© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1212.6924 · Physical Review B

Two-particle entanglement in capacitively coupled Mach-Zehnder interferometers

Andrey A. Vyshnevyy, A. V. Lebedev, Gordey B. Lesovik, G. Blatter

Published Apr 12, 2013• 13 citations

Abstract

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave packets into four components, of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching $\mathcal{B}=2.18>2$ in our setup.

DOI: 10.1103/physrevb.87.165302

Related papers

Entanglement in mesoscopic structures: Role of projection

A. V. Lebedev, G. Blatter, C. W. J. Beenakker +1 more

We present a theoretical analysis of the appearance of entanglement in noninteracting mesoscopic structures. Our setup involves two oppositely polarized sources injecting electrons of opposite spin into the two incoming leads. The mixing of these polarized streams in an ideal four-channel beam splitter produces two outgoing streams with particular tunable correlations. A Bell inequality test involving cross-correlated spin currents in opposite leads signals the presence of spin entanglement between particles propagating in different leads. We identify the role of fermionic statistics and projective measurement in the generation of these spin-entangled electrons.

arXiv:cond-mat/0311649•Physical Review B•Jun 15, 2004•38 citations

Postselective measurement of the electronic entanglement in the system of two Mach-Zehnder interferometers with coulomb interaction

A. A. Vishnevyy, Gordey B. Lesovik

The parameters at which the maximally entangled two-particle state appears in the system of two ideal electronic Mach-Zehnder interferometers are known. In this work, the operation of nonideal devices with finite scattering in splitters and with reflection in the region of the Coulomb Interaction has been considered. It has been shown that, under the condition of postselection of experimental results, these factors can increase the observed Bell parameter to values exceeding Cirel’son’s (or Tsirelson’s) bound equal to 2√2 up to the mathematical limit equal to 4. A simple postselective measurement scheme providing B = 4 has been described. Although the results of such measurements are not as fundamental as the observation of the violation of Bell’s inequality, they can indirectly indicate the existence of an entangled state in the system. The measurement system is more stable against fluctuations of the phase than a system without postselection. Furthermore, it has been found that the proposed system is optimal for investigation of cross correlations between interferometers in the dc regime (beyond the paradigm of the violation of Bell’s inequality) because they cannot be generated by coordinated fluctuations of Aharonov-Bohm phases.

Journal of Experimental and Theoretical Physics Letters•Dec 1, 2013•0 citations

Setup of three Mach-Zehnder interferometers for production and observation of Greenberger-Horne-Zeilinger entanglement of electrons

Andrey A. Vyshnevyy, Gordey B. Lesovik, Thibaut Jonckheere +1 more

We propose a new single-step scheme for the generation of a Greenberger-Horne-Zeilinger (GHZ) entangled state of three single-electron excitations (flying qubits). We also present a method to get a generalized GHZ state. Our idea relies upon the most recent progress in the field of on-demand electron sources and mesoscopic Mach-Zehnder interferometry. We also provide the recipe for the unambiguous detection of this GHZ state via correlation measurements at the output, which imply the violation of a Bell-type inequality which is generalized to the case of three particles. We explain how such measurements can be achieved in the context of Mach-Zehnder interferometry and draw an actual prototype device which could be achieved with point contacts and metallic gates placed on a GaAs sample, in the integer quantum Hall effect regime.

arXiv:1204.5850•Physical Review B•Apr 9, 2013•7 citations

Entanglement in a Noninteracting Mesoscopic Structure

A. V. Lebedev

We study time dependent electron‐electron and electron‐hole correlations in a mesoscopic device splitting an incident current of free fermions into two spacially separated particle streams. We analyze the appearance of entanglement as manifested through a Bell inequality test and identify its origin as the Fermi statistics forcing the reservoir to inject spin‐singlet pairs. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies.

AIP conference proceedings•Jan 1, 2005•0 citations

Two-Particle Nonlocal Aharonov-Bohm Effect from Two Single-Particle Emitters

Janine Splettstoesser, Michael V. Moskalets, Μ. Büttiker

We propose a mesoscopic circuit in the quantum Hall effect regime comprising two uncorrelated single-particle sources and two distant Mach-Zehnder interferometers with magnetic fluxes, which allows us in a controllable way to produce orbitally entangled electrons. Two-particle correlations appear as a consequence of erasing of which-path information due to collisions taking place at distant interferometers and in general at different times. The two-particle correlations manifest themselves as an Aharonov-Bohm effect in noise, while the current is insensitive to magnetic fluxes. In an appropriate time interval the concurrence reaches a maximum and a Bell inequality is violated.

arXiv:0905.0787•Physical Review Letters•Aug 13, 2009•88 citations

Entanglement in a noninteracting mesoscopic structure

A. V. Lebedev, Gordey B. Lesovik, G. Blatter

We study the time-dependent electron-electron and electron-hole correlations in a mesoscopic device which is splitting an incident current of free fermions into two spatially separated particle streams. We analyze the appearance of entanglement as manifested in a Bell inequality test and discuss its origin in terms of local spin-singlet correlations already present in the initial channel and the action of post-selection during the Bell-type measurement. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies. We compare our results with alternative Bell inequality tests based on coincidence probabilities.

arXiv:cond-mat/0311423•Physical Review B•Jan 11, 2005•47 citations

We propose and analyze a mesoscopic device producing on-demand entangled pairs of electrons. The system consists of two capacitively coupled Mach-Zehnder interferometers implemented in a quantum Hall structure. A pair of electron wave packets is injected into the chiral edge states of two (of the four) incoming arms; scattering on the incoming interferometers splits the wave packets into four components, of which two interact. The resulting interaction phase associated with this component leads to the entanglement of the state; the latter is scattered at the outgoing beam splitter and analyzed in a Bell violation test measuring the presence of particles in the four outgoing leads. We study the two-particle case and determine the conditions to reach and observe full entanglement. We extend our two-particle analysis to include the underlying Fermi seas in the quantum Hall device; the change in shape of the wave function, the generation of electron-hole pairs in the interaction regime, and a time delay between the pulses all reduce the degree of visible entanglement and the violation of the Bell inequality, effects which we analyze quantitatively. We determine the device settings optimizing the entanglement and the Bell test and find that violation is still possible in the presence of the Fermi seas, with a maximal Bell parameter reaching

\mathcal{B}=2.18>2

in our setup.

We present a theoretical analysis of the appearance of entanglement in noninteracting mesoscopic structures. Our setup involves two oppositely polarized sources injecting electrons of opposite spin into the two incoming leads. The mixing of these polarized streams in an ideal four-channel beam splitter produces two outgoing streams with particular tunable correlations. A Bell inequality test involving cross-correlated spin currents in opposite leads signals the presence of spin entanglement between particles propagating in different leads. We identify the role of fermionic statistics and projective measurement in the generation of these spin-entangled electrons.

The parameters at which the maximally entangled two-particle state appears in the system of two ideal electronic Mach-Zehnder interferometers are known. In this work, the operation of nonideal devices with finite scattering in splitters and with reflection in the region of the Coulomb Interaction has been considered. It has been shown that, under the condition of postselection of experimental results, these factors can increase the observed Bell parameter to values exceeding Cirel’son’s (or Tsirelson’s) bound equal to 2√2 up to the mathematical limit equal to 4. A simple postselective measurement scheme providing B = 4 has been described. Although the results of such measurements are not as fundamental as the observation of the violation of Bell’s inequality, they can indirectly indicate the existence of an entangled state in the system. The measurement system is more stable against fluctuations of the phase than a system without postselection. Furthermore, it has been found that the proposed system is optimal for investigation of cross correlations between interferometers in the dc regime (beyond the paradigm of the violation of Bell’s inequality) because they cannot be generated by coordinated fluctuations of Aharonov-Bohm phases.

We propose a new single-step scheme for the generation of a Greenberger-Horne-Zeilinger (GHZ) entangled state of three single-electron excitations (flying qubits). We also present a method to get a generalized GHZ state. Our idea relies upon the most recent progress in the field of on-demand electron sources and mesoscopic Mach-Zehnder interferometry. We also provide the recipe for the unambiguous detection of this GHZ state via correlation measurements at the output, which imply the violation of a Bell-type inequality which is generalized to the case of three particles. We explain how such measurements can be achieved in the context of Mach-Zehnder interferometry and draw an actual prototype device which could be achieved with point contacts and metallic gates placed on a GaAs sample, in the integer quantum Hall effect regime.

We study time dependent electron‐electron and electron‐hole correlations in a mesoscopic device splitting an incident current of free fermions into two spacially separated particle streams. We analyze the appearance of entanglement as manifested through a Bell inequality test and identify its origin as the Fermi statistics forcing the reservoir to inject spin‐singlet pairs. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies.

We propose a mesoscopic circuit in the quantum Hall effect regime comprising two uncorrelated single-particle sources and two distant Mach-Zehnder interferometers with magnetic fluxes, which allows us in a controllable way to produce orbitally entangled electrons. Two-particle correlations appear as a consequence of erasing of which-path information due to collisions taking place at distant interferometers and in general at different times. The two-particle correlations manifest themselves as an Aharonov-Bohm effect in noise, while the current is insensitive to magnetic fluxes. In an appropriate time interval the concurrence reaches a maximum and a Bell inequality is violated.

We study the time-dependent electron-electron and electron-hole correlations in a mesoscopic device which is splitting an incident current of free fermions into two spatially separated particle streams. We analyze the appearance of entanglement as manifested in a Bell inequality test and discuss its origin in terms of local spin-singlet correlations already present in the initial channel and the action of post-selection during the Bell-type measurement. The time window over which the Bell inequality is violated is determined in the tunneling limit and for the general situation with arbitrary transparencies. We compare our results with alternative Bell inequality tests based on coincidence probabilities.