An elegant proof of self-testing for multipartite Bell inequalities

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-Żukowski-Brukner (WWWŻB) family of linear Bell inequalities, and Uffink's family of N party quadratic Bell-inequalities.

First draft, comments are welcome

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• Supersinglets can be self-tested with perfect quantum strategies
• Robust self-testing and certified randomness based on chained Bell inequality
• Communication scenario enables robust self-testing of n-party Greenberger-Horne-Zeilinger basis measurements
• Certification of multi-qubit quantum systems with temporal inequalities
• An approach using geometric diagrams to generic Bell inequalities with multiple observables