Abstract
We present a new S-matrix, a solution of the braid relation and obtain a unitary solution of the Yang-Baxter equation (YBE) via Yang-Baxterization acting on the solution. We show that arbitrary two-qubit entangled states can be achieved by relating the unitary matrix to entanglement. An oscillator Hamiltonian can be constructed from the matrix. The Berry phase of the Yang-Baxter system is investigated.