Sharing of Genuine Tripartite Nonlocality with Multiple Observers on one Side

In this paper, we study the sharing of genuine tripartite nonlocality with multiple observers on one side. For the generalized GHZ state under different parameter values, there are at most 0, 1 and 2 Charlies on one side respectively, which can simultaneously demonstrate genuine tripartite nonlocality with the single Alice and single Bob. Furthermore, for the standard GHZ state, we design an optimal protocol of genuine nonlocality sharing among multiple observers. After Charlie\(^{1}\) using unsharp measurements with near-maximum strength, Charlie\(^{2}\) can also demonstrate genuine tripartite nonlocality with the single Alice and single Bob. Our protocol has expanded the region of double Svetlichny inequality violation. Our results shed light on the interplay between nonlocality and quantum measurements, especially highlighting the impact of unsharp measurements, including the role of sharpness parameters and the design of measurement settings, on the sharing of nonlocality. These findings can be applied to various quantum information processing tasks, such as unbounded randomness certification, quantum steering and quantum communication network.