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AIP conference proceedings

Noise and entanglement in quantum conductors

Gordey B. Lesovik, A. V. Lebedev, Vladimir Lebedev, M. V. Feigel’man

Published Jan 1, 2009• 0 citations
Publisher

Abstract

In this article we discuss our two recent proposals on producing and detecting of entangled states in quantum conductors. First we analyze a setup where two electrons are scattered on a quantum dot with Coulomb repulsion and became orbitally entangled. Second, for identical noninteracting particles we suggest an operating scheme for the deliberate generation of spin‐entangled electron pairs in a normal‐metal mesoscopic structure with a fork geometry. The spin‐entangled pair is created through a post‐selection in the two branches of the fork. We also make comments on different ways of producing and quantifying the degree of entanglement.

DOI
10.1063/1.3149483

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In this article we discuss our two recent proposals on producing and detecting of entangled states in quantum conductors. First we analyze a setup where two electrons are scattered on a quantum dot with Coulomb repulsion and became orbitally entangled. Second, for identical noninteracting particles we suggest an operating scheme for the deliberate generation of spin‐entangled electron pairs in a normal‐metal mesoscopic structure with a fork geometry. The spin‐entangled pair is created through a post‐selection in the two branches of the fork. We also make comments on different ways of producing and quantifying the degree of entanglement.
We suggest an operating scheme for the deliberate generation of spin-entangled electron pairs in a normal-metal mesoscopic structure with fork geometry. Voltage pulses with associated Faraday flux equal to one flux unit ${\ensuremath{\Phi}}_{0}=hc∕e$ drive individual singlet pairs of electrons toward the beam splitter. The spin-entangled pair is created through a post-selection in the two branches of the fork. We analyze the appearance of entanglement in a Bell inequality test formulated in terms of the number of transmitted electrons with a given spin polarization.
Mesoscopic shot noise is not only probabilistic: it has features which reflect quantum mechanical entanglement. We discuss recent proposals of orbital entanglement generation and detection in mesoscopic coherent conductors. Orbital entanglement avoids the difficulty of manipulating spin and leads to simpler structures. Orbital entanglement schemes invoke two two‐particle sources. The index of the source plays the role of a pseudo‐spin. The rotation of qubits can be implemented with beam‐splitters or even just quantum point contacts. Entanglement is detected via violation of a Bell inequality. The necessary correlations can be extracted from shot noise measurements.
We present an investigation of orbital entanglement in mesoscopic conductors. Several schemes for generation of orbital entanglement are discussed, such as normal‐superconducting, electron‐hole and dynamic orbital entanglers. The generated, orbitally entangled state is investigated with the focus on the state emitted in an electronic analog of the optical Hanbury Brown Twiss experiment. The one and two particle properties of the emitted state are described in terms of reduced density matrices. Approaches to detect and characterize the entanglement based on zero frequency shot noise are discussed, with the focus on a complete reconstruction of the emitted state via quantum state tomography.
We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.
In this article, we have discussed about the scattering of charge and spin in spin-resolved mesoscopic systems. We have proposed a method to generate and detect the entanglement of electronic spin and electronic orbital degrees of freedom. It is observed that in a spin-resolved mesoscopic system, all form of entanglement existing between different electronic degrees of freedom can be generated. A method to detect Bell's inequality violation in terms of zero frequency current cross-correlators has been mentioned. Further, we have also studied the effect of quantum interference between spin flip and non-spin flip scattering matrices in determining the current and noise. We have obtained the expression for shot noise of spin and charge current when an arbitrarily polarised charge current is scattered at the spin resolved potential.
Mesoscopic shot noise is not only probabilistic: it has features which reflect quantum mechanical entanglement. We discuss recent proposals of orbital entanglement generation and detection in mesoscopic coherent conductors. Orbital entanglement avoids the difficulty of detecting spin and leads to simpler structures. Orbital entanglement schemes invoke two two-particle sources. The index of the source plays the role of a pseudo-spin. The rotation of qubits can be implemented with beam-splitters or even just quantum point contacts. Entanglement is detected via violation of a Bell inequality. The necessary correlations can be extracted from shot noise measurements. Possible two particle sources are Cooper pairs emitted from superconductors or even simpler electron-hole pairs generated at tunnel contacts or generated dynamically with the help of oscillating potentials.