Genuine network quantum nonlocality and self-testing

TL;DR

This paper introduces the concept of genuine network quantum nonlocality, demonstrating its unique correlations in network structures and presenting a self-testing example that distinguishes it from standard Bell nonlocality.

Contribution

It defines genuine network quantum nonlocality, provides examples within bilocality networks, and introduces a novel self-testing method based on network structure.

Findings

Identified correlations that are genuinely network nonlocal

Demonstrated quantum self-testing relying on network structure

Showed correlations are non-bilocal but Bell local

Abstract

The network structure offers in principle the possibility for novel forms of quantum nonlocal correlations, that are proper to networks and cannot be traced back to standard quantum Bell nonlocality. Here we define a notion of genuine network quantum nonlocality. Our approach is operational and views standard quantum nonlocality as a resource for producing correlations in networks. We show several examples of correlations that are genuine network nonlocal, considering the so-called bilocality network of entanglement swapping. In particular, we present an example of quantum self-testing which relies on the network structure; the considered correlations are non-bilocal, but are local according to the usual definition of Bell locality.