  A family of Bell-type inequalities is present, which are constructed directly
from the "standard" Bell inequalities involving two dichotomic observables per
site. It is shown that the inequalities are violated by all the generalized
Greenberger-Horne-Zeilinger states of multiqubits. Remarkably, our new
inequalities can provide stronger non-locality tests in a sense that the local
reality inequalities are exponentially stronger than the corresponding
multipartite separability inequalities. This reveals that the exponential
violation of local realism by separable states is an interesting consequence of
quantum fluctuation of multipartite systems.
