Entanglement in a noninteracting mesoscopic structure

Abstract

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.

Generating spin-entangled electron pairs in normal conductors using voltage pulses

“…8, where a constant voltage V has been applied to the source lead 's'. In this case, the source reservoir injects a regular sequence of spin-singlet pairs of electrons separated by the voltage time τ V = h/eV ; the Bell inequality then is violated at short times only.…”

“…Early proposals for structures generating streams of entangled particles exploit the interaction between electrons as a resource for producing entanglement, the pairing interaction in superconductors 1 or the repulsive Coulomb interaction in confined geometries 2,3 . Recently, another class of devices has been suggested which avoids direct interparticle interaction; instead, the entanglement originates from a proper post-selection of orbital 4,5,6 or spin 7,8,9 degrees of freedom. The majority of these proposals deals with the situation where the entangled particles are emitted in a random and uncontrolled fashion, while entanglement on demand is implicit in the scheme proposed in Ref.…”

“…In this device, spin-entangled electron pairs are generated via the injection of spin-singlet pairs into the source lead from the reservoir 8 . This entanglement is made accessible by splitting the pair into the two leads 'u' and 'd' and subsequent projection (through the Bell measurement) to that part of the wave function describing separated electrons travelling in different leads 8,9 . Rather then quantum pumping with a cyclic potential as in Refs.…”

Bell’s inequality test with time-delayed two-particle correlations

“…Choosing different space separations between the regions A and B allows one to change the phase ϕ AB and mixing by U ⊗ U generates a second rotation parametrized by the angle θ. Calculating the joint probabilities P α1α2 (AB) ∝ | α 1 α 2 |Ψ out AB | 2 for the four settings α 1 α 2 ∈ {uu, ud, du, dd} we find the Bell correlation functions E AB as given by (9) and choosing appropriate angles ϕ AB , ϕ AB ′ , ϕ A ′ B , ϕ A ′ B ′ and θ one finds the Bell inequalities violated.…”

Orbital entanglement and electron localization in quantum wires

“…In addition, the concept has been remarkably useful to shed new light on well-studied fields such as mesoscopic transport. Electron entanglement can be produced either by interacting mechanisms [3][4][5][6][7][8] (e.g., exchange coupling and superconducting pairing) or noninteracting ones [9][10][11][12][13][14][15] (based on exchange correlations in scattering processes from external potentials). Electronic devices such as quantum dots and quantum wires have been proposed to produce entanglement of electrons without interactions [16,17].…”