Entanglement in mesoscopic structures: Role of projection

Abstract

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.

Controllable spin entanglement production in a quantum spin Hall ring

“…We project this state to the realization that each detector receives exactly one electron. This process is referred to as postselection [37,38]. Thus, we keep only the terms in Eq.…”

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

“…Furthermore, this violation is independent of the transparencies T u , T d and hence universal; moreover, the Bell inequality (20) scat onto the spin-entangled component. Thus the origin of the entanglement is found in the post-selection during the crosscorrelation measurement effectuated in the Bell inequality test 6,9 . From an experimental point of view it may be difficult to produce voltage pulses driving exactly one (spinless) particle n = 1.…”

“…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.…”

“…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.…”

Suppression of visibility in a two-electron Mach-Zehnder interferometer

“…4 for recent review͒; most of them use interaction to create entangled pairs. For noninteracting electrons, the proposals include spatial separation of spin-polarized particles 5,6 or, indeed, edge states in the quantum Hall effect regime. 2,7 We also note that proposals for manifestations of non-Abelian statistics 8,9 rely, in fact, on entanglement of the appropriate quasiparticles.…”