Tight upper bound for the maximal expectation value of the $N$-partite generalized Svetlichny operator

Abstract

Genuine multipartite non-locality is not only of fundamental interest but also serves as an important resource for quantum information theory. We consider 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. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger-Horne-Zeilinger (GHZ) 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 we defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, our results give feasible experimental implementations in detecting the genuine multipartite non-locality and can potentially be applied to other quantum information processing tasks.

arXiv comment13 pages, 1 figure

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Cited by in corpus (2)

• Violation of Svetlichny's inequality in a system of spins $j$
• Multipartite entanglement vs nonlocality for two families of $N$-qubit states