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arXiv · 1809.10530

Probability Measures and projections on Quantum Logics

Oľga Nánásiová·Ľubica Valášková·Viera Čerňanová
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Abstract

The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a $G$-map, which is a special map on it. We follow the work in which the probability of logical conjunction, disjunction and symmetric difference and their negations for non-compatible propositions are studied. We study such a $ G $-map on quantum logics, which is a probability measure of a projection and show, that unlike classical (Boolean) logic, probability measure of projections on a quantum logic are not necessarilly pure projections. We compare properties of a $G$-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.

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Oľga Nánásiová, Ľubica Valášková, Viera Čerňanová. 2018-09-27. Probability Measures and projections on Quantum Logics. https://doi.org/10.1007/978-3-030-18058-4_25

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