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Identifying the nonlocality of a multiparty quantum state is an importanttask in quantum mechanics. Seevinck and Svetlichny [Phys. Rev. Lett. 89, 060401(2002)], and independently, Collins and co-workers [Phys. Rev. Lett. 88, 170405(2002)] have generalized the tripartite notion of Svetlichny nonlocality ton-parties. Here we have developed a tight upper bound for genuine four partySvetlichny type nonlocality. The constraints on the quantum states for thetightness of the bound are also presented. The method enables us to providenecessary and sufficient conditions for violating the four qubit Svetlichnytype inequality for several quantum states. The relations between the genuinemultipartite entanglement and the maximal quantum value of the Seevinck andSvetlichny operators for pure four qubit states are also discussed.Consequently, we have exhibited genuine four qubit hidden nonlocality underlocal filtering. Our result provides an effective and operational method forfurther study of multipartite quantum nonlocality.

Tight upper bound of genuine four party Svetlichny type nonlocality with and without local filtering