Functional Bell inequalities can serve as a stronger entanglement witness than conventional Bell inequalities

We consider a Bell inequality for a continuous range of settings of the apparatus at each site. This “functional” Bell inequality gives a better range of violation for generalized Greenberger, Horne, and Zeilinger states. Also a family of N-qubit bound entangled states violate this inequality for $N>\mathrm{}5.\mathrm{}$