Certified Quantum Measurement of Majorana Fermions

Abstract

We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $⟨W⟩\le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $⟨W⟩=5$ indicates the degree of confidence in the detection of Majorana fermions.

arXiv comment13 pages, 3 figures

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Cited by in corpus (10)

• Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism
• An elegant proof of self-testing for multipartite Bell inequalities
• Quantum sets of the multicolored-graph approach to contextuality
• Scalable noncontextuality inequalities and certification of multiqubit quantum systems
• Self-testing in a constrained prepare-measure scenario sans assuming quantum dimension
• Dynamics of quantum resources in regular and Majorana fermion systems
• Certification of two-qubit quantum systems with temporal inequality
• Contextuality, superlocality and nonclassicality of supernoncontextuality
• Certification of multi-qubit quantum systems with temporal inequalities