Nonlocal correlations in the star-network configuration

TL;DR

This paper extends the concept of bilocality to a star-network configuration, deriving new inequalities for local correlations, demonstrating quantum violations, and analyzing robustness to noise and losses.

Contribution

It introduces a generalized star-network scenario with new inequalities and explores quantum violations, expanding understanding of nonlocal correlations in complex networks.

Findings

Derived new inequalities for star-network local correlations.

Demonstrated quantum violations of these inequalities.

Analyzed robustness of violations to noise and losses.

Abstract

The concept of bilocality was introduced to study the correlations which arise in an entanglement swapping scenario, where one has two sources which can naturally taken to be independent. This additional constraint leads to stricter requirements than simply imposing locality, in the form of bilocality inequalities. In this work we consider a natural generalisation of the bilocality scenario, namely the star-network consisting of a single central party surrounded by $n$ edge parties, each of which shares an independent source with the centre. We derive new inequalities which are satisfied by all local correlations in this scenario, for the cases when the central party performs (i) two dichotomic measurements (ii) a single Bell state measurement. We demonstrate quantum violations of these inequalities and study both the robustness to noise and to losses.