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Conditional probability and a posteriori states in quantum mechanics. (English) Zbl 0576.60005
Summary: In order to develop a statistical theory of quantum measurements including continuous observables, a concept of a posteriori states is introduced, which generalizes the notion of regular conditional probability distributions in classical probability theory. Its statistical interpretation in measuring processes is discussed and its existence is proved. As an application, we also give a complete proof of the E. B. Davies and J. T. Lewis [Commun. Math. Phys. 17, 239-260 (1970; Zbl 0194.583)] conjecture that there are no (weakly) repeatable instruments for non-discrete observables in the standard formulation of quantum mechanics, using the notion of a posteriori states.

MSC:
60A99Foundations of probability theory
81P20Stochastic mechanics (including stochastic electrodynamics)