Tight Upper Bound for the Maximal Expectation Value of the N $N$ -Partite Generalized Svetlichny Operator

Genuine multipartite non-locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The $N$-partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary $N$-qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger-Horne-Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non-locality and can potentially be applied to other quantum information processing tasks.