Dephasing of entangled electron-hole pairs in a degenerate electron gas

A tunnel barrier in a degenerate electron gas was recently discovered as a source of entangled electron-hole pairs. Here, we investigate the loss of entanglement by dephasing. We calculate both the maximal violation E_max of the Bell inequality and the degree of entanglement (concurrence) C. If the initially maximally entangled electron-hole pair is in a Bell state, then the Bell inequality is violated for arbitrary strong dephasing. The same relation E_max=2\sqrt{1+C^{2}} then holds as in the absence of dephasing. More generally, for a maximally entangled superposition of Bell states, the Bell inequality is satisfied for a finite dephasing strength and the entanglement vanishes for somewhat stronger (but still finite) dephasing strength. There is then no one-to-one relation between E_max and C.Comment: 7 pages with 3 figures, special style file included; To appear in a special issue on "Quantum Computation at the Atomic Scale" in Turkish Journal of Physic

Scattering theory of plasmon-assisted entanglement transfer and distillation

We analyse the quantum mechanical limits to the plasmon-assisted entanglement transfer observed by E. Altewischer, M.P. van Exter, and J.P. Woerdman [Nature, 418, 304 (2002)]. The maximal violation S of Bell's inequality at the photodetectors behind two linear media (such as the perforated metal films in the experiment) can be described by two ratio's tau_1, tau_2 of polarization-dependent transmission probabilities. A fully entangled incident state is transferred without degradation for tau_1=tau_2, but a relatively large mismatch of tau_1 and tau_2 can be tolerated with a small reduction of S. We predict that fully entangled Bell pairs can be distilled out of partially entangled radiation if tau_1 and tau_2 satisfy a pair of inequalities.Comment: 4 pages including 2 figures; two references added, plasmon model include

Entanglement detection for electrons via witness operators

We discuss an implementation of the entanglement witness, a method to detect entanglement with few local measurements, in systems where entangled electrons are generated both in the spin and orbital degrees of freedom. We address the efficiency of this method in various setups, including two different particle-hole entanglement structures, and we demonstrate that it can also be used to infer information on the possible dephasing afflicting the devices.Comment: 12 pages, 5 figures; published versio

Production and detection of entangled electron-hole pairs in a degenerate electron gas

We demonstrate theoretically that the shot noise produced by a tunnel barrier in a two-channel conductor violates a Bell inequality. The non-locality is shown to originate from entangled electron-hole pairs created by tunneling events -- without requiring electron-electron interactions. The degree of entanglement (concurrence) equals 2(T_1 T_2)^1/2 (T_1+T_2)^-1, with T_1,T_2 << 1 the transmission eigenvalues. A pair of edge channels in the quantum Hall effect is proposed as experimental realization.Comment: 4 pages including 1 figure; three comments have been added to the reference list, addressing the entanglement of formation, the Clauser-Horne inequality, and the dephasing effect of a finite voltag

Proposal for production and detection of entangled electron-hole pairs in a degenerate electron gas

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Clauser-Horne inequality and decoherence in mesoscopic conductors

We analyze the effect of decoherence on the violation of the Clauser-Horne (CH) inequality for the full electron counting statistics in a mesoscopic multiterminal conductor. Our setup consists of an entangler that emits a flux of entangled electrons into two conductors characterized by a scattering matrix and subject to decoherence. Loss of phase memory is modeled phenomenologically by introducing fictitious extra leads. The outgoing electrons are detected using spin-sensitive electron counters. Given a certain average number of incoming entangled electrons, the CH inequality is evaluated as a function of the numbers of detected particles and on the various quantities characterizing the scattering matrix. When decoherence is turned on, we show that the amount of violation of the CH inequality is effectively reduced. Interestingly we find that, by adjusting the parameters of the system, there exists a protected region of $Q$ values for which violation holds for arbitrary strong decoherence.Comment: 14 pages, 10 figures. Published versio

Hamiltonian dynamics of the two-dimensional lattice phi^4 model

The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the presence of the continuous phase transition at a finite energy density and are consistent both qualitatively and quantitatively with the predictions of equilibrium statistical mechanics. The Hamiltonian microscopic dynamics also exhibits critical slowing down close to the transition. Moreover, the relationship between chaos and the phase transition is considered, and interpreted in the light of a geometrization of dynamics.Comment: REVTeX, 24 pages with 20 PostScript figure

Production and detection of three-qubit entanglement in the Fermi sea

Building on a previous proposal for the entanglement of electron-hole pairs in the Fermi sea, we show how 3 qubits can be entangled without using electron-electron interactions. As in the 2-qubit case, this electronic scheme works even if the sources are in (local) thermal equilibrium -- in contrast to the photonic analogue. The 3 qubits are represented by 4 edge-channel excitations in the quantum Hall effect (2 hole excitations plus 2 electron excitations with identical channel index). The entangler consists of an adiabatic point contact flanked by a pair of tunneling point contacts. The irreducible 3-qubit entanglement is characterized by the tangle, which is expressed in terms of the transmission matrices of the tunneling point contacts. The maximally entangled Greenberger-Horne-Zeilinger (GHZ) state is obtained for channel-independent tunnel probabilities. We show how low-frequency noise measurements can be used to determine an upper and lower bound to the tangle. The bounds become tighter the closer the electron-hole state is to the GHZ state.Comment: 8 pages including 4 figures; [2017: fixed broken postscript figures