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- At its core, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form “the value of physical quantity A lies in the range B ” is represented by a projection operator on a Hilbert space H.
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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.
- Quantum Theory and Mathematical Rigor
A brief explanation for this shift is provided below. See...
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- Quantum Theory and Mathematical Rigor
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.
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 ...
Jan 13, 2016 · The main point of such an approach lies in a correct definition of quantum probability that would be applicable for any type of measurements and events, operationally testable or inconclusive, elementary or composite, corresponding to commuting or non-commuting observables.
- Vyacheslav I. Yukalov, Didier Sornette
- 2016
Quantum Probability. Potentiality and Actuality. Final Remarks. References and Further Reading. 1. Logic and Physics. QL relates the two seemingly different disciplines of physics and logic. These disciplines have been intimately related since their origin.
ically relevant differences between abelian (classical) probability theory, nonabelian type I probability theory and non-type–I probability theory will be indicated in Section 7. 2 Algebras of Bounded Operators In this section we shall briefly describe the aspects of operator algebra theory which are most relevant to our topic.
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.
