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:1403.0916 · Physical Review B

Demonstrating entanglement by testing Bell's theorem in Majorana wires

David E. Drummond, Alexey A. Kovalev, Chang-Yu Hou, Kirill Shtengel, Leonid P. Pryadko

Published Sep 4, 2014• 9 citations
arXivHTMLPDF

Abstract

We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple ``keyboard'' gating, and projective measurement. Theoretical models and simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.

DOI
10.1103/physrevb.90.115404

Related papers

Ubiquitous Nonlocal Entanglement with Majorana Zero Modes

Alessandro Romito, Yuval Gefen

Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.

arXiv:1703.01841•Physical Review Letters•Oct 13, 2017•16 citations

Experimental Entangled Entanglement

Philip John Walther, Kevin J. Resch, Časlav Brukner +1 more

All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement."

arXiv:quant-ph/0508183•Physical Review Letters•Jul 11, 2006•50 citations

Experimental Methods for Detecting Entanglement

Joseph B. Altepeter, Evan R. Jeffrey, Paul G. Kwiat +3 more

Here we present experimental realizations of two new entanglement detection methods: a three-measurement Bell inequality inequivalent to the Clauser-Horne-Shimony-Holt inequality and a nonlinear Bell-type inequality based on the negativity measure. In addition, we provide an experimental and theoretical comparison between these new methods and several techniques already in use: the traditional Clauser-Horne-Shimony-Holt inequality, the entanglement witness, and complete state tomography.

Physical Review Letters•Jul 15, 2005•67 citations

Detection of entanglement and Bell's inequality violation

Kai Chen, Ling-An Wu

We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.

arXiv:quant-ph/0306137•Jun 20, 2003•1 citation

Quantum entanglement with Freedman's inequality

Jed Brody, Charlotte Selton

The assumption of local realism imposes constraints, such as Bell inequalities, on quantities obtained from measurements. In recent years, various tests of local realism have gained popularity in undergraduate laboratories, giving students the exciting opportunity to experimentally contradict this philosophical assumption. The standard test of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality requires 16 measurements, whereas a test of Freedman's inequality requires only three measurements. The calculations required to test Freedman's inequality are correspondingly simpler and the theory is less abstract. We suggest that students may benefit from testing Freedman's inequality before proceeding to the CHSH inequality and other more complicated experiments. Our measured data violated Freedman's inequality by more than six standard deviations.

American Journal of Physics•May 18, 2018•7 citations

Majorana braiding simulations with projective measurements

Philipp Frey, Themba Hodge, Eric Mascot +1 more

We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical qubit encodings, and on the transitions between them via projective parity measurements. Combined with hybridization, these operations extend the computational capabilities beyond braiding alone and enable universal gate sets. In addition to outlining the theoretical foundations-including the algebra of Majorana operators, along with the stabilizer formalism-we introduce an efficient numerical method for simulating the time-dependent dynamics of such systems. This method, based on the time dependent Pfaffian formalism, allows for the classical simulation of realistic device architectures that incorporate braiding, projective measurements, and disorder. The result is a semi-pedagogical overview and computational toolbox designed to support further exploration of topological quantum computing platforms.

arXiv:2508.10106•Physical review. B./Physical review. B•Feb 18, 2026•2 citations
We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is viable with realistic system parameters, simple ``keyboard'' gating, and projective measurement. Theoretical models and simulation results indicate entanglement can be demonstrated with moderately accurate gate operations. In addition to providing further evidence for the existence of the Majorana bound states, our proposal could be used as an experimental stepping stone to more complicated braiding experiments.
Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.
All previous tests of local realism have studied correlations between single-particle measurements. In the present experiment, we have performed a Bell experiment on three particles in which one of the measurements corresponds to a projection onto a maximally entangled state. We show theoretically and experimentally that correlations between these entangled measurements and single-particle measurements are too strong for any local-realistic theory and are experimentally exploited to violate a Clauser-Horne-Shimony-Holt-Bell inequality by more than 5 standard deviations. We refer to this possibility as "entangled entanglement."
We propose a new method for detecting entanglement of two qubits and discuss its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. Without the need for full quantum tomography for the density matrix we can experimentally detect the entanglement by measuring less than 9 local observables for any given state. We show that this test is stronger than the CHSH-Bell inequality and also gives an estimation for the degree of entanglement. If prior knowledge is available we can further greatly reduce the number of required local observables. The test is convenient and feasible with present experimental technology.
The assumption of local realism imposes constraints, such as Bell inequalities, on quantities obtained from measurements. In recent years, various tests of local realism have gained popularity in undergraduate laboratories, giving students the exciting opportunity to experimentally contradict this philosophical assumption. The standard test of the CHSH (Clauser–Horne–Shimony–Holt) Bell inequality requires 16 measurements, whereas a test of Freedman's inequality requires only three measurements. The calculations required to test Freedman's inequality are correspondingly simpler and the theory is less abstract. We suggest that students may benefit from testing Freedman's inequality before proceeding to the CHSH inequality and other more complicated experiments. Our measured data violated Freedman's inequality by more than six standard deviations.
We summarize the key ingredients required for universal topological quantum computation using Majorana zero modes in networks of topological superconductor nanowires. Particular emphasis is placed on the use of both sparse and dense logical qubit encodings, and on the transitions between them via projective parity measurements. Combined with hybridization, these operations extend the computational capabilities beyond braiding alone and enable universal gate sets. In addition to outlining the theoretical foundations-including the algebra of Majorana operators, along with the stabilizer formalism-we introduce an efficient numerical method for simulating the time-dependent dynamics of such systems. This method, based on the time dependent Pfaffian formalism, allows for the classical simulation of realistic device architectures that incorporate braiding, projective measurements, and disorder. The result is a semi-pedagogical overview and computational toolbox designed to support further exploration of topological quantum computing platforms.