YANG–BAXTER EQUATION, MAJORANA FERMIONS AND THREE BODY ENTANGLING STATES

Abstract

In this paper, we review some results obtained in our works with extension. The new type of braiding matrices called type-II has been extended to the solutions of Yang–Baxter equations (YBE). It is related to quantum entangling states. The four-dimensional realization is connected with Majorana fermions and the two-dimensional realization for the topological basis is the wigner DJ-function with J = 1/2. The YBE leads to the conclusion that the additivity rule of velocities for two anyons obeys Lorentz rather than Galilean. The discussion is extended to three body S-matrix formed by three two-body S-matrices. The three-qubit entanglement based on two-qubit entanglements is discussed.