An elegant proof of self-testing for multipartite Bell inequalities

TL;DR

This paper introduces a simple, general proof method for self-testing in multipartite Bell inequalities, extending the concept beyond bipartite scenarios and applicable to various inequality families.

Contribution

It provides a new, broadly applicable self-testing proof technique for N-partite Bell inequalities, not limited to linear cases, enhancing device certification in quantum physics.

Findings

Self-testing statements for MABK and WWWZB inequalities

Applicable to quadratic Bell inequalities

Generalizes previous bipartite methods

Abstract

The predictions of quantum theory are incompatible with local-causal explanations. This phenomenon is called Bell non-locality and is witnessed by violation of Bell-inequalities. The maximal violation of certain Bell-inequalities can only be attained in an essentially unique manner. This feature is referred to as self-testing and constitutes the most accurate form of certification of quantum devices. While self-testing in bipartite Bell scenarios has been thoroughly studied, self-testing in the more complex multipartite Bell scenarios remains largely unexplored. This work presents a simple and broadly applicable self-testing argument for N-partite correlation Bell inequalities with two binary outcome observables per party. Our proof technique forms a generalization of the Mayer-Yao formulation and is not restricted to linear Bell-inequalities, unlike the usual sum of squares method. To showcase the versatility of our proof technique, we obtain self-testing statements for N party Mermin-Ardehali-Belinskii-Klyshko (MABK) and Werner-Wolf-Weinfurter-\.Zukowski-Brukner (WWW\.ZB) family of linear Bell inequalities, and Uffink's family of N party quadratic Bell-inequalities.