Entangled States of Qutrit Bipartite System

TL;DR

This paper introduces a systematic method for constructing entangled states of bipartite qutrit systems using group theory, extending concepts from qubit systems and proposing a new fidelity measure related to Bell inequalities.

Contribution

It presents a novel group-theoretic approach to generate entangled states for higher-dimensional systems and introduces an $SU(2)$ fidelity concept applicable to Bell-CHSH inequalities.

Findings

Method can derive all entangled states for bipartite qutrits.

Proposes $SU(2)$ and $SU(3)$ fidelity measures.

Identifies inequalities specific to qutrit bipartite systems.

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.