Sharing tripartite nonlocality sequentially using only projective measurements

TL;DR

This paper explores how tripartite nonlocality can be sequentially shared among multiple observers using only projective measurements and classical randomness, revealing limitations and possibilities for sharing genuine and standard nonlocality.

Contribution

It demonstrates the sharing of tripartite nonlocality with projective measurements and classical randomness, including conditions for sharing genuine nonlocality with multiple observers.

Findings

Two Charlies can share standard tripartite nonlocality with Alice and Bob.

At most one Charlie can share genuine tripartite nonlocality with Alice and Bob.

Biased measurements can increase the number of Charlies sharing genuine nonlocality.

Abstract

Bell nonlocality is a valuable resource in quantum information processing tasks. Scientists are interested in whether a single entangled state can generate a long sequence of nonlocal correlations. Previous work has accomplished sequential tripartite nonlocality sharing through unsharp measurements. In this paper, we investigate the sharing of tripartite nonlocality using only projective measurements and sharing classical randomness. For the generalized GHZ state, we have demonstrated that using unbiased measurement choices, two Charlies can share the standard tripartite nonlocality with a single Alice and a single Bob, while at most one Charlie can share the genuine tripartite nonlocality with a single Alice and a single Bob. However, with biased measurement choices, the number of Charlies sharing the genuine tripartite nonlocality can be increased to two. Nonetheless, we find that using biased measurements does not increase the number of sequential observers sharing the standard tripartite nonlocality. Moreover, we provide the feasible range of double violation for the parameters of the measurement combination probability with respect to the state.