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Quantum Simulation Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations Quantum Entropy Information Measures

Probability Measures and projections on Quantum Logics

arXiv
Authors: Oľga Nánásiová, Ľubica Valášková, Viera Čerňanová

Year

2018

Paper ID

7347

Status

Preprint

Abstract Read

~2 min

Abstract Words

113

Citations

N/A

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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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1809.10530 [2] arXiv https://arxiv.org/abs/1809.10530 [3] Publisher https://arxiv.org/abs/1809.10530

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