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1. plato.stanford.edu › entries › qt-quantlogQuantum Logic and Probability Theory (Stanford Encyclopedia ...

   plato.stanford.edu › entries › qt-quantlog

   Feb 4, 2002 · 1. Quantum Mechanics as a Probability Calculus. 1.1 Quantum Probability in a Nutshell. 1.2 The “Logic” of Projections. 1.3 Probability Measures and Gleason’s Theorem. 1.4 The Reconstruction of QM. 2. Interpretations of Quantum Logic. 2.1 Realist Quantum Logic. 2.2 Operational Quantum Logic. 3. Generalized Probability Theory.

   • Quantum Theory and Mathematical Rigor

     A brief explanation for this shift is provided below. See...

   • The Basic Theory of Ordering Relations

     Supplement to Quantum Logic and Probability Theory. The...

   • Bell's Theorem

     Bell’s Theorem is the collective name for a family of...

2. plato.stanford.edu › entries › qt-quantlogQuantum Logic and Probability Theory > Notes (Stanford ...

   plato.stanford.edu › entries › qt-quantlog

   Throughout this paper, I use the term “logic” rather narrowly to refer to the algebraic and order-theoretic aspect of propositional logic. There exists a substantial technical literature devoted to non-classical formal deductive systems that are intended to stand to quantum propositional logics rather as classical deductive systems stand to ...

3. People also ask

   What is quantum probability?

   • The other notion we introduce with an eye to quantum probability is that of a state, defined as a family of overlapping probability measures over the outcomes of all possible experiments, i.e., a mapping p from the response functions to the reals, such that:

   26 Quantum Probability: An Introduction - Oxford Academic

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   What is quantum logic?

   • The standard semantics of quantum logic is that quantum logic is the logic of projection operators in a separable Hilbert or pre-Hilbert space, where an observable p is associated with the set of quantum states for which p (when measured) has eigenvalue 1. From there,

   Quantum logic - Wikipedia

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   Is quantum mechanics a generalization of classical probability?

   • It is uncontroversial (though remarkable) that the formal apparatus of quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over by the “quantum logic” of projection operators on a Hilbert space. [ 1]

   Quantum Logic and Probability Theory - Stanford Encyclopedia of Philosophy

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   Can quantum logic generalize the event spaces of classical probability?

   • Research in quantum logic opened yet further routes into generalized probability by providing various generalizations of Boolean algebras (orthomodular lattices, orthomodular posets, partial Boolean algebras, orthoalgebras, effect algebras etc.), thus generalizing the event spaces of classical probability.

   26 Quantum Probability: An Introduction - Oxford Academic

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4. en.wikipedia.org › wiki › Quantum_logicQuantum logic - Wikipedia

   en.wikipedia.org › wiki › Quantum_logic

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   In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manip­ulation of propositions inspired by the structure of quantum theory.

5. link.springer.com › chapter › 10Quantum Logic and Quantum Probability | SpringerLink

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   Quantum Logic and Quantum Probability. Chapter. pp 339–347. Cite this chapter. Download book PDF. Enrico G. Beltrametti. 289 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.

   • Author: Enrico G. Beltrametti

   • Publish Year: 2004

6. www.jstor.org › stable › 30227147Quantum Logic and Generalized Probability Theory - JSTOR

   www.jstor.org › stable › 30227147

   DEFINITION: A state function of LQ is a map P: X each observable X a probability distribution Px on. real valued Borel function u and any observable. To describe the state function in terms of the. LQ we define. DEFINITION: A quasimeasure m on LQ is a function q E L, such that. (1) m is real valued and 0 < m(q) ~ 1.

7. academic.oup.com › edited-volume › 43657Quantum Probability: An Introduction | The Oxford Handbook of ...

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   The topic of probability in quantum mechanics is rather vast. In this chapter it is discussed from the perspective of whether and in what sense quantum mechanics requires a generalization of the usual (Kolmogorovian) concept of probability.

8. arxiv.org › pdf › quant-phQuantum Probability Theory - arXiv.org

   arxiv.org › pdf › quant-ph

   The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in the early thirties, as well. To precisely this end, von Neumann initiated the study of