Entangled States of Qutrit Bipartite System

Abstract

We develop a systematic method to construct the Bell states of a qubit bipartite system while taking $SU(2)$ group as the basis group. An alternative formulation of fidelity, called $SU(2)$ fidelity, is proposed which gives the Bell-CHSH inequality. Taking analogy from the octet theory governed by the $SU(3)$ group, it is shown that the method can be easily generalized to derive all possible entangled states and the $SU(3)$ fidelity of the higher dimensional bipartite qutrit system. The properties of these states are studied which reveal the existence of some inequalities for the qutrit bipartite system.

This paper is withdrawn for further revision