A study on Heisenberg-Weyl linear maps

TL;DR

This paper explores the properties of Heisenberg-Weyl operators, generalizing Pauli operators to higher dimensions, and investigates positive maps and algebraic structures arising from these operators.

Contribution

It introduces a framework for analyzing Heisenberg-Weyl operators and their positive maps, extending the understanding of Pauli-type maps in higher-dimensional operator algebras.

Findings

Heisenberg-Weyl operators generalize Pauli operators to higher dimensions.

Positive maps from Heisenberg-Weyl operators exhibit specific algebraic and spectral properties.

The study broadens the theoretical foundation for higher-dimensional quantum operator analysis.

Abstract

Heisenberg-Weyl operators provide a Hermitian generalization of Pauli operators in higher dimensions. Positive maps arising from Heisenberg-Weyl operators have been studied along with several algebraic and spectral properties of Heisenberg-Weyl observables. This allows to generalize the study of Pauli type maps in higher dimesional algebra of operators.