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Feb 4, 2002 · Quantum Logic and Probability Theory. First published Mon Feb 4, 2002; substantive revision Tue Aug 10, 2021. Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic.
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Quantum Logic and Quantum Probability. Chapter. pp 339–347. Cite this chapter. Download book PDF. Enrico G. Beltrametti. 290 Accesses. 1 Citations. Abstract. By events, or yes-no experiments, pertaining to some physical system we understand the physical quantities, or observables, that admit only two outcomes.
- Enrico G. Beltrametti
- 2004
QP theory refers to the rules for assigning probabilities to events from quantum mechanics, without the physics. QP theory is potentially applicable to any area where there is a need to compute probabilities.
- Jennifer S. Trueblood, Emmanuel M. Pothos, Jerome R. Busemeyer
- 2014
Notes to Quantum Logic and Probability Theory. 1. A few qualifications are in order already: In a more general formulation, one considers the lattice of projections of a von Neumann algebra. Only in the context of non-relativistic quantum mechanics, and then only absent superselection rules, is this algebra a type I factor.
This article is a concise introduction to quantum probability theory, quantum mechanics, and quan-tum computation for the mathematically prepared reader. Chapters 2 and 3 depend on Section 1 but not on each other, so the reader who is interested in quantum computation can go directly from Chap-ter 1 to Chapter 3.
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We are convinced that starting from simple, intuitive, general principles (“information loss” and “entanglement generation”) and then elucidating the mathematical structure inherent in quantum mechanics will lead to a better understanding of its deep message.
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Using the concept of "correlation" carefully analyzed in the context of classical probability and in quantum theory, the author provides a framework to compare these approaches. He also develops an extension of probability theory to construct a local hidden variable theory.
