Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1904.12207 · Physical Review A

Certified quantum measurement of Majorana fermions

Abu Ashik Irfan, Karl Mayer, Gerardo Ortíz, Emanuel H. Knill

Published Mar 12, 2020• 14 citations
arXivHTMLPDF

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. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\ensuremath{\langle}W\ensuremath{\rangle}\ensuremath{\le}3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\ensuremath{\langle}W\ensuremath{\rangle}=5$ indicates the degree of confidence in the detection of Majorana fermions.

DOI
10.1103/physreva.101.032106

Related papers

Certifying Majorana Fermions with Elegant-Like Bell Inequalities and a New Self-Testing Equivalence

Patryk Michalski, Arturo Konderak, Wojciech Bruzda +1 more

Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable through quantum strategies, is rarely accessible analytically. In this work, we introduce a general construction of Bell inequalities for which this bound can be computed exactly. Our framework generalizes both the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, yielding Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, our inequalities also enable the device-independent certification of Majorana fermions, understood as multiqubit realizations of Clifford algebra generators. Importantly, we identify an additional equivalence that must be incorporated into the definition of self-testing beyond invariance under local isometries and transposition. This equivalence arises from partial transposition applied to the shared state and to the measurements, which in specific cases leaves all observed correlations unchanged.

quant-pharXiv:2511.17764•Nov 25, 2025•0 citations

A Robust Protocol for Self-Testing Majorana Fermions

Karl Mayer

Majorana fermions arising in superconducting nanowires are of interest both for fundamental reasons and due to their potential use as building blocks for a topological quantum computer. While recent experiments have reported strong evidence of Majorana fermions in the form of occupation of a zero-energy fermionic mode, there is still disagreement about whether the observed data can be explained by other mechanisms. Furthermore, to be useful for quantum computation, the fermionic parities of zero-energy modes must be measured with high fidelity. In this thesis, we apply a quantum information protocol known as self-testing to a system of Majorana fermions. A self-testing protocol is a statistical test for certifying a quantum state and a set of measurement operators from experimentally determined expectation values, under minimal physical assumptions. Such a test treats the system as a black-box and relies only on the distributions of measurement outcomes given device settings. For the protocol described in this thesis, if the test is passed, then a set of measurements that ideally are of fermionic parities are certified to have the exact anticommutation relations as determined by the anticommutativity of Majorana fermion operators. The protocol is robust in the sense that bounds on the state and operator fidelities can still be established in the presence of small experimental imperfections. Finally, a rigorous statistical analysis is used to derive a confidence interval for the certified fidelities given a finite experimental data set.

•Jan 1, 2019•0 citations

Self-testing nonprojective quantum measurements in prepare-and-measure experiments

Armin Tavakoli, Massimiliano Smania, Tamás Vértesi +2 more

Self-testing represents the strongest form of certification of a quantum system. Here, we theoretically and experimentally investigate self-testing of nonprojective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension and develop methods for (i) robustly self-testing extremal qubit POVMs and (ii) certifying that an uncharacterized qubit measurement is nonprojective. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data imply that the implemented measurements are very close to certain ideal three- and four-outcome qubit POVMs and hence non-projective. In the latter case, the data certify a genuine four-outcome qubit POVM. Our results open interesting perspective for semi-device-independent certification of quantum devices.

arXiv:1811.12712•Science Advances•Apr 17, 2020•84 citations

Practical Tests and Witnesses of Fermionic non-Gaussianity

Tobias Haug, Xhek Turkeshi, Piotr Sierant

Fermionic Gaussian states describe free fermions and underlie the mean-field picture of matter, from metals to superconductors; they are also efficiently simulable on classical computers. Departures from Gaussianity -- the correlations produced by interactions -- are therefore what make a fermionic system hard to simulate classically and useful for quantum computation, analogous to the role of magic in stabilizer-based quantum computation. Yet detecting and quantifying such non-Gaussianity at scale has remained challenging. Here we introduce practical tests and witnesses of fermionic non-Gaussianity built on fermionic antiflatness, a measure derived from the two-point covariance matrix. We estimate it with two protocols -- a two-copy Bell measurement and a single-copy scheme using commuting Majorana bilinears -- that determine whether a state is Gaussian or far from it at lower measurement cost than existing approaches, using only operations native to fault-tolerant hardware. For mixed states, a purity-corrected witness certifies non-Gaussianity and remains robust under strong noise; running it on the IQM quantum processor, we find that noise can both reduce and enhance non-Gaussianity. Finally, we show that preparing pseudorandom fermionic states requires extensive non-Gaussianity. Together, these tools enable the study and certification of non-Gaussian fermionic resources on present-day quantum devices.

quant-pharXiv:2605.26218•May 27, 2026•0 citations

Certification of two-qubit quantum systems with temporal inequality

Chellasamy Jebarathinam, Gautam Sharma, Sk Sazim +1 more

Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Irfan et al. [A. A. M. Irfan, K. Mayer, G. Ortiz, and E. Knill, Phys. Rev. A 101, 032106 (2020)] a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this paper, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from noncontextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.

arXiv:2307.06710•Physical Review A•Aug 6, 2024•2 citations

Protocol for detecting the nonlocality of the multi-Majorana Systems

Liu, Bai-Ting, Qian, Peng, Cao, Zhan +1 more

Majorana zero modes (MZMs) are non-Abelian quasiparticles with the potential to serve as topological qubits for fault-tolerant quantum computing due to their ability to encode quantum information nonlocally. In multi-Majorana systems configured into two separated subsystems, nontrivial quantum correlations persist, but the presence of trivial Andreev bound states (ABSs) can obscure this nonlocality if MZM preparation fails. To address this, we propose a protocol using an entanglement witness based solely on parity measurements to distinguish the nonlocal characteristics of MZM systems. Our framework, which is experimentally implementable, achieves a detection probability of approximately 18% in a 6-site system and demonstrates robustness under environmental noise, albeit with a reduced detection rate in the resence of quasiparticle contamination.

arXiv:2506.17003•Jun 20, 2025•0 citations
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. We propose to analyze experimental outcomes in terms of a contextuality witness WWW, which satisfies \ensuremath⟨W\ensuremath⟩\ensuremath≤3\ensuremath{\langle}W\ensuremath{\rangle}\ensuremath{\le}3\ensuremath⟨W\ensuremath⟩\ensuremath≤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 \ensuremath⟨W\ensuremath⟩=5\ensuremath{\langle}W\ensuremath{\rangle}=5\ensuremath⟨W\ensuremath⟩=5 indicates the degree of confidence in the detection of Majorana fermions.
Bell inequalities provide a fundamental tool for probing nonlocal correlations, yet their quantum bound, that is, the maximal value attainable through quantum strategies, is rarely accessible analytically. In this work, we introduce a general construction of Bell inequalities for which this bound can be computed exactly. Our framework generalizes both the Clauser-Horne-Shimony-Holt and Gisin's elegant inequalities, yielding Bell expressions maximally violated by any number of pairwise anticommuting Clifford observables together with the corresponding maximally entangled state. Under suitable assumptions, our inequalities also enable the device-independent certification of Majorana fermions, understood as multiqubit realizations of Clifford algebra generators. Importantly, we identify an additional equivalence that must be incorporated into the definition of self-testing beyond invariance under local isometries and transposition. This equivalence arises from partial transposition applied to the shared state and to the measurements, which in specific cases leaves all observed correlations unchanged.
Majorana fermions arising in superconducting nanowires are of interest both for fundamental reasons and due to their potential use as building blocks for a topological quantum computer. While recent experiments have reported strong evidence of Majorana fermions in the form of occupation of a zero-energy fermionic mode, there is still disagreement about whether the observed data can be explained by other mechanisms. Furthermore, to be useful for quantum computation, the fermionic parities of zero-energy modes must be measured with high fidelity. In this thesis, we apply a quantum information protocol known as self-testing to a system of Majorana fermions. A self-testing protocol is a statistical test for certifying a quantum state and a set of measurement operators from experimentally determined expectation values, under minimal physical assumptions. Such a test treats the system as a black-box and relies only on the distributions of measurement outcomes given device settings. For the protocol described in this thesis, if the test is passed, then a set of measurements that ideally are of fermionic parities are certified to have the exact anticommutation relations as determined by the anticommutativity of Majorana fermion operators. The protocol is robust in the sense that bounds on the state and operator fidelities can still be established in the presence of small experimental imperfections. Finally, a rigorous statistical analysis is used to derive a confidence interval for the certified fidelities given a finite experimental data set.
Self-testing represents the strongest form of certification of a quantum system. Here, we theoretically and experimentally investigate self-testing of nonprojective quantum measurements. That is, how can one certify, from observed data only, that an uncharacterized measurement device implements a desired nonprojective positive-operator valued measure (POVM). We consider a prepare-and-measure scenario with a bound on the Hilbert space dimension and develop methods for (i) robustly self-testing extremal qubit POVMs and (ii) certifying that an uncharacterized qubit measurement is nonprojective. Our methods are robust to noise and thus applicable in practice, as we demonstrate in a photonic experiment. Specifically, we show that our experimental data imply that the implemented measurements are very close to certain ideal three- and four-outcome qubit POVMs and hence non-projective. In the latter case, the data certify a genuine four-outcome qubit POVM. Our results open interesting perspective for semi-device-independent certification of quantum devices.
Fermionic Gaussian states describe free fermions and underlie the mean-field picture of matter, from metals to superconductors; they are also efficiently simulable on classical computers. Departures from Gaussianity -- the correlations produced by interactions -- are therefore what make a fermionic system hard to simulate classically and useful for quantum computation, analogous to the role of magic in stabilizer-based quantum computation. Yet detecting and quantifying such non-Gaussianity at scale has remained challenging. Here we introduce practical tests and witnesses of fermionic non-Gaussianity built on fermionic antiflatness, a measure derived from the two-point covariance matrix. We estimate it with two protocols -- a two-copy Bell measurement and a single-copy scheme using commuting Majorana bilinears -- that determine whether a state is Gaussian or far from it at lower measurement cost than existing approaches, using only operations native to fault-tolerant hardware. For mixed states, a purity-corrected witness certifies non-Gaussianity and remains robust under strong noise; running it on the IQM quantum processor, we find that noise can both reduce and enhance non-Gaussianity. Finally, we show that preparing pseudorandom fermionic states requires extensive non-Gaussianity. Together, these tools enable the study and certification of non-Gaussian fermionic resources on present-day quantum devices.
Self-testing of quantum devices based on observed measurement statistics is a method to certify quantum systems using minimal resources. In Irfan et al. [A. A. M. Irfan, K. Mayer, G. Ortiz, and E. Knill, Phys. Rev. A 101, 032106 (2020)] a scheme based on observing measurement statistics that demonstrate Kochen-Specker contextuality has been shown to certify two-qubit entangled states and measurements without the requirement of spatial separation between the subsystems. However, this scheme assumes a set of compatibility conditions on the measurements which are crucial to demonstrating Kochen-Specker contextuality. In this paper, we propose a self-testing protocol to certify the above two-qubit states and measurements without the assumption of the compatibility conditions, and at the same time without requiring the spatial separation between the subsystems. Our protocol is based on the observation of sequential correlations leading to the maximal violation of a temporal inequality derived from noncontextuality inequality. Moreover, our protocol is robust to small experimental errors or noise.
Majorana zero modes (MZMs) are non-Abelian quasiparticles with the potential to serve as topological qubits for fault-tolerant quantum computing due to their ability to encode quantum information nonlocally. In multi-Majorana systems configured into two separated subsystems, nontrivial quantum correlations persist, but the presence of trivial Andreev bound states (ABSs) can obscure this nonlocality if MZM preparation fails. To address this, we propose a protocol using an entanglement witness based solely on parity measurements to distinguish the nonlocal characteristics of MZM systems. Our framework, which is experimentally implementable, achieves a detection probability of approximately 18% in a 6-site system and demonstrates robustness under environmental noise, albeit with a reduced detection rate in the resence of quasiparticle contamination.