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. doi: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. doi: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
Works referenced in this record:
New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012
 Alicea, Jason
 Reports on Progress in Physics, Vol. 75, Issue 7
Teoria simmetrica dell’elettrone e del positrone
journal, April 1937
 Majorana, Ettore
 Il Nuovo Cimento, Vol. 14, Issue 4
Signatures of Majorana Fermions in Hybrid SuperconductorSemiconductor Nanowire Devices
journal, April 2012
 Mourik, V.; Zuo, K.; Frolov, S. M.
 Science, Vol. 336, Issue 6084
The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles
journal, September 2012
 Rokhinson, Leonid P.; Liu, Xinyu; Furdyna, Jacek K.
 Nature Physics, Vol. 8, Issue 11
ZeroBias Peaks in the Tunneling Conductance of SpinOrbitCoupled Superconducting Wires with and without Majorana EndStates
journal, December 2012
 Liu, Jie; Potter, Andrew C.; Law, K. T.
 Physical Review Letters, Vol. 109, Issue 26
ManyBody Characterization of ParticleConserving Topological Superfluids
journal, December 2014
 Ortiz, Gerardo; Dukelsky, Jorge; Cobanera, Emilio
 Physical Review Letters, Vol. 113, Issue 26
What is a particleconserving Topological Superfluid? The fate of Majorana modes beyond meanfield theory
journal, September 2016
 Ortiz, Gerardo; Cobanera, Emilio
 Annals of Physics, Vol. 372
Measurementonly topological quantum computation via anyonic interferometry
journal, April 2009
 Bonderson, Parsa; Freedman, Michael; Nayak, Chetan
 Annals of Physics, Vol. 324, Issue 4
DeviceIndependent Security of Quantum Cryptography against Collective Attacks
journal, June 2007
 Acín, Antonio; Brunner, Nicolas; Gisin, Nicolas
 Physical Review Letters, Vol. 98, Issue 23
Private randomness expansion with untrusted devices
journal, February 2011
 Colbeck, Roger; Kent, Adrian
 Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 9
Scalable designs for quasiparticlepoisoningprotected topological quantum computation with Majorana zero modes
journal, June 2017
 Karzig, Torsten; Knapp, Christina; Lutchyn, Roman M.
 Physical Review B, Vol. 95, Issue 23
Which states violate Bell's inequality maximally?
journal, October 1992
 Popescu, Sandu; Rohrlich, Daniel
 Physics Letters A, Vol. 169, Issue 6
Ubiquitous Nonlocal Entanglement with Majorana Zero Modes
journal, October 2017
 Romito, Alessandro; Gefen, Yuval
 Physical Review Letters, Vol. 119, Issue 15
Incompatible results of quantum measurements
journal, December 1990
 Peres, Asher
 Physics Letters A, Vol. 151, Issue 34
Simple unified form for the major nohiddenvariables theorems
journal, December 1990
 Mermin, N. David
 Physical Review Letters, Vol. 65, Issue 27
Robust selftesting of the threequbit $W$ state
journal, October 2014
 Wu, Xingyao; Cai, Yu; Yang, Tzyh Haur
 Physical Review A, Vol. 90, Issue 4
Analytic and Nearly Optimal SelfTesting Bounds for the ClauserHorneShimonyHolt and Mermin Inequalities
journal, August 2016
 Kaniewski, Jędrzej
 Physical Review Letters, Vol. 117, Issue 7
All pure bipartite entangled states can be selftested
journal, May 2017
 Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio
 Nature Communications, Vol. 8, Issue 1
Rigidity of the magic pentagram game
journal, November 2017
 Kalev, Amir; Miller, Carl A.
 Quantum Science and Technology, Vol. 3, Issue 1
Selftesting of binary observables based on commutation
journal, June 2017
 Kaniewski, Jędrzej
 Physical Review A, Vol. 95, Issue 6
Robust and Versatile BlackBox Certification of Quantum Devices
journal, July 2014
 Yang, Tzyh Haur; Vértesi, Tamás; Bancal, JeanDaniel
 Physical Review Letters, Vol. 113, Issue 4
Physical characterization of quantum devices from nonlocal correlations
journal, February 2015
 Bancal, JeanDaniel; Navascués, Miguel; Scarani, Valerio
 Physical Review A, Vol. 91, Issue 2
Efficient eigenvalue determination for arbitrary Pauli products based on generalized spinspin interactions
journal, December 2017
 Leibfried, D.; Wineland, D. J.
 Journal of Modern Optics, Vol. 65, Issue 56
Proposed Experiment for Testing Quantum Contextuality with Neutrons
journal, April 2008
 Cabello, Adán; Filipp, Stefan; Rauch, Helmut
 Physical Review Letters, Vol. 100, Issue 13
Experimental Test of Quantum Contextuality in Neutron Interferometry
journal, July 2009
 Bartosik, H.; Klepp, J.; Schmitzer, C.
 Physical Review Letters, Vol. 103, Issue 4
Unveiling contextual realities by microscopically entangling a neutron
journal, February 2020
 Shen, J.; Kuhn, S. J.; Dalgliesh, R. M.
 Nature Communications, Vol. 11, Issue 1
Neumark's theorem and quantum inseparability
journal, December 1990
 Peres, Asher
 Foundations of Physics, Vol. 20, Issue 12
Deviceindependent quantum key distribution secure against collective attacks
journal, April 2009
 Pironio, Stefano; Acín, Antonio; Brunner, Nicolas
 New Journal of Physics, Vol. 11, Issue 4