skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Certified quantum measurement of Majorana fermions

Abstract

Here, we propose a quantum self-testing 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.

Authors:
 [1];  [2]; ORCiD logo [1];  [2]
  1. Indiana Univ., Bloomington, IN (United States)
  2. 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 2469-9926
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 self-testing 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

New directions in the pursuit of Majorana fermions in solid state systems
journal, June 2012


Teoria simmetrica dell’elettrone e del positrone
journal, April 1937


Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices
journal, April 2012


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
  • DOI: 10.1038/nphys2429

Zero-Bias Peaks in the Tunneling Conductance of Spin-Orbit-Coupled Superconducting Wires with and without Majorana End-States
journal, December 2012


Many-Body Characterization of Particle-Conserving Topological Superfluids
journal, December 2014


What is a particle-conserving Topological Superfluid? The fate of Majorana modes beyond mean-field theory
journal, September 2016


Measurement-only topological quantum computation via anyonic interferometry
journal, April 2009


Device-Independent Security of Quantum Cryptography against Collective Attacks
journal, June 2007


Private randomness expansion with untrusted devices
journal, February 2011


Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes
journal, June 2017


Which states violate Bell's inequality maximally?
journal, October 1992


Ubiquitous Nonlocal Entanglement with Majorana Zero Modes
journal, October 2017


Incompatible results of quantum measurements
journal, December 1990


Simple unified form for the major no-hidden-variables theorems
journal, December 1990


Robust self-testing of the three-qubit W state
journal, October 2014


Analytic and Nearly Optimal Self-Testing Bounds for the Clauser-Horne-Shimony-Holt and Mermin Inequalities
journal, August 2016


All pure bipartite entangled states can be self-tested
journal, May 2017

  • Coladangelo, Andrea; Goh, Koon Tong; Scarani, Valerio
  • Nature Communications, Vol. 8, Issue 1
  • DOI: 10.1038/ncomms15485

Rigidity of the magic pentagram game
journal, November 2017


Self-testing of binary observables based on commutation
journal, June 2017


Robust and Versatile Black-Box Certification of Quantum Devices
journal, July 2014


Physical characterization of quantum devices from nonlocal correlations
journal, February 2015


Efficient eigenvalue determination for arbitrary Pauli products based on generalized spin-spin interactions
journal, December 2017


Proposed Experiment for Testing Quantum Contextuality with Neutrons
journal, April 2008


Experimental Test of Quantum Contextuality in Neutron Interferometry
journal, July 2009


Unveiling contextual realities by microscopically entangling a neutron
journal, February 2020


Neumark's theorem and quantum inseparability
journal, December 1990


Device-independent quantum key distribution secure against collective attacks
journal, April 2009