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

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.