We reformulate the generalized Bell inequality for multipartite high-dimensional systems intro-
duced by one of the authors in order to compare it with the Collins-Gisin-Linden-Massar-Popescu
(CGLMP) inequality. Quantum theory violates these inequal...
We reformulate the generalized Bell inequality for multipartite high-dimensional systems intro-
duced by one of the authors in order to compare it with the Collins-Gisin-Linden-Massar-Popescu
(CGLMP) inequality. Quantum theory violates these inequalities that any local realistic theories
must obey. We show that maximal entanglement leads to maximal violation of our Bell inequality
whereas a non-maximally entangled state maximally violates the CGLMP inequality. In addition,
we analyze the probabilistic structures of the two types by representing them in terms of joint
probabilities and correlation weights. We show that both types have the equivalent probabilistic
structure with respect to the joint probabilities, but they have dierent correlation weights for the
measurement outcomes. We remark that the correlation weight plays a crucial role in determining
the violation conditions.