Open AccessConditional Probability and A Posteriori States in Quantum Mechanics
Author(s) -
Masanao Ozawa
Publication year - 1985
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195179625
Subject(s) - mathematics , conditional probability , observable , a priori and a posteriori , quantum probability , probability amplitude , law of total probability , probability theory , quantum statistical mechanics , statistical mechanics , statistical physics , interpretations of quantum mechanics , calculus (dental) , quantum , quantum mechanics , quantum operation , quantum process , quantum dynamics , physics , statistics , posterior probability , medicine , bayesian probability , philosophy , epistemology , dentistry
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 Davies-Lewis 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.
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