# Experimental verification of time-order-dependent correlations in three-qubit Greenberger-Horne-Zeilinger-class states

## TL;DR

This study experimentally verifies that generalized GHZ states exhibit genuine three-way nonlocality through Bell-type inequalities, even without Svetlichny inequality violation, highlighting the robustness of tripartite quantum correlations.

## Contribution

It demonstrates that gGHZ states can show genuine three-way nonlocality under time-order-dependent principles regardless of Svetlichny inequality violation, both theoretically and experimentally.

## Key findings

- gGHZ states violate tripartite Bell inequalities at all entanglement levels
- gGHZ states exhibit nonlocality without Svetlichny inequality violation
- maximal noise tolerance for maintaining nonlocality identified

## Abstract

In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.