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International Journal of Innovative Research in Computer and Communication Engineering

n-Dimensional Copulas on Quantum Logic

Ahmed Al-Adilee, Ammar Jalil Almosawi

Published Apr 16, 2016• 1 citation
OpenAlex

Abstract

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.

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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.
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].
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers. More specifically, we look for a way to feed a quantum computer with algebraic equations of n-th order underlying an infinite dimensional Hilbert space description of quantum systems. A number of new results on states defined on Hilbert lattices are presented and discussed and a number of recently obtained results in the field of Hilbert space equations are reviewed.