An elegant scheme of self-testing for multipartite Bell inequalities

Abstract

Self-testing is 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. We present a simple and broadly applicable self-testing scheme for N-partite correlation Bell inequalities with two binary outcome observables per party. To showcase the versatility of our proof technique, we obtain self-testing statements for the MABK and WWWŻB family of linear Bell inequalities and Uffink’s family of quadratic Bell inequalities. In particular, we show that the N-partite MABK and Uffink’s quadratic Bell inequalities self-test the GHZ state and anti-commuting observables for each party. While the former uniquely specifies the state, the latter allows for an arbitrary relative phase. To demonstrate the operational relevance of the relative phase, we introduce Uffink’s complex-valued N partite Bell expression, whose extremal values self-test the GHZ states and uniquely specify the relative phase.