An Inequality for Entangled Qutrits in SU(3) basis

It is well-known from the representation theory of particle physics that the tensor product of two fundamental representation of SU(2) and SU(3) group can be decomposed to obtain the desired spectrum of the physical states. In this paper, we apply this tenet in case of two {\it non-local} qubits and qutrits, which leads the complete spectrum of their entangled states in their respective basis. For qutrit system, the study of their properties reveals the existence of a new $\sqrt{2}$ inequality, in addition to usual Bell-CHSH type $2\sqrt{2}$ inequality, which is significant from the experimental point of view.