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

H. M. Wiseman·John A. Vaccaro
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Abstract

An open quantum system in steady state $\hatρ_{ss}$ can be represented by a weighted ensemble of pure states $\hatρ_{ss}=\sum_{k}\wp_{k}\ket{ψ_k} \bra{ψ_k}$ 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 $\ket{ψ(t)}$, stochastically evolving such that the proportion of time for which $\ket{ψ(t)} = \ket{ψ_{k}}$ 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.

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H. M. Wiseman, John A. Vaccaro. 2001-12-20. Inequivalence of pure state ensembles for open quantum systems: the preferred ensembles are those that are physically realizable. https://doi.org/10.1103/physrevlett.87.240402

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