Probability Measures and projections on Quantum Logics
Mathematical Physics
2020-08-27 v1 math.MP
Quantum Algebra
Quantum Physics
Abstract
The present paper is devoted to modelling of a probability measure of logical connectives on a quantum logic (QL), via a -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 -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 -map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra.
Cite
@article{arxiv.1809.10530,
title = {Probability Measures and projections on Quantum Logics},
author = {Oľga Nánásiová and Ľubica Valášková and Viera Čerňanová},
journal= {arXiv preprint arXiv:1809.10530},
year = {2020}
}