Generalized coherent states as preferred states of open quantum systems

We investigate the connection between quasi-classical (pointer) states and generalized coherent states ({GCSs}) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the {GCS} set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras, stringent symmetry constraints must be obeyed for the {GCS} set to be preferred. The relationship between {GCSs}, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.