Quantum State Tomography of a Single Qubit: Comparison of Methods

The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix of a single qubit: (scaled) direct inversion, maximum likelihood estimation (MLE), minimum Fisher information distance, and Bayesian mean estimation (BME). We discuss the different prior densities in the space of density matrices, on which both MLE and BME depend, as well as ways of including experimental errors and of estimating tomography errors. As a measure of the accuracy of these methods we average the trace distance between a given density matrix and the tomographic density matrices it can give rise to through experimental measurements. We find that the BME provides the most accurate estimate of the density matrix, and suggest using either the pure-state prior, if the system is known to be in a rather pure state, or the Bures prior if any state is possible. The MLE is found to be slightly less accurate. We comment on the extrapolation of these results to larger systems.Comment: 15 pages, 4 figures, 2 tables; replaced previous figure 5 by new table I. in Journal of Modern Optics, 201

Spectral density analysis of time correlation functions in lattice QCD using the maximum entropy method

We study various aspects of extracting spectral information from time correlation functions of lattice QCD by means of Bayesian inference with an entropic prior, the maximum entropy method (MEM). Correlator functions of a heavy-light meson-meson system serve as a repository for lattice data with diverse statistical quality. Attention is given to spectral mass density functions, inferred from the data, and their dependence on the parameters of the MEM. We propose to employ simulated annealing, or cooling, to solve the Bayesian inference problem, and discuss practical issues of the approach.Comment: 11 pages, 30 figure files (eps), some references added and updated, requires REVTeX 4.0 and prerequisites (AMS-LaTeX 2.0, graphicx, dcolumn, bm) see http://publish.aps.org/revtex4

Assessment of check dams’ role in flood hazard mapping in a semi-arid environment

This study aimed to examine flood hazard zoning and assess the role of check dams as effective hydraulic structures in reducing flood hazards. To this end, factors associated with topographic, hydrologic and human characteristics were used to develop indices for flood mapping and assessment. These indices and their components were weighed for flood hazard zoning using two methods: (i) a multi-criterion decision-making model in fuzzy logic and (ii) entropy weight. After preparing the flood hazard map by using the above indices and methods, the characteristics of the change‐point were used to assess the role of the check dams in reducing flood risk. The method was used in the Ilanlu catchment, located in the northwest of Hamadan province, Iran, where it is prone to frequent flood events. The results showed that the area of ‘very low’, ‘low’ and ‘moderate’ flood hazard zones increased from about 2.2% to 7.3%, 8.6% to 19.6% and 22.7% to 31.2% after the construction of check dams, respectively. Moreover, the area of ‘high’ and ‘very high’ flood hazard zones decreased from 39.8% to 29.6%, and 26.7% to 12.2%, respectively

Comparing Entropy Weighting Method and AHP for JIT implementation in a Manufacturing System

Although some important criteria, such as work in process (WIP) and inventory, are recognized to have an impact on Just-in-Time (JIT) implementations, the exact weights of these criteria for different systems are not known. Consequently, the decision maker will not be able to predict the size of change in the system when implementing his JIT strategy. On the other hand, different weighting methods result in different weight values which makes it more confusing for the decision maker. We therefore consider entropy weighting method and Analytic Hierarchy Process (AHP) to compute the weights of the selected criteria. A case study is also discussed to demonstrate the differences between these two weighting methods. Simulation modeling is used to validate and compare the results

Excitation Spectra in a Heavy-Light Meson-Meson System

A system of two static quarks, at fixed distances r, and two light quarks is studied on an anisotropic lattice. Excitations by operators emphasizing quark or gluon degrees of freedom are examined. The maximum entropy method is applied in the spectral analysis. These simulations ultimately aim at learning about mechanisms of hadronic interaction.Comment: 5 pages, latex (uses espcrc2, psfig), contriubution to: Workshop on Lattice Hadron Physics (LHP2001), Cairns, July 9-18, 200

Comprehensive entropy weight observability-controllability risk analysis and its application to water resource decision-making

Decision making for water resource planning is often related to social, economic and environmental factors. There are various methods for making decisions about water resource planning alternatives and measures with various shortcomings. A comprehensive entropy weight observability-controllability risk analysis approach is presented in this study. Computing methods for entropy weight (EW) and subjective weight (SW) are put forward based on information entropy theory and experimental psychology principles, respectively. Comprehensive weight (CW) consisting of EW and SW is determined. The values of observability-controllability risk (Roc) and gain by comparison (Gbc) are obtained based on the CWs. The quantitative analysis of alternatives and measures is achieved based on Roc and Gbc. A case study on selection of water resource planning alternatives and measures in the Yellow River Basin, China, was performed. Results demonstrate that the approach presented in this study can achieve optimal decision-making results

Country Evaluation of Islamic Economic Criteria: An Application Using Entropy Weight and TOPSIS Methodologies

[EN] While Islamic economy is growing in all sectors, Halal compliance is carried out by more countries worldwide. The purpose of this paper is toestablish a methodology based on MCDM methods in order to create an accurate ranking of countries according to the basis of the Halal standards, which can be used by public and private institutions. Although Islamic economy is evaluated globally by different institutions every year, those reports are based on indicators which are equally weighted. In this paper, weights of the six Islamic economy criteria are determined by the EWM (Entropy Weight Method) and theTechnique for Order Preference by Similarity to Ideal Solution (TOPSIS) has been used to create a ranking of countries in terms of the Halal principles.Mayor-Vitoria, F.; Garcia-Bernabeu, A.; Abdul Rahman, NA.; Mohammad, MF. (2021). Country Evaluation of Islamic Economic Criteria: An Application Using Entropy Weight and TOPSIS Methodologies. International Journal of Science and Research. 10(2):979-986. https://doi.org/10.21275/SR21216022424S97998610

Entropy Driven Dimerization in a One-Dimensional Spin-Orbital Model

We study a new version of the one-dimensional spin-orbital model with spins S=1 relevant to cubic vanadates. At small Hund's coupling J_H we discover dimerization in a pure electronic system solely due to a dynamical spin-orbital coupling. Above a critical value J_H, a uniform ferromagnetic state is stabilized at zero temperature. More surprisingly, we observe a temperature driven dimerization of the ferrochain, which occurs due to a large entropy released by dimer states. This dynamical dimerization seems to be the mechanism driving the peculiar intermediate phase of YVO_3.Comment: 5 pages, 4 figure