Sharing of tripartite nonlocality by multiple observers measuring sequentially at one side

Abstract: Standard tripartite nonlocality and genuine tripartite nonlocality can be detected by the violations of Mermin inequality and Svetlichny inequality, respectively. Since tripartite quantum nonlocality has novel applications in quantum information and quantum computation, it is important to investigate whether more than three observers can share tripartite nonlocality, simultaneously. In the present study we answer this question in the affirmative. In particular, we consider a scenario where three spin-$\frac{1}{2}$ particles are spatially separated and shared between Alice, Bob and multiple Charlies. Alice performs measurements on the first particle; Bob performs measurements on the second particle and multiple Charlies perform measurements on the third particle sequentially. In this scenario we investigate how many Charlies can simultaneously demonstrate standard tripartite nonlocality and genuine tripartite nonlocality with single Alice and single Bob. The interesting result revealed by the present study is that at most six Charlies can simultaneously demonstrate standard tripartite nonlocality with single Alice and single Bob. On the other hand, at most two Charlies can simultaneously demonstrate genuine tripartite nonlocality with single Alice and single Bob. Hence, the present study shows that standard tripartite nonlocality can be simultaneously shared by larger number of Charlies compared to genuine tripartite nonlocality in the aforementioned scenario, which implies that standard tripartite nonlocality is more effective than genuine tripartite nonlocality in the context of simultaneous sharing by multiple observers.