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

TL;DR

This paper derives a tight analytical upper bound for the maximal expectation value of the generalized Svetlichny operator in multipartite quantum systems, providing insights into non-locality detection and quantum information applications.

Contribution

It introduces new techniques to analytically bound the Svetlichny operator's expectation value and characterizes states where this bound is tight, advancing understanding of multipartite non-locality.

Findings

Derived a tight upper bound for the generalized Svetlichny operator

Identified conditions for states achieving the bound, including noisy GHZ states

Proposed operational methods for experimental detection of non-locality

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.