Violation Of Quantum Bilocal Inequality

Quantum nonlocality is one of fundamental topics of quantum theory.In recent years,multipartite non-locality research has become a hot topic in the field of quantum physics re-search.Does entanglement lead to the violation of bilocal inequalities?It has been proved that the tensor product of two entangled pure states can violate the bilocal inequality.However,there is no answering the question for mixed Bell diagonal states.In the text,the entangle-ment of the Bell diagonal depend on three parameters.The previous bilocal inequality only contains two parameters.On the one hand,we will inprove the lower bound of the bilocal inequality,so that the new bound includes all three eigenvalues of the correlation matrix of a Bell diagonal states,and thus obtain a new bilocal inequality,This help us determine what entangled Bell diagonal states can violate the bilocal inequality.On the other hand,we try to find mixed Bell diagonal state(?,?)that can violate the bilocal inequality,Fistly,By choosing available joint measurements A_x,B_y,C_z,then calculate the value ofS(???,A_x,B_y,C_z)to determine whether it can violate the double local inequality.thus we find three classes of mixed Bell diagonal states that can violate the bilocal inequality.