Device-independent certification of Majorana fermions and a new self-testing equivalence
Abstract
Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable by 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. The construction is based on a class of rectangular matrices with pairwise orthogonal rows and normalized columns, which we call row-orthogonal, column-normalized (ROCN) matrices. Our framework generalizes both the Clauser–Horne–Shimony–Holt inequality and Gisin’s elegant Bell inequality, yielding Bell expressions maximally violated by arbitrary families of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, these 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 self-testing, beyond the standard equivalences generated by local isometries, the addition of auxiliary degrees of freedom, and complex conjugation. This equivalence arises from applying partial transposition jointly to the shared state and the measurements, which, whenever it is well-defined, preserves all observed correlations.
Related
- Free Majorana fermions with superconducting quantum wires and a magnetic impurity
- Global anomalies in sigma models with Majorana-Weyl fermions
- Topological superconductors and Majorana fermions based on X-wave magnets with $X=p,d,f,g,i $
- Topological Quantum Spin Liquids in a Ladder with Majorana fermions and p-wave Superconductivity
- Semi-Device-Independent Certification of multi-qubit Entangled Basis Measurement
BibTeX
@article{michalski2026deviceindependent,
title = {{Device-independent certification of Majorana fermions and a new self-testing equivalence}},
author = {Patryk Michalski and Arturo Konderak and Wojciech Bruzda and Remigiusz Augusiak},
journal = {npj Quantum Information},
year = {2026},
month = oct,
doi = {10.1038/s41534-026-01383-z},
url = {https://www.nature.com/articles/s41534-026-01383-z},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Device-independent certification of Majorana fermions and a new self-testing equivalence
AU - Patryk Michalski
AU - Arturo Konderak
AU - Wojciech Bruzda
AU - Remigiusz Augusiak
PY - 2026
DA - 2026/10/24
JO - npj Quantum Information
DO - 10.1038/s41534-026-01383-z
UR - https://www.nature.com/articles/s41534-026-01383-z
AB - Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable by 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. The construction is based on a class of rectangular matrices with pairwise orthogonal rows and normalized columns, which we call row-orthogonal, column-normalized (ROCN) matrices. Our framework generalizes both the Clauser–Horne–Shimony–Holt inequality and Gisin’s elegant Bell inequality, yielding Bell expressions maximally violated by arbitrary families of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, these 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 self-testing, beyond the standard equivalences generated by local isometries, the addition of auxiliary degrees of freedom, and complex conjugation. This equivalence arises from applying partial transposition jointly to the shared state and the measurements, which, whenever it is well-defined, preserves all observed correlations.
SN - 2056-6387
ER -