Quantum Algebras Associated With Bell States

TL;DR

This paper explores the quantum algebra derived from the Bell matrix, a solution to the braided Yang-Baxter equation, revealing its structure and representations relevant to quantum information processing.

Contribution

It introduces the quantum algebra associated with the Bell matrix using FRT construction and analyzes its four-dimensional representations.

Findings

Identifies algebraic structures like composition series and direct sums.

Provides a FRT-based quantum algebra formulation of the Bell matrix.

Analyzes the algebra's representations in quantum information context.

Abstract

The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.