Inequivalence of pure state ensembles for open quantum systems: the preferred ensembles are those that are physically realizable

Abstract

An open quantum system in steady state ${\hat{\rho }}_{ss}$ can be represented by a weighted ensemble of pure states ${\hat{\rho }}_{ss}={\sum }_k{\wp }_k|{\psi }_k⟩⟨{\psi }_k|$ 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 $|\psi (t)⟩$, stochastically evolving such that the proportion of time for which $|\psi (t)⟩=|{\psi }_k⟩$ equals ${\wp }_k$. Some, but not all, ensembles are PR. This constitutes the preferred ensemble fact, with the PR ensembles being the preferred ensembles. 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.

5 pages, no figures

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