# Limits on correlations in networks for quantum and no-signaling resources

## TL;DR

This paper derives nonlinear bounds on quantum correlations in networks based solely on their topology, with a focus on the triangle network, and discusses implications for device-independent network characterization.

## Contribution

It introduces new nonlinear inequalities constraining quantum correlations in networks, applicable to general no-signaling theories, and analyzes the complex triangle network case.

## Key findings

- Derived bounds depend only on network topology
- Proved inequalities hold for no-signaling boxes in the triangle network
- Discussed application to device-independent network topology characterization

## Abstract

A quantum network consists of independent sources distributing entangled states to distant nodes which can then perform entangled measurements, thus establishing correlations across the entire network. But how strong can these correlations be? Here we address this question, by deriving bounds on possible quantum correlations in a given network. These bounds are nonlinear inequalities that depend only on the topology of the network. We discuss in detail the notably challenging case of the triangle network. Moreover, we conjecture that our bounds hold in general no-signaling theories. In particular, we prove that our inequalities for the triangle network hold when the sources are arbitrary no-signaling boxes which can be wired together. Finally, we discuss an application of our results for the device-independent characterization of the topology of a quantum network.