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Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem

Busch, Paul (2003) Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem. Physical Review Letters, 91 (12/120). pp. 1-4. ISSN 1079-7114

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A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple proof of the result, analogous to Gleason’s theorem, that any quantum state is given by a density operator. As a corollary we obtain a von Neumann–type argument against noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 23 Feb 2009 15:31
Last Modified: 27 Apr 2010 09:36
Published Version: http://dx.doi.org/10.1103/PhysRevLett.91.120403
Status: Published
Publisher: The American Physical Society.
Identification Number: 10.1103/PhysRevLett.91.120403
URI: http://eprints.whiterose.ac.uk/id/eprint/7250

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