Certified quantum measurement of Majorana fermions
Abstract
Here, we propose a quantum selftesting protocol to certify measurements of fermion parity involving Majorana fermion modes. We further 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. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\u3008W\u3009\le 3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\u3008W\u3009=5$ indicates the degree of confidence in the detection of Majorana fermions.
 Authors:

 Indiana Univ., Bloomington, IN (United States)
 National Inst. of Standards and Technology (NIST), Boulder, CO (United States); Univ. of Colorado, Boulder, CO (United States)
 Publication Date:
 Research Org.:
 Indiana Univ., Bloomington, IN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES); National Institute of Standards and Technology (NIST)
 OSTI Identifier:
 1630822
 Alternate Identifier(s):
 OSTI ID: 1604501
 Grant/Contract Number:
 SC0020343
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 101; Journal Issue: 3; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE
Citation Formats
Irfan, Abu Ashik Md., Mayer, Karl, Ortiz, Gerardo, and Knill, Emanuel. Certified quantum measurement of Majorana fermions. United States: N. p., 2020.
Web. doi:10.1103/PhysRevA.101.032106.
Irfan, Abu Ashik Md., Mayer, Karl, Ortiz, Gerardo, & Knill, Emanuel. Certified quantum measurement of Majorana fermions. United States. https://doi.org/10.1103/PhysRevA.101.032106
Irfan, Abu Ashik Md., Mayer, Karl, Ortiz, Gerardo, and Knill, Emanuel. Thu .
"Certified quantum measurement of Majorana fermions". United States. https://doi.org/10.1103/PhysRevA.101.032106. https://www.osti.gov/servlets/purl/1630822.
@article{osti_1630822,
title = {Certified quantum measurement of Majorana fermions},
author = {Irfan, Abu Ashik Md. and Mayer, Karl and Ortiz, Gerardo and Knill, Emanuel},
abstractNote = {Here, we propose a quantum selftesting protocol to certify measurements of fermion parity involving Majorana fermion modes. We further 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. We propose to analyze experimental outcomes in terms of a contextuality witness W, which satisfies 〈W〉≤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.},
doi = {10.1103/PhysRevA.101.032106},
journal = {Physical Review A},
number = 3,
volume = 101,
place = {United States},
year = {2020},
month = {3}
}
Web of Science
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