Algebras of measurements: The logical structure of quantum mechanics

Daniel Lehmann; Kurt Engesser; Dov M. Gabbay

doi:10.1007/s10773-006-9062-y

Algebras of measurements: The logical structure of quantum mechanics

Daniel Lehmann, Kurt Engesser, Dov M. Gabbay

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.

Original language	English
Pages (from-to)	715-741
Number of pages	27
Journal	International Journal of Theoretical Physics
Volume	45
Issue number	4
DOIs	https://doi.org/10.1007/s10773-006-9062-y
State	Published - Apr 2006
Externally published	Yes

Bibliographical note

Funding Information:
This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence, by the Israel Science Foundation grant 183/03 on “Quantum and other cumulative logics” and by EPSRC Visiting Fellowship GR/T 24562 on “Quantum Logic.”

Keywords

Measurement algebras
Quantum logic
Quantum measurements

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10.1007/s10773-006-9062-y

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Algebras of measurements: The logical structure of quantum mechanics

Abstract

Bibliographical note

Keywords

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