Tight upper bound for the maximal quantum value of the Svetlichny operators

It is a challenging task to detect genuine multipartite nolocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequalities (SI) for several quantum states, including the white and color noised GHZ states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation on GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.