Optimal Quantum Measurements of Expectation Values of Observables

Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and coupling the system to an apparatus. For this method, the precision of the measured value scales as 1/sqrt(N) for N repetitions of the experiment. For the problem of estimating the parameter phi in an evolution exp(-i phi H), it is possible to achieve precision 1/N (the quantum metrology limit) provided that sufficient information about H and its spectrum is available. We consider the more general problem of estimating expectations of operators A with minimal prior knowledge of A. We give explicit algorithms that approach precision 1/N given a bound on the eigenvalues of A or on their tail distribution. These algorithms are particularly useful for simulating quantum systems on quantum computers because they enable efficient measurement of observables and correlation functions. Our algorithms are based on a method for efficiently measuring the complex overlap of |psi> and U|psi>, where U is an implementable unitary operator. We explicitly consider the issue of confidence levels in measuring observables and overlaps and show that, as expected, confidence levels can be improved exponentially with linear overhead. We further show that the algorithms given here can typically be parallelized with minimal increase in resource usage.Comment: 22 page

(R1510) A Special Case of Rodriguez-Lallena and Ubeda-Flores Copula Based on Ruschendorf Method

Measure of dependence is a particular way of looking at the association between random variables, and one way to capture stochastic dependence is through the use of copula. In this study, a Rushendorf Method was applied to a bivariate function to obtain a copula through the use of a special case of Rodriguez-Lallena and Ubeda-Flores (RLUF) copula. Properties of the RLUF copula such as the density, measures of dependence, and lower and upper tail dependence were studied. In particular, measures of dependence such as Spearman’s rho, Kendall’s tau and Blomqvist’s beta of RLUF copula are given. Moreover, the Root-Mean-Square Error (RMSE), Sum-Square Error (SSE), Mean Absolute Error (MAE), Mean Square Error (MSE), Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used in deriving the best joint distribution between monthly precipitation and temperature in the Philippines from 1974 to 2013. The results showed that considering the monthly precipitation and temperature datas, RLUF copula outperformed the other existing bivariate copulas such as Ali-Mikhail-Haq (AHM), Farlie-Gumbel-Morgenstern (FGM), and Clayton copulas

Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently ("exactly") solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.Comment: 6 pages; no figure

Brans-Dicke-type theories and avoidance of the cosmological singularity

We tudy flat Friedmann-Robertson-Walker cosmology in Brans-Dicke-type theories of gravitation with minimal coupling between the scalar field and the matter fields in the Einstein frame (general relativity with an extra scalar field) for arbitrary values of the Brans-Dicke parameter $\omega>-{3/2}$. It is shown that the cosmological singularity occuring in the Einstein frame formulation of this theory is removed in the Jordan frame in the range $-{3/2}<\omega<\leq-{4/3}$. This result is interpreted in the ligth of a viewpoint (first presented in reference gr-qc/9905071) asserting that both Jordan frame and Einstein frame formulations of general relativity are physically equivalent. The implications of the obtained result for string theory are outlined.Comment: 9 pages, LaTeX, no figures. Improved version accepted for publication in PR

The edge of the young galactic disk

In this work, we report and discuss the detection of two distant diffuse stellar groups in the third Galactic quadrant. They are composed of young stars, with spectral types ranging from lateOto late B, and lie at galactocentric distances between 15 and 20 kpc. These groups are located in the area of two cataloged open clusters (VdB-Hagen 04 and Ruprecht 30), projected toward the Vela-Puppis constellations, and within the core of the Canis Major overdensity. Their reddening and distances have been estimated by analyzing their color-color and color-magnitude diagrams, derived from deep UBV photometry. The existence of young star aggregates at such extreme distances from the Galactic center challenges the commonly accepted scenario in which the Galactic disk has a sharp cutoff at about 14 kpc from the Galactic center and indicates that it extends to much greater distances (as also supported by the recent detection of CO molecular complexes well beyond this distance). While the groups we find in the area of Ruprecht 30 are compatible with the Orion and Norma-Cygnus spiral arms, respectively, the distant group we identify in the region of VdB-Hagen 04 lies in the external regions of the Norma-Cygnus arm, at a galactocentric distance (∼20 kpc) where no young stars have been detected so far in the optical.Facultad de Ciencias Astronómicas y Geofísica

The edge of the young galactic disk

In this work, we report and discuss the detection of two distant diffuse stellar groups in the third Galactic quadrant. They are composed of young stars, with spectral types ranging from lateOto late B, and lie at galactocentric distances between 15 and 20 kpc. These groups are located in the area of two cataloged open clusters (VdB-Hagen 04 and Ruprecht 30), projected toward the Vela-Puppis constellations, and within the core of the Canis Major overdensity. Their reddening and distances have been estimated by analyzing their color-color and color-magnitude diagrams, derived from deep UBV photometry. The existence of young star aggregates at such extreme distances from the Galactic center challenges the commonly accepted scenario in which the Galactic disk has a sharp cutoff at about 14 kpc from the Galactic center and indicates that it extends to much greater distances (as also supported by the recent detection of CO molecular complexes well beyond this distance). While the groups we find in the area of Ruprecht 30 are compatible with the Orion and Norma-Cygnus spiral arms, respectively, the distant group we identify in the region of VdB-Hagen 04 lies in the external regions of the Norma-Cygnus arm, at a galactocentric distance (∼20 kpc) where no young stars have been detected so far in the optical.Facultad de Ciencias Astronómicas y Geofísica

Mixture design and multivariate image analysis to monitor the colour of strawberry yoghurt purée

Food colour is a commercial added value, since it represents the first appealing factor for consumers. In this context, this study was aimed at evaluating the effect of strawberry yoghurt purée (SYP) formulation on the corresponding colour and on its variation over time, which is mainly due to degradation and browning phenomena. To this aim, a combined approach was used that included mixture design and multivariate analysis of RGB images. Strawberry purée, sugar, lemon juice and two types of thickener were mixed in different proportions by I-optimal mixture design to obtain 44 SYP formulations. The samples were subjected to light and temperature stress conditions for five weeks; during this time the RGB images of the samples were acquired using a flatbed scanner, along with the images of the corresponding control samples. The dimensionality of the acquired images was reduced by two different approaches: i) the conversion of images into signals, namely colourgrams, which can be seen as the colour fingerprint of the imaged samples, and ii) the calculation of the median values of various colour-related parameters. The colourgrams dataset was then subjected to exploratory data analysis using Principal Component Analysis, while the median values of colour-related parameters were analysed using Response Surface Methodology and Partial Least Squares-Discriminant Analysis. The aim of data analysis was both to find the best colour parameters to describe colour variability over time, and to investigate the cause-effect relationship between mixture proportions and colour response. The results highlighted that, among the considered colour parameters, relative green (i.e., the ratio of green to lightness) and red could be used to monitor colour changes. Colour variation due to stress conditions was more pronounced for samples with a high percentage of strawberry purée, and the type of thickener also affected the colour degradation kinetics

Minimum quench power dissipation and current non-uniformity in ITER type NbTi cable-in-conduit conductor samples under DC conditions

The level of current non-uniformity in NbTi CICCs sections near the joints in combination with the magnet field profile needs attention in view of proper joint design. The strand Joule power and current distribution at quench under DC conditions of two samples of ITER Poloidal Field Coil conductors, as tested in the SULTAN facility and of the so called PFCI Model Coil Insert, have been analyzed with the numerical cable model JackPot. The precise trajectories of all individual strands, joint design, cabling configuration, spatial distribution of the magnetic field, sample geometry and using experimentally determined interstrand resistance distributions have been taken into account. Although unable to predict the quench point due to the lack of a thermal-hydraulic routine, the model allows to assess the instantaneous strand power at quench and its local distribution in the cable, showing the hot spots, once the quench conditions in terms of current and temperature are experimentally known., The analysis points out the relation of the above mentioned factors with the DC quench stability of both short samples and coils. The possible small scale and local electrical-thermal interactions were ignored in order to examine the relevance of such effects in the overall prediction of the CICC performance The electromagnetic code shows an excellent quantitative predictive potential for CICC transport properties, excluding any freedom for matching the results. The influence of the local thermal effects in the modeling is identified as being marginal and far less than the generally accepted temperature margin for safe operation