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AIP conference proceedings

A notion of positively correlated elements on orthoalgebra

Wasan Al-Shemmari, Ahmed Al-Adilee

Published Jan 1, 2023• 0 citations
Publisher

Abstract

This study is concerned with a definition of dependences on orthoalgebra. Such dependences have been illustrated via special maps that are defined on an orthoalgebra too. In fact, those dependences deals with a notion of non-compatibility which is one of the basic important issues in quantum logic studies. Several results have been presented to show various situations of each constructed dependence. Eventually, we have mentioned several notions related to the results that we have obtained and show some properties relevant to the proposed ideas.

DOI
10.1063/5.0121807

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This study is concerned with a definition of dependences on orthoalgebra. Such dependences have been illustrated via special maps that are defined on an orthoalgebra too. In fact, those dependences deals with a notion of non-compatibility which is one of the basic important issues in quantum logic studies. Several results have been presented to show various situations of each constructed dependence. Eventually, we have mentioned several notions related to the results that we have obtained and show some properties relevant to the proposed ideas.
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This paper deals with the topics of modeling joint distributions on a generalized probability space. An algebraic structure known as quantum logic is taken as the basic model. There is a brief summary of some earlier published findings concerning a function s-map, which is a mathematical tool suitable for constructing virtual joint probabilities of even non-compatible propositions. The paper completes conclusions published in 2020 and extends the results for three or more random variables if the marginal distributions are known. The existence of a (n+1)-variate joint distribution is shown in special cases when the quantum logic consists of at most n blocks of Boolean algebras.