Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

TL;DR

This paper demonstrates that in tripartite quantum systems, an unlimited number of independent Charlies can sequentially observe different forms of nonlocality with Alice and Bob, surpassing previous limits on sharing genuine nonlocality.

Contribution

It introduces methods for multiple Charlies to sequentially observe nonlocality with Alice and Bob in tripartite states, expanding the understanding of nonlocality sharing.

Findings

Arbitrarily many Charlies can observe standard nonlocality via Mermin inequality violations.

Multiple Charlies can also observe genuinely nonsignal nonlocality.

This surpasses previous limits where only two Charlies could share genuine nonlocality.

Abstract

There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob.