Quantum Computation and Spin Electronics

In this chapter we explore the connection between mesoscopic physics and quantum computing. After giving a bibliography providing a general introduction to the subject of quantum information processing, we review the various approaches that are being considered for the experimental implementation of quantum computing and quantum communication in atomic physics, quantum optics, nuclear magnetic resonance, superconductivity, and, especially, normal-electron solid state physics. We discuss five criteria for the realization of a quantum computer and consider the implications that these criteria have for quantum computation using the spin states of single-electron quantum dots. Finally, we consider the transport of quantum information via the motion of individual electrons in mesoscopic structures; specific transport and noise measurements in coupled quantum dot geometries for detecting and characterizing electron-state entanglement are analyzed.Comment: 28 pages RevTeX, 4 figures. To be published in "Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics," eds. I. O. Kulik and R. Ellialtioglu (NATO Advanced Study Institute, Turkey, June 13-25, 1999

Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer

It was recently suggested that a novel type of phase transition may occur in the visibility of electronic Mach-Zehnder Interferometers. Here, we present experimental evidence for the existence of this transition. The transition is induced by strongly non-Gaussian noise that originates from the strong coupling of a quantum point contact to the interferometer. We provide a transparent physical picture of the effect, by exploiting a close analogy to the neutrino-oscillations of particle physics. In addition, our experiment constitutes a probe of the singularity of the elusive full counting statistics of a quantum point contact.Comment: 7 pages, 4 figures (+Supplement 8 pages, 9 figures

Multiparticle Interference, GHZ Entanglement, and Full Counting Statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown--Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.Comment: 4 pages, 1 figure, published versio

Detection of non-Gaussian Fluctuations in a Quantum Point Contact

An experimental study of current fluctuations through a tunable transmission barrier, a quantum point contact, are reported. We measure the probability distribution function of transmitted charge with precision sufficient to extract the first three cumulants. To obtain the intrinsic quantities, corresponding to voltage-biased barrier, we employ a procedure that accounts for the response of the external circuit and the amplifier. The third cumulant, obtained with a high precision, is found to agree with the prediction for the statistics of transport in the non-Poissonian regime.Comment: 4 pages, 4 figures; published versio

Orbital entanglement and violation of Bell inequalities in mesoscopic conductors

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.Comment: 4 pages, 2 figure

Semi-classical Theory of Conductance and Noise in Open Chaotic Cavities

Conductance and shot noise of an open cavity with diffusive boundary scattering are calculated within the Boltzmann-Langevin approach. In particular, conductance contains a non-universal geometric contribution, originating from the presence of open contacts. Subsequently, universal expressions for multi-terminal conductance and noise valid for all chaotic cavities are obtained classically basing on the fact that the distribution function in the cavity depends only on energy and using the principle of minimal correlations.Comment: 4 pages, 1 .eps figur

Cascade Boltzmann - Langevin approach to higher-order current correlations in diffusive metal contacts

The Boltzmann - Langevin approach is extended to calculations of third and fourth cumulants of current in diffusive-metal contacts. These cumulants result from indirect correlations between current fluctuations, which may be considered as "noise of noise". The calculated third cumulant coincides exactly with its quantum-mechanical value. The fourth cumulant tends to its quantum-mechanical value $-e^3I/105$ at high voltages and to a positive value $2e^2T/3R$ at V=0 changing its sign at $eV \sim 20T$.Comment: 6 pages, 2 eps figures, typo corrected, minor change