Network Nonlocality Sharing in Generalized Star Network from Bipartite Bell Inequalities

TL;DR

This paper explores how quantum nonlocality can be shared across a generalized star network using bipartite Bell inequalities, providing analytical tools and demonstrating simultaneous violations in complex configurations.

Contribution

It introduces an analytical expression for bipartite quantum correlators in star networks and demonstrates network nonlocality sharing with diverse Bell inequalities beyond CHSH.

Findings

Simultaneous violations in (2,2,6) and (2,2,465) network configurations.

Analytical formula for bipartite quantum correlator in arbitrary settings.

Robustness of nonlocality sharing increases with network complexity.

Abstract

This work investigates network nonlocality sharing for a broad class of bipartite Bell inequalities in a generalized star network with an $(n,m,k)$ configuration, comprising $n$ independent branches, $m$ sequential Alices per branch, and $k$ measurement settings per party. On each branch, the intermediate Alices implement optimal weak measurements, whereas the final Alice and the central Bob perform sharp projective measurements. Network nonlocality sharing is witnessed when the quantum values of the network correlations associated with relevant parties simultaneously violate a star-network Bell inequality generated from the given class of bipartite Bell inequalities. We streamline the calculation of the quantum values of the network correlations and derive an analytical expression for the bipartite quantum correlator, valid for arbitrary measurement settings and weak-measurement strengths. The network nonlocality sharing for V\'ertesi inequalities has been studied within the framework, and simultaneous violations are found in $(2,2,6)$ and $(2,2,465)$ cases, with the latter exhibiting greater robustness. Our approach suggests a practical route to studying network nonlocality sharing by utilizing diverse bipartite Bell inequalities beyond the commonly used CHSH-type constructions.