Certifying Majorana Fermions with Elegant-Like Bell Inequalities and a New Self-Testing Equivalence

Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound is rarely accessible analytically. In my talk, I will present a general construction of Bell inequalities whose quantum bound can be computed exactly. This framework generalizes the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, and yields Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, these inequalities also enable device-independent certification of Majorana fermions, viewed as multiqubit realizations of Clifford algebra generators. Finally, I will highlight an additional equivalence (beyond local isometries and transposition) that must be included in self-testing: partial transposition applied to the shared state and measurements, which can leave all observable correlations invariant.