GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

TL;DR

This paper explores the connection between quantum information, GHZ states, and the Yang--Baxter equation, introducing a generalized Bell matrix that forms a unitary braid representation and provides new solutions.

Contribution

It introduces a generalized Bell matrix based on almost-complex structures that generates GHZ states and solves the quantum Yang--Baxter equation with new algebraic insights.

Findings

Generalized Bell matrix generates all GHZ states from product bases.

The matrix forms a unitary braid representation.

Provides new solutions to the quantum Yang--Baxter equation.

Abstract

Recent study suggests that there are natural connections between quantum information theory and the Yang--Baxter equation. In this paper, in terms of the generalized almost-complex structure and with the help of its algebra, we define the generalized Bell matrix to yield all the GHZ states from the product base, prove it to form a unitary braid representation and present a new type of solution of the quantum Yang--Baxter equation. We also study Yang-Baxterization, Hamiltonian, projectors, diagonalization, noncommutative geometry, quantum algebra and FRT dual algebra associated with this generalized Bell matrix.