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

TL;DR

This paper introduces a new class of Bell inequalities with exactly computable quantum bounds, enabling device-independent certification of Majorana fermions and revealing a novel self-testing equivalence involving partial transposition.

Contribution

It generalizes existing Bell inequalities, provides a method for exact quantum bound computation, and uncovers a new self-testing equivalence involving partial transposition.

Findings

Bell inequalities with exactly computable quantum bounds

Device-independent certification of Majorana fermions

Identification of a new self-testing equivalence involving partial transposition

Abstract

Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable through quantum strategies, is rarely accessible analytically. In this work, we introduce a general construction of Bell inequalities for which this bound can be computed exactly. Our framework generalizes both the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, yielding Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, our inequalities also enable the device-independent certification of Majorana fermions, understood as multiqubit realizations of Clifford algebra generators. Importantly, we identify an additional equivalence that must be incorporated into the definition of self-testing beyond invariance under local isometries and transposition. This equivalence arises from partial transposition applied to the shared state and to the measurements, which in specific cases leaves all observed correlations unchanged.