Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Copula Function and Quantum Logic

Ahmed Al-Adilee, Theor Phys

Published Dec 18, 2014• 0 citations
OpenAlex

Abstract

A partially ordered relation (.,≤) is useful to define functions of observables either observables are compatible or non-compatible. In our case, we use an OML (L,≤) as a partially ordered relation instead of Boolean algebra because of the property of non-compatibility of random events, which is invalid under Boolean algebra. We introduce models of special functions such that, OML-Copula, and OML-Co-Copula.

Related papers

Qausi-Copulas on Orthomodular Lattice

Ahmed Al-Adilee, Adel Hashem Nouri

Abstract One of the possible mathematical systems to represent non-compatible random events is a quantum logic. In this paper, we propose and illustrate function called quasi-copula on an orthomodular lattice (briefly QO-copula). Also, we compare such function to its classical definition. Finally, we present several relations and calculations that involve QO-copula and its relationship to a function known by s-map, which has firstly been presented by [4].

Journal of Physics Conference Series•Mar 1, 2021•0 citations

n-Dimensional Copulas on Quantum Logic

Ahmed Al-Adilee, Ammar Jalil Almosawi

In this paper, we study a new type of sub-copulas, which is defined on quantum logic. We review the most common definitions, relations and properties of such functions. We extend the definition of what is recently called 2-dimensional QL-copula to n-dimensional QL-copula with respect to order difference instead of the summation approach, see [5]. We compose this paper to present an alternative interpretation of QL-copula rather thanthe one that we have already defined by AlAdilee and Nanasiova (2009) using an approach depends on definingsub-copulason quantum logic.

International Journal of Innovative Research in Computer and Communication Engineering•Apr 16, 2016•1 citation

On joint distribution in quantum logics. I. Compatible observables

Anatolij Dvurečenskij

The notion of a joint distribution in $\sigma$-finite measures of observables of a quantum logic defined on some system of $\sigma$-independent Boolean sub-$\sigma$-algebras of a Boolean $\sigma$-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.

Applications of Mathematics•Jan 1, 1987•2 citations

A Generalization of the bounds of copulas on quantum logic

Ahmed Al-Adilee, Sami Kadhem Kareem Althabhaw

Our paper is concerned with a generalization of the boundaries of copula that are well-known by Frechet-Hoeffding conditions [4], and study copula boundaries as functions defined on quantum logic ., While there are many properties that have been presented according to our proposed generalization throughout these modified functions and show that some important propositions that have different forms to those of classical copulas. Indeed, it has been shown two main results relevant to the lower and upper boundaries of what we have defined and named by quantum logic copulas, see [1].

International Journal of Engineering & Technology•Dec 9, 2018•1 citation

Three-dimensional distributions on Quantum logics and MV algebras

Martin Kalina

It means that if we put two conditions on the event A, the resulting conditional probability is independent of the order of conditions. We show that this is not true in quantum logics (OML) and in MV-algebras. The conditional measure (probability) in OML can be defined by using the so-called s-map. Let L be an OML. The map pn : L n → [0, 1] will be called an sn-map if the following conditions hold: (s1) pn(1, ..., 1) = 1; (s2) if there exist i, j, such that ai ⊥ aj, then pn(a1, ..., an) = 0; (s3) if ai ⊥ bi for some i = 1, ..., n, then pn(a1, ..., ai ∨ bi, ..., an) = pn(a1, ..., ai, ..., an) + pn(a1, ..., bi, ..., an).

•Jan 1, 2004•0 citations

Problem of Existence of Joint Distribution on Quantum Logic

Oľga Nánásiová, Karla Čipková, Michal Zákopčan

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.

Entropy•Dec 21, 2024•0 citations
A partially ordered relation (.,≤) is useful to define functions of observables either observables are compatible or non-compatible. In our case, we use an OML (L,≤) as a partially ordered relation instead of Boolean algebra because of the property of non-compatibility of random events, which is invalid under Boolean algebra. We introduce models of special functions such that, OML-Copula, and OML-Co-Copula.
In this paper, we study a new type of sub-copulas, which is defined on quantum logic. We review the most common definitions, relations and properties of such functions. We extend the definition of what is recently called 2-dimensional QL-copula to n-dimensional QL-copula with respect to order difference instead of the summation approach, see [5]. We compose this paper to present an alternative interpretation of QL-copula rather thanthe one that we have already defined by AlAdilee and Nanasiova (2009) using an approach depends on definingsub-copulason quantum logic.
The notion of a joint distribution in σ\sigmaσ-finite measures of observables of a quantum logic defined on some system of σ\sigmaσ-independent Boolean sub-σ\sigmaσ-algebras of a Boolean σ\sigmaσ-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
Our paper is concerned with a generalization of the boundaries of copula that are well-known by Frechet-Hoeffding conditions [4], and study copula boundaries as functions defined on quantum logic ., While there are many properties that have been presented according to our proposed generalization throughout these modified functions and show that some important propositions that have different forms to those of classical copulas. Indeed, it has been shown two main results relevant to the lower and upper boundaries of what we have defined and named by quantum logic copulas, see [1].
It means that if we put two conditions on the event A, the resulting conditional probability is independent of the order of conditions. We show that this is not true in quantum logics (OML) and in MV-algebras. The conditional measure (probability) in OML can be defined by using the so-called s-map. Let L be an OML. The map pn : L n → [0, 1] will be called an sn-map if the following conditions hold: (s1) pn(1, ..., 1) = 1; (s2) if there exist i, j, such that ai ⊥ aj, then pn(a1, ..., an) = 0; (s3) if ai ⊥ bi for some i = 1, ..., n, then pn(a1, ..., ai ∨ bi, ..., an) = pn(a1, ..., ai, ..., an) + pn(a1, ..., bi, ..., an).
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.