# Bounding the sets of classical and quantum correlations in networks

## TL;DR

This paper introduces a semidefinite programming method to analyze classical and quantum correlations in complex networks, revealing new nonlocal phenomena and the activation of measurement nonlocality.

## Contribution

It extends the Navascués-Pironio-Acín hierarchy to complex networks, enabling the study of correlations beyond standard scenarios and demonstrating activation of measurement nonlocality.

## Key findings

- Identifies correlations unattainable in entanglement swapping scenarios.
- Shows activation of measurement nonlocality in networks.
- Provides a new computational tool for quantum network analysis.

## Abstract

We present a method that allows the study of classical and quantum correlations in networks with causally-independent parties, such as the scenario underlying entanglement swapping. By imposing relaxations of factorization constraints in a form compatible with semidefinite programming, it enables the use of the Navascu\'es-Pironio-Ac\'in hierarchy in complex quantum networks. We first show how the technique successfully identifies correlations not attainable in the entanglement-swapping scenario. Then we use it to show how the nonlocal power of measurements can be activated in a network: there exist measuring devices that, despite being unable to generate nonlocal correlations in the standard Bell scenario, provide a classical-quantum separation in an entanglement swapping configuration.