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A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement

In this work, we present a new class of genuine multipartite Bell inequalities, that is particularly designed for multipartite device-independent (DI) quantum key distribution (QKD), also called DI conference key agreement. We prove the classical bounds of this inequality, discuss how to maximally violate it and show its usefulness by calculating achievable conference key rates via the violation of this Bell inequality. To this end, semidefinite programming techniques based on [Nat. Commun. 2, 238 (2011)] are employed and extended to the multipartite scenario. Our Bell inequality represents a nontrivial multipartite generalization of the Clauser-Horne-Shimony-Holt inequality and is motivated by the extension of the bipartite Bell state to the n-partite Greenberger-Horne-Zeilinger state. For DIQKD, we suggest an honest implementation for any number of parties and study the effect of noise on achievable asymptotic conference key rates.