A Relation Between the Chrestenson Operator, Weyl Operator Basis, and Kronecker-Pauli Operator Basis

TL;DR

This paper explores the mathematical relationships between the Chrestenson operator, Weyl operator basis, and Kronecker-Pauli operator basis in prime-dimensional quantum systems, revealing new algebraic connections and illustrating them with specific cases.

Contribution

It establishes a novel algebraic relation linking these three operator bases in prime-dimensional Hilbert spaces, expanding understanding of their interconnections.

Findings

New algebraic relation connecting the operators

Illustrative examples for dimensions 3 and 5

Enhanced understanding of operator bases in quantum theory

Abstract

Within the framework of quantum theory, we review the Chrestenson operator, the Weyl operator basis, and the Kronecker-Pauli operator basis in $d$-dimensional Hilbert spaces using Dirac notation, where $d$ is a prime integer strictly greater than 2. We establish a new algebraic relation connecting these operators and present the cases $d=3$ and $d=5$ as illustrative examples.