Journal of Mathematical Physics

Measurements, Hilbert space and quantum logics

Stanley Gudder, Gottfried T. Rüttimann, Richard J. Greechie

Published Dec 1, 1982• 13 citations

Abstract

We consider single and multiple measurements on a quantum logic (P,S) as well as states and propositions conditioned by a measurement. We show that corresponding to any measurement A, there is a canonically associated Hilbert space HA. Algebraic and statistical properties of (P,S) that are preserved in HA are found. We then study the problem of embedding a quantum logic in Hilbert space.

DOI: 10.1063/1.525331

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