Sharing quantum nonlocality and genuine nonlocality with independent observables

TL;DR

This paper shows that multiple independent observers can share quantum nonlocality with a single party across various entangled states, extending previous results beyond maximally entangled two-qubit states.

Contribution

It generalizes sharing of quantum nonlocality to arbitrary dimensional bipartite states and analyzes genuine nonlocality sharing with generalized GHZ states.

Findings

Arbitrarily many observers can share nonlocality with a single party in arbitrary bipartite states.

Maximum of two observers can share genuine nonlocality in generalized GHZ states.

Extends previous results from maximally entangled two-qubit states to more general states.

Abstract

Recently the authors in [Phys. Rev. Lett. 125, 090401 (2020)] considered the following scenario: Alice and Bob each have half of a pair of entangled qubit state. Bob measures his half and then passes his part to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality with the single Alice. By taking the maximally entangled pure two-qubit state as an example, it has been constructively proved that arbitrarily many independent Bobs can share the nonlocality with the single Alice. Here we demonstrate that arbitrarily many independent observers can share the nonlocality of a single arbitrary dimensional bipartite entangled but not necessary two-qubit entangled state. Further, taking the generalized GHZ states as an example, we show that at most two Charlies can share the genuine nonlocality of a single generalized GHZ state with an Alice and a Bob.