Quantum nonlocality of generic family of four-qubit entangled pure states**Project supported by the National Natural Science Foundation of China (Grant Nos. 11475054 and 11371005), Hebei Natural Science Foundation of China (Grant Nos. A2012205013 and A2014205060), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. 3142014068 and 3142014125), and Langfang Key Technology Research and

Abstract

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.