Extremal quantum cloning machines

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are "extremal" in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called "double-Bell states", whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our result can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacements.Comment: revised version accepted for publicatio

Size and Shape Dependence of the Electronic Structure of Gold Nanoclusters on TiO2

Understanding the mechanism behind the superior catalytic power of single- or few-atom heterogeneous catalysts has become an important topic in surface chemistry. This is particularly the case for gold, with TiO2 being an efficient support. Here we use scanning tunneling microscopy/spectroscopy with theoretical calculations to investigate the adsorption geometry and local electronic structure of several-atom Au clusters on rutile TiO2(110), with the clusters fabricated by controlled manipulation of single atoms. Our study confirms that Au1 and Au2 clusters prefer adsorption at surface O vacancies. Au3 clusters adsorb at O vacancies in a linear-chain configuration parallel to the surface; in the absence of O vacancies they adsorb at Ti5c sites with a structure of a vertically pointing upright triangle. We find that both the electronic structure and cluster–substrate charge transfer depend critically on the cluster size, bonding configuration, and local environment. This suggests the possibility of engineering cluster selectivity for specific catalytic reactions

Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning

We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in [Devetak and Winter, Proc. of the Roy. Soc. of London Series A, 461, 207 (2005); Kraus, Gisin and Renner, Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in d-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, d and d+1 mutually unbiased bases where d is a prime, and show that for the protocols with 2 and d+1 MUBs the optimal attack is an optimal cloner, but for the protocols with d MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the BB84 protocol or the 6-state protocol

Lattice worldline representation of correlators in a background field

We use a discrete worldline representation in order to study the continuum limit of the one-loop expectation value of dimension two and four local operators in a background field. We illustrate this technique in the case of a scalar field coupled to a non-Abelian background gauge field. The first two coefficients of the expansion in powers of the lattice spacing can be expressed as sums over random walks on a d-dimensional cubic lattice. Using combinatorial identities for the distribution of the areas of closed random walks on a lattice, these coefficients can be turned into simple integrals. Our results are valid for an anisotropic lattice, with arbitrary lattice spacings in each direction.Comment: 54 pages, 14 figure

Neutrino Telescopes' Sensitivity to Dark Matter

The nature of the dark matter of the Universe is yet unknown and most likely is connected with new physics. The search for its composition is under way through direct and indirect detection. Fundamental physical aspects such as energy threshold, geometry and location are taken into account to investigate proposed neutrino telescopes of km^3 volume sensitivities to dark matter. These sensitivities are just sufficient to test a few WIMP scenarios. Telescopes of km^3 volume, such as IceCube, can definitely discover or exclude superheavy (M > 10^10 GeV) Strong Interacting Massive Particles (Simpzillas). Smaller neutrino telescopes such as ANTARES, AMANDA-II and NESTOR can probe a large region of the Simpzilla parameter space.Comment: 28 pages, 9 figure

Search for Point Sources of High Energy Neutrinos with AMANDA

This paper describes the search for astronomical sources of high-energy neutrinos using the AMANDA-B10 detector, an array of 302 photomultiplier tubes, used for the detection of Cherenkov light from upward traveling neutrino-induced muons, buried deep in ice at the South Pole. The absolute pointing accuracy and angular resolution were studied by using coincident events between the AMANDA detector and two independent telescopes on the surface, the GASP air Cherenkov telescope and the SPASE extensive air shower array. Using data collected from April to October of 1997 (130.1 days of livetime), a general survey of the northern hemisphere revealed no statistically significant excess of events from any direction. The sensitivity for a flux of muon neutrinos is based on the effective detection area for through-going muons. Averaged over the Northern sky, the effective detection area exceeds 10,000 m^2 for E_{mu} ~ 10 TeV. Neutrinos generated in the atmosphere by cosmic ray interactions were used to verify the predicted performance of the detector. For a source with a differential energy spectrum proportional to E_{nu}^{-2} and declination larger than +40 degrees, we obtain E^2(dN_{nu}/dE) <= 10^{-6}GeVcm^{-2}s^{-1} for an energy threshold of 10 GeV.Comment: 46 pages, 22 figures, 4 tables, submitted to Ap.

Weak Lensing from Space I: Instrumentation and Survey Strategy

A wide field space-based imaging telescope is necessary to fully exploit the technique of observing dark matter via weak gravitational lensing. This first paper in a three part series outlines the survey strategies and relevant instrumental parameters for such a mission. As a concrete example of hardware design, we consider the proposed Supernova/Acceleration Probe (SNAP). Using SNAP engineering models, we quantify the major contributions to this telescope's Point Spread Function (PSF). These PSF contributions are relevant to any similar wide field space telescope. We further show that the PSF of SNAP or a similar telescope will be smaller than current ground-based PSFs, and more isotropic and stable over time than the PSF of the Hubble Space Telescope. We outline survey strategies for two different regimes - a ``wide'' 300 square degree survey and a ``deep'' 15 square degree survey that will accomplish various weak lensing goals including statistical studies and dark matter mapping.Comment: 25 pages, 8 figures, 1 table, replaced with Published Versio

Limits to the muon flux from WIMP annihilation in the center of the Earth with the AMANDA detector

A search for nearly vertical up-going muon-neutrinos from neutralino annihilations in the center of the Earth has been performed with the AMANDA-B10 neutrino detector. The data sample collected in 130.1 days of live-time in 1997, ~10^9 events, has been analyzed for this search. No excess over the expected atmospheric neutrino background is oberved. An upper limit at 90% confidence level on the annihilation rate of neutralinos in the center of the Earth is obtained as a function of the neutralino mass in the range 100 GeV-5000 GeV, as well as the corresponding muon flux limit.Comment: 14 pages, 11 figures. Version accepted for publication in Physical Review

Limits on diffuse fluxes of high energy extraterrestrial neutrinos with the AMANDA-B10 detector

Data from the AMANDA-B10 detector taken during the austral winter of 1997 have been searched for a diffuse flux of high energy extraterrestrial muon-neutrinos, as predicted from, e.g., the sum of all active galaxies in the universe. This search yielded no excess events above those expected from the background atmospheric neutrinos, leading to upper limits on the extraterrestrial neutrino flux. For an assumed E^-2 spectrum, a 90% classical confidence level upper limit has been placed at a level E^2 Phi(E) = 8.4 x 10^-7 GeV cm^-2 s^-1 sr^-1 (for a predominant neutrino energy range 6-1000 TeV) which is the most restrictive bound placed by any neutrino detector. When specific predicted spectral forms are considered, it is found that some are excluded.Comment: Submitted to Physical Review Letter

Supernova / Acceleration Probe: A Satellite Experiment to Study the Nature of the Dark Energy

The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to study the dark energy and alternative explanations of the acceleration of the Universe's expansion by performing a series of complementary systematics-controlled measurements. We describe a self-consistent reference mission design for building a Type Ia supernova Hubble diagram and for performing a wide-area weak gravitational lensing study. A 2-m wide-field telescope feeds a focal plane consisting of a 0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. The SNAP mission will obtain high-signal-to-noise calibrated light-curves and spectra for several thousand supernovae at redshifts between z=0.1 and 1.7. A wide-field survey covering one thousand square degrees resolves ~100 galaxies per square arcminute. If we assume we live in a cosmological-constant-dominated Universe, the matter density, dark energy density, and flatness of space can all be measured with SNAP supernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe, the density-to-pressure ratio of dark energy can be similarly measured to 5% for the present value w0 and ~0.1 for the time variation w'. The large survey area, depth, spatial resolution, time-sampling, and nine-band optical to NIR photometry will support additional independent and/or complementary dark-energy measurement approaches as well as a broad range of auxiliary science programs. (Abridged)Comment: 40 pages, 18 figures, submitted to PASP, http://snap.lbl.go