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Certified Quantum Measurement of Majorana Fermions

Published

Author(s)

Emanuel H. Knill, Abu Ashik Md. Irfan, Karl H. Mayer, Gerardo Ortiz

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 anticommutativity 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. For convenience, we propose to analyze experimental outcomes in terms of a contextuality witness W, which satisfies <= 3 for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the departure from the maximum ideal value =5 indicates the degree of confidence in the detection of Majorana fermions.
Citation
Physical Review A
Volume
101
Issue
3

Keywords

Contextuality, Majorana fermions, Quantum self testing

Citation

Knill, E. , Md., A. , Mayer, K. and Ortiz, G. (2020), Certified Quantum Measurement of Majorana Fermions, Physical Review A, [online], https://doi.org/10.1103/PhysRevA.101.032106 (Accessed May 18, 2021)
Created March 12, 2020, Updated May 19, 2020