# Constraints on nonlocality in networks from no-signaling and independence

## TL;DR

This paper explores the constraints on correlations in quantum networks, specifically the triangle network, under no-signaling and source independence assumptions, revealing potential nonlocal correlations beyond classical models.

## Contribution

It derives strong, tight constraints on correlations in the triangle network and highlights the possibility of nonlocal correlations that cannot be explained by local models.

## Key findings

- Some constraints are tight and can be saturated by local models.
- Other constraints cannot be saturated, indicating potential nonlocal correlations.
- The study advances understanding of nonlocality in complex quantum networks.

## Abstract

Generalising the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is however challenging. Here we investigate constraints on correlations in networks under the two natural assumptions of no-signaling and independence of the sources. We consider the ``triangle network'', and derive strong constraints on correlations even though the parties receive no input, i.e. each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network.