Extended quantum conditional entropy and quantum uncertainty inequalities

Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. All the recently derived uncertainty relations utilize the strong subadditivity (SSA) theorem; our contribution relies on directly utilizing the proof technique of the original derivation of SSA.Comment: 4 page

Large-Scale Structure at z~2.5

We have made a statistically complete, unbiased survey of C IV systems toward a region of high QSO density near the South Galactic Pole using 25 lines of sight spanning $1.5<z<2.8$. Such a survey makes an excellent probe of large-scale structure at early epochs. We find evidence for structure on the $15-35h^{-1}$ proper Mpc scale ($H_0 \equiv 100$ km $s^{-1}$ Mpc${-1}$) as determined by the two point C IV - C IV absorber correlation function, and reject the null hypothesis that C IV systems are distributed randomly on such scales at the $\sim 3.5\sigma$ level. The structure likely reflects the distance between two groups of absorbers subtending $\sim~ 13 \times 5 \times 21h^{-3}$ and $\sim 7 \times 1 \times 15h^{-3}$ Mpc$^3$ at $z\sim 2.3$ and $z \sim 2.5$ respectively. There is also a marginal trend for the association of high rest equivalent width C IV absorbers and QSOs at similar redshifts but along different lines of sight. The total number of C IV systems detected is consistent with that which would be expected based on a survey using many widely separated lines of sight. Using the same data, we also find 11 Mg II absorbers in a complete survey toward 24 lines of sight; there is no evidence for Mg II - Mg II or Mg II - QSO clustering, though the sample size is likely still small to detect such structure if it exists.Comment: 56 pages including 32 of figures, in gzip-ed uuencoded postscript format, 1 long table not included, aastex4 package. Accepted for publication in ApJ Supplement

A study of dye anchoring points in half-squarylium dyes for dye-sensitized solar cells

This paper reports the synthesis of a series of new half-squaraine dyes (Hf-SQ) based around a common chromophoric unit consisting of linked indoline and squaric acid moieties. Carboxylate groups have been incorporated onto this core structure at four different points to study the influence of the anchoring group position on dye-sensitized solar cell (DSC) device performance. Dyes have been linked to TiO2 directly through the squaric acid moiety, through a modified squaric acid unit where a vinyl dicyano group has replaced one carbonyl, via an alkyl carboxylate attached to the indole N or through a carboxylate attached to the 4 position of a benzyl indole. Contact angle measurements have been studied to investigate the hydrophobic/hydrophilic properties of the dyes and the results have been compared to N719 and Z907. Full characterization data of all the dyes and synthetic intermediates are reported including single-crystal X-ray structural analysis for dye precursors; the indole (2a) and the half-squarylium esters (3a) and (6b), as well as the dyes (4c), (8) and (12). Dye colours range from yellow to red/brown in solution (λmax range from 430 to 476 nm) with ε ranging from 38 000 to 133 100 M−1 cm−1. The performance of the dyes in DSCs shows the highest efficiency yet reported for a Hf-SQ dye (η = 5.0%) for 1 cm2 devices with a spectral response ranging from 400 to 700 nm depending on the dye substituents. Co-sensitization of half-squarylium dye (7b) with squaraine dye (SQ2) resulted in a broader spectral response and an improved device efficiency (η = 6.1%). Density functional theory (DFT) calculations and cyclic voltammetry have been used to study the influence of linker position on dye HOMO–LUMO levels and the data has been correlated with I–V and EQE data

Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.Algorithms and the Foundations of Software technolog

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. At temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multi-layer parallel beta-sheet structure. This structure has an inter-strand distance of 0.48 nm and an inter-sheet distance of 1.0 nm, which agree with experimental observations. In this model, the hydrogen bond interactions give rise to the inter-strand spacing in beta-sheets, while the Go interactions among side chains make beta-strands parallel to each other and allow beta-sheets to pack into layers. The aggregates also contain free edges which may allow for further aggregation of model peptides to form elongated fibrils.Comment: 15 pages, 8 figure

Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter $g_{NL}$. The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of $g_{NL}$ and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for $g_{NL}>0$ and less of both for $g_{NL}<0$. The deviation increases linearly with $g_{NL}$ and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of $g_{NL}$ that are clearly distinct from the quadratic order perturbations, encoded in the parameter $f_{NL}$. Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between $g_{NL}$ and $f_{NL}$ type non-Gaussianities.Comment: 18+1 page

Characterization of optical properties and surface roughness profiles: The Casimir force between real materials

The Lifshitz theory provides a method to calculate the Casimir force between two flat plates if the frequency dependent dielectric function of the plates is known. In reality any plate is rough and its optical properties are known only to some degree. For high precision experiments the plates must be carefully characterized otherwise the experimental result cannot be compared with the theory or with other experiments. In this chapter we explain why optical properties of interacting materials are important for the Casimir force, how they can be measured, and how one can calculate the force using these properties. The surface roughness can be characterized, for example, with the atomic force microscope images. We introduce the main characteristics of a rough surface that can be extracted from these images, and explain how one can use them to calculate the roughness correction to the force. At small separations this correction becomes large as our experiments show. Finally we discuss the distance upon contact separating two rough surfaces, and explain the importance of this parameter for determination of the absolute separation between bodies.}Comment: 33 pages, 14 figures, to appear in Springer Lecture Notes in Physics, Volume on Casimir Physics, edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Ros

Interacting new agegraphic viscous dark energy with varying GG

We consider the new agegraphic model of dark energy with a varying gravitational constant, $G$, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.Comment: 12 pages, accepted for publication in IJTP (2010

Detector Description and Performance for the First Coincidence Observations between LIGO and GEO

For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.Comment: 41 pages, 9 figures 17 Sept 03: author list amended, minor editorial change