# Genuine quantum nonlocality in the triangle network

## TL;DR

This paper introduces new forms of quantum nonlocality in network settings, demonstrating genuine nonlocal correlations without input settings, especially in triangle and odd-cycle networks, using entangled states and measurements.

## Contribution

It presents the first examples of genuine quantum nonlocality in networks that do not rely on Bell inequality violations, expanding understanding of quantum correlations.

## Key findings

- Demonstrated quantum nonlocality without inputs in triangle networks
- Extended the concept to odd-cycle networks
- Used entangled states and measurements to achieve nonlocal correlations

## Abstract

Quantum networks allow in principle for completely novel forms of quantum correlations. In particular, quantum nonlocality can be demonstrated here without the need of having various input settings, but only by considering the joint statistics of fixed local measurement outputs. However, previous examples of this intriguing phenomenon all appear to stem directly from the usual form of quantum nonlocality, namely via the violation of a standard Bell inequality. Here we present novel examples of 'quantum nonlocality without inputs', which we believe represent a new form of quantum nonlocality, genuine to networks. Our simplest examples, for the triangle network, involve both entangled states and joint entangled measurements. A generalization to any odd-cycle network is also presented. Finally, we conclude with some open questions.