# Scalable Bell inequalities for qubit graph states and robust self-testing

## TL;DR

This paper introduces scalable Bell inequalities tailored for multiqubit graph states, enabling efficient and robust self-testing with fewer correlations, thus reducing experimental complexity in quantum nonlocality verification.

## Contribution

It presents a simple, scalable construction of Bell inequalities maximally violated by graph states, improving efficiency and robustness in self-testing protocols.

## Key findings

- Bell inequalities with linear scaling in the number of observers
- Enhanced robustness in self-testing of multiqubit graph states
- Potential generalizations to non-Pauli stabilizer states

## Abstract

Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a very simple and intuitive construction of Bell inequalities that are maximally violated by the multiqubit graph states and can be used for their robust self-testing. The main advantage of our inequalities over previous constructions for these states lies in the fact that the number of correlations they contain scales only linearly with the number of observers, which presents a significant reduction of the experimental effort needed to violate them. We also discuss possible generalizations of our approach by showing that it is applicable to entangled states whose stabilizers are not simply tensor products of Pauli matrices.