# A nonlocal game for witnessing quantum networks

## TL;DR

This paper introduces a unified method to construct nonlocal games for quantum networks, enabling the testing of nonlocality in complex entangled systems beyond traditional Bell inequalities.

## Contribution

It proposes a graph-based framework for creating multipartite nonlocal games with quantum advantages, extending the scope of nonlocality tests in quantum networks.

## Key findings

- First linear test of nonlocality in general quantum networks
- Method to generate numerous multipartite games from graphs
- Beyond traditional CHSH game scenarios

## Abstract

Nonlocal game as a novel witness of the nonlocality of entanglement is of fundamental importance in various fields. The known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We first propose an efficient method to construct numerous multipartite games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply the first linear testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond well-known CHSH games. Our result has interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.