The classification of two-particle spin states and generalized Bell inequalities

Abstract

The structure of two-particle spin states is investigated. The special operator P is defined for this aim. The whole set of two-particle spin states is divided into three nonintersecting parts: P-factorizable, P-separable and P-entangled states. The correlation between these states and usual factorizable, separable and entangled states is found. The generalized Bell inequalities are constructed. Their right-hand sides depend on the norm of the operator P. The collection of states for which the Bell inequalities are satisfied is found. It is shown that this collection contains all factorizable and separable states and some entangled states.