# Certified Quantum Measurement of Majorana Fermions

## TL;DR

This paper introduces a quantum self-testing protocol to certify Majorana fermion measurements, demonstrating anti-commutativity and quantum contextuality, with robustness to experimental errors and fidelity bounds.

## Contribution

It provides a novel, robust protocol for certifying Majorana fermions through measurement statistics and contextuality witnesses, advancing experimental verification methods.

## Key findings

- Ideal measurement statistics imply anti-commutativity of Majorana operators
- The protocol is robust to experimental errors with linear fidelity bounds
- Violation of the contextuality inequality confirms quantum nature of measurements

## 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 $\langle W \rangle \le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\langle W \rangle=5$ indicates the degree of confidence in the detection of Majorana fermions.