Generalized Bell inequality and a method for its verification

We use the reduced density matrix of the two-particle spin state to construct a generalized Bell-Clauser-Horne-Shimony-Holt inequality. For each specific state and under a special choice of the vectors , this inequality becomes an exact equality. We show how such vectors can be found using the reduced density matrix. Both sides of this equality have a specific numerical value. We indicate the connection of this number with the measure of entanglement of the two-particle spin state. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 488–501, September, 2007.