Hilbert's projective metric in quantum information theory

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical distinguishability of quantum states and on the decrease of entanglement under LOCC protocols or other cone-preserving operations. The results are formulated in terms of general cones and base norms and lead to contractivity bounds for quantum channels, for instance improving Ruskai's trace-norm contraction inequality. A new duality between distinguishability measures and base norms is provided. For two given pairs of quantum states we show that the contraction of Hilbert's projective metric is necessary and sufficient for the existence of a probabilistic quantum operation that maps one pair onto the other. Inequalities between Hilbert's projective metric and the Chernoff bound, the fidelity and various norms are proven.Comment: 32 pages including 3 appendices and 3 figures; v2: minor changes, published versio

Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches

We compare pseudopure state ensemble implementations, quantified by their initial polarization and ensemble size, of Grover's search algorithm to probabilistic classical sequential search algorithms in terms of their success and failure probabilities. We propose a criterion for quantifying the resources used by the ensemble implementation via the aggregate number of oracle invocations across the entire ensemble and use this as a basis for comparison with classical search algorithms. We determine bounds for a critical polarization such that the ensemble algorithm succeeds with a greater probability than the probabilistic classical sequential search. Our results indicate that the critical polarization scales as N^(-1/4) where N is the database size and that for typical room temperature solution state NMR, the polarization is such that the ensemble implementation of Grover's algorithm would be advantageous for N > 10^2

Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator

We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or raising the energy of a single photon trapped in an optical resonator under active tuning of the resonator. We show that our fully quantum mechanical approach reproduces the semi-classical result in the appropriate limit and that the adiabatic invariant has the same form in each case. Finally, we explore the trapping of a single photon in a system of dynamically tuned, coupled optical cavities.Comment: 24 pages, 10 figure

New Reports of Exotic and Native Ambrosia and Bark Beetle Species (Coleoptera: Curculionidae: Scolytinae) From Ohio

In a 2007 survey of ambrosia and bark beetles (Coleoptera: Curculionidae: Scolytinae) along a transect in northeastern Ohio, we collected six exotic and three native species not previously reported from the state. These species include the exotic ambrosia beetles Ambrosiodmus rubricollis (Eichhoff), Dryoxylon onoharaensum (Murayama), Euwallacea validus (Eichhoff), Xyleborus californicus Wood, Xyleborus pelliculosusEichhoff, and Xylosandrus crassiusculus (Motschulsky). The native ambrosia beetle Corthylus columbianus Hopkins, and the native bark beetles Dryocoetes autographus (Ratzeburg) and Hylastes tenuis Eichhoff are also reported from Ohio for the first time. Our study suggests a northward range expansion for five of the six exotic species including, X. crassiusculus, which is an important pest of nursery and orchard crops in the southeastern United States

Fermionic Linear Optics Revisited

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible, see quant-ph/0401066.Comment: 16 pages, submitted to the special issue of Foundation of Physics in honor of Asher Peres' 70th birthda

Monovalent counterion distributions at highly charged water interfaces: Proton-transfer and Poisson-Boltzmann theory

Surface sensitive synchrotron-X-ray scattering studies reveal the distributions of monovalent ions next to highly charged interfaces. A lipid phosphate (dihexadecyl hydrogen-phosphate) was spread as a monolayer at the air-water interface, containing CsI at various concentrations. Using anomalous reflectivity off and at the $L_3$ Cs$^+$ resonance, we provide, for the first time, spatial counterion distributions (Cs$^+$) next to the negatively charged interface over a wide range of ionic concentrations. We argue that at low salt concentrations and for pure water the enhanced concentration of hydroniums H$_3$O$^+$ at the interface leads to proton-transfer back to the phosphate group by a high contact-potential, whereas high salt concentrations lower the contact-potential resulting in proton-release and increased surface charge-density. The experimental ionic distributions are in excellent agreement with a renormalized-surface-charge Poisson-Boltzmann theory without fitting parameters or additional assumptions