Daniel Lehmann
ABSTRACT
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way. The mystery presented by the algebraic equations satisfied by (non-commuting) observables that cannot be observed in the same states is elucidated.
- Garret Birkhoff and John von Neumann. The logic of quantum mechanics. Annals of Mathematics, 37:823--843, 1936.Google Scholar
Cross Ref
- Maria Luisa Dalla Chiara. Quantum logic. In D. M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 6, pages 129--228. Kluwer, Dordrecht, 2nd edition edition, 2001.Google Scholar
- Daniel Lehmann. A presentation of quantum logic based on an "and then" connective. Journal of Logic and Computation, 18(1):59--76, February 2008. DOI: 10.1093/logcom/exm054. Google ScholarCross Ref
- Daniel Lehmann. Quantic superpositions and the geometry of complex Hilbert spaces. International Journal of Theoretical Physics, 47(5):1333--1353, May 2008. DOI:10.1007/s10773-007-9576-y.Google ScholarCross Ref
- Daniel Lehmann. Similarity-projection structures: the logical geometry of quantum physics. International Journal of Theoretical Physics, 48(1):261--281, 2009. DOI: 10.1007/s10773-008-9801-3.Google ScholarCross Ref
- Gleason A. M. Measures on the closed subspaces of a hilbert space. Journal of Mathematics and Mechanics, 6:885--893, 1957.Google Scholar
- Asher Peres. Quantum Theory: Concepts and Methods. Kluwer, Dordrecht, The Netherlands, 1995.Google Scholar
- Itamar Pitowsky. Quantum mechanics as a theory of probability. In W. Demopoulos and I. Pitowsky, editors, Festschrift in Honor of Jeffrey Bub. forthcoming.Google Scholar
Index Terms
- Foundations of non-commutative probability theory
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