A construction of swap or switch polynomials

TL;DR

This paper explores methods to construct swap polynomials, which are matrix polynomials that act as the swap operator on tensor products, contributing to the understanding of tensor algebra and polynomial constructions.

Contribution

The paper introduces new constructions of swap polynomials, expanding the toolkit for tensor polynomial analysis and applications.

Findings

New explicit constructions of swap polynomials

Enhanced understanding of tensor polynomial properties

Potential applications in tensor algebra and quantum information

Abstract

We discuss several constructions of swap polynomials, that is 2--tensor valued matrix polynomials which are multiples of the swap or switch operator.