weak symmetry constraint on the distribution.
We use those examples to motivate a broader class of phase-covariant ensembles,
which include both unital and non-unital channels. We demonstrate the physical
properties captured by the late-time limit of the average map over the
ensemble.
