Quantum nonlocality of generic family of four-qubit entangled pure states

We directly introduce a Bell-type inequality for four-qubit systems. Using the inequality we investigate quantum nonlocality of a generic family of states ｜Gabcd〉[Phys. Rev. A 65 052112（2002）] and several canonical four-qubit entangled states. It has been demonstrated that the inequality is maximally violated by the so called ＂four-qubit the maximally entangled state ｜Gm〉＂ and it is also violated by four-qubit W state and a special family of states ｜Gab00〉. Moreover, a useful entanglement-nonlocality relationship for the family of states ｜Gab00〉is derived. Finally, we present a scheme of preparation of the state ｜Gm〉with linear optics and cross-Kerr nonlinearities.