Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cram\'er-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost important in realistic scenarios, such as observational astronomy.Comment: 5 pages, 3 figures. Comments welcome

Implementation of quantum search algorithm using classical Fourier optics

We report on an experiment on Grover's quantum search algorithm showing that {\em classical waves} can search a $N$-item database as efficiently as quantum mechanics can. The transverse beam profile of a short laser pulse is processed iteratively as the pulse bounces back and forth between two mirrors. We directly observe the sought item being found in $\sim\sqrt{N}$ iterations, in the form of a growing intensity peak on this profile. Although the lack of quantum entanglement limits the {\em size} of our database, our results show that entanglement is neither necessary for the algorithm itself, nor for its efficiency.Comment: 4 pages, 3 figures; minor revisions plus extra referenc

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.Comment: 55 pages, uses JHEP3.cls. v2: Minor errors corrected, small changes in introductio

HKT Geometry and Fake Five Dimensional Supergravity

Recent results on the relation between hyper-Kahler geometry with torsion and solutions admitting Killing spinors in minimal de sitter supergravity are extended to more general supergravity models with vector multiplets.Comment: 14 pages, latex. Minor typos corrected, references adde

Indications of superconductivity in doped highly oriented pyrolytic graphite

We have observed possible superconductivity using standard resistance vs. temperature techniques in phosphorous ion implanted Highly Oriented Pyrolytic Graphite. The onset appears to be above 100 K and quenching by an applied magnetic field has been observed. The four initial boron implanted samples showed no signs of becoming superconductive whereas all four initial and eight subsequent samples that were implanted with phosphorous showed at least some sign of the existence of small amounts of the possibly superconducting phases. The observed onset temperature is dependent on both the number of electron donors present and the amount of damage done to the graphene sub-layers in the Highly Oriented Pyrolytic Graphite samples. As a result the data appears to suggest that the potential for far higher onset temperatures in un-damaged doped graphite exists.Comment: 7 pages, 1 table, 5 figures, 11 references, Acknowledgments section was correcte

Single-Step Quantum Search Using Problem Structure

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT allows determining the asymptotic average behavior of these algorithms, showing they improve on quantum algorithms, such as amplitude amplification, that ignore detailed problem structure but remain exponential for hard problem instances. Compared to good classical methods, the algorithm performs better, on average, for weakly and highly constrained problems but worse for hard cases. The analytic techniques introduced here also apply to other quantum algorithms, supplementing the limited evaluation possible with classical simulations and showing how quantum computing can use ensemble properties of NP search problems.Comment: 39 pages, 12 figures. Revision describes further improvement with multiple steps (section 7). See also http://www.parc.xerox.com/dynamics/www/quantum.htm

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure

Pressure-Induced Superconductivity in Sc to 74 GPa

Using a diamond anvil cell with nearly hydrostatic helium pressure medium we have significantly extended the superconducting phase diagram Tc(P) of Sc, the lightest of all transition metals. We find that superconductivity is induced in Sc under pressure, Tc increasing monotonically to 8.2 K at 74.2 GPa. The Tc(P) dependences of the trivalent d-electron metals Sc, Y, La, and Lu are compared and discussed within a simple s-d charge transfer framework.Comment: to be published in Phys. Rev. B (Brief Reports