Inequivalence of Pure State Ensembles for Open Quantum Systems: The Preferred Ensembles Are Those That Are Physically Realizable

An open quantum system in steady state ρ̂_ss can be represented by a weighted ensemble of pure states ρ̂_ss = Σk℘_k|ψ_k〉〈ψ_k| in infinitely many ways. A physically realizable (PR) ensemble is one for which some continuous measurement of the environment will collapse the system into a pure state |ψ(t)〉, stochastically evolving such that the proportion of time for which |ψ(t)〉 = |ψ_k〉 equals ℘_k. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact. We present the necessary and sufficient conditions for a given ensemble to be PR, and illustrate the method by showing that the coherent state ensemble is not PR for an atom laser.