On validity of the original Bell inequality for the Werner nonseparable state

Abstract

In quant-ph/0406139, we have introduced in a very general setting the new class of quantum states, density source-operator states, satisfying any classical CHSH-form inequality, and shown that any separable state belongs to this class. In the present paper, we prove that the Werner nonseparable state also belongs to the class of density source-operator states. Moreover, for any dimension d>2, the Werner state is in such a subclass of this class where each density source-operator state satisfies also the perfect correlation form of the original Bell inequality regardless of whether or not the Bell perfect correlation restriction is fulfilled. The latter earlier unknown property of the Werner state can be verified experimentally.