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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.
An extensive debate on quantum non-demolition (QND) measurement, reviewed in Grangier et al. [Nature, {bf 396}, 537 (1998)], finds that true QND measurements must have both non-classical state-preparation capability and non-classical information-dama
We study multiband semiconducting nanowires proximity-coupled with an s-wave superconductor and calculate the topological phase diagram as a function of the chemical potential and magnetic field. The non-trivial topological state corresponds to a sup
A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also a quantum
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum rev
Quantum non-demolition (QND) measurements improve sensitivity by evading measurement back-action. The technique was first proposed to detect mechanical oscillations in gravity wave detectors,and demonstrated in the measurement of optical fields, lead