David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Studies in History and Philosophy of Science Part B 35 (2):177-194 (2004)
Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.
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References found in this work BETA
J. S. Bell (2004). On the Problem of Hidden Variables in Quantum Mechanics. In Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press 1--13.
Simon Kochen & E. P. Specker (1967). The Problem of Hidden Variables in Quantum Mechanics. Journal of Mathematics and Mechanics 17:59--87.
Itamar Pitowsky (2003). Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability. Studies in History and Philosophy of Science Part B 34 (3):395-414.
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