All Pure Two-Qudit Entangled States Generated via a Universal Yang-Baxter Matrix Assisted by Local Unitary Transformations

José Manuel Méndez Martínez

Jing‐Ling Chen, Kang Xue, Mo‐Lin Ge

We show that all pure entangled states of two d-dimensional quantum systems (i.e., two qudits) can be generated from an initial separable state via a universal Yang–Baxter matrix if one is assisted by local unitary transformations.

Andrzej Veitia

Chunfang Sun, Gangcheng Wang, Kang Xue

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution $\breve{R}(θ,φ_{1},φ_{2})$ of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $\breve{R}$-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $\breve{R}$-matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.

G. Najarbashi, S. Mirzaei

Louis H Kauffman, Samuel J Lomonaco

This paper explores the role of unitary braiding operators in quantum computing. We show that a single specific solution R (the Bell basis change matrix) of the Yang–Baxter equation is a universal gate for quantum computing, in the presence of local unitary transformations. We show that this same R generates a new non-trivial invariant of braids, knots and links. Other solutions of the Yang–Baxter equation are also shown to be universal for quantum computation. The paper discusses these results in the context of comparing quantum and topological points of view. In particular, we discuss quantum computation of link invariants, the relationship between quantum entanglement and topological entanglement, and the structure of braiding in a topological quantum field theory.