Genuine multipartite Bell inequality for device-independent conference key agreement

A class of genuine multipartite Bell inequalities is presented, which is designed for multipartite device-independent (DI) quantum key distribution (QKD). We prove the classical bounds of this inequality and compute DI secret-key rates based on its violation. To this end, semidefinite programming techniques are employed and extended to the multipartite case. Our Bell inequality is a nontrivial generalization of the Clauser-Horne-Shimony-Holt inequality. For DIQKD, we suggest an honest implementation for any number of parties and study the effect of noise on achievable conference key rates.