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Zbl 0576.60005
Ozawa, Masanao
Conditional probability and a posteriori states in quantum mechanics. (English)
[J] Publ. Res. Inst. Math. Sci. 21, 279-295 (1985). ISSN 0034-5318; ISSN 1663-4926/e

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 {\it E. B. Davies} and {\it 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 2000:: *60A99 Foundations of probability theory
81P20 Stochastic mechanics (including stochastic electrodynamics)

Keywords: statistical theory of quantum measurements; quantum mechanics

Citations: Zbl 0194.583

Cited in: Zbl 0645.60007

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