Proofs of network quantum nonlocality in continuous families of distributions

TL;DR

This paper proves quantum nonlocality in continuous families of distributions within network scenarios, using inflation techniques and binary-outcome reductions, advancing understanding of quantum correlations beyond bipartite setups.

Contribution

It introduces a novel method to extend nonlocality proofs across continuous parameter ranges and provides new network Bell inequalities for the triangle scenario.

Findings

Proved that certain quantum distributions do not admit triangle-local models.

First successful use of inflation technique in network nonlocality proof.

Produced a large collection of network Bell inequalities for binary outcomes.

Abstract

The study of nonlocality in scenarios that depart from the bipartite Einstein-Podolsky-Rosen setup is allowing to uncover many fundamental features of quantum mechanics. Recently, an approach to building network-local models based on machine learning lead to the conjecture that the family of quantum triangle distributions of [arXiv:1905.04902] did not admit triangle-local models in a larger range than the original proof. We prove part of this conjecture in the affirmative. Our approach consists in reducing the family of original, four-outcome distributions to families of binary-outcome ones, and then using the inflation technique to prove that these families of binary-outcome distributions do not admit triangle-local models. This constitutes the first successful use of inflation in a proof of quantum nonlocality in networks whose nonlocality could not be proved with alternative methods. Moreover, we provide a method to extend proofs of network nonlocality in concrete distributions of a parametrized family to continuous ranges of the parameter. In the process, we produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.