Quantum data gathering

Measurement of a quantum system – the process by which an observer gathers information about it – provides a link between the quantum and classical worlds. The nature of this process is the central issue for attempts to reconcile quantum and classical descriptions of physical processes. Here, we show that the conventional paradigm of quantum measurement is directly responsible for a well-known disparity between the resources required to extract information from quantum and classical systems. We introduce a simple form of quantum data gathering, “coherent measurement”, that eliminates this disparity and restores a pleasing symmetry between classical and quantum statistical inference. To illustrate the power of quantum data gathering, we demonstrate that coherent measurements are optimal and strictly more powerful than conventional one-at-a-time measurements for the task of discriminating quantum states, including certain entangled many-body states (e.g., matrix product states)

The Biophysical Toolbox: a Biophysical Modelling Tool Developed within the IWRAM-DSS

With rapid intensification of agricultural catchments in northern Thailand a suite of environmental issues have surfaced. The Integrated Water Resources Assessment and Management (IWRAM) project was instigated in response to these issues. The project developed a Decision Support System for the exploration of biophysical and socio-economic impacts of water resources use option. The IWRAM-DSS is comprised of a 'Biophysical Toolbox' that can be implemented alone or an 'Integrated Toolbox' that links socioeconomic models with the biophysical toolbox to explore economic trade-offs and impacts of various scenarios. The Biophysical Toolbox is comprised of three modules - the CATCHCROP crop model, a hydrologic module based upon the IHACRES rainfall-runoff model, and a Universal Soil Loss Equation (USLE) approach modified to suit conditions in northern Thailand. This working paper describes and implements the Fortran 77 version of the Biophysical Toolkit developed jointly by Dr. Barry Croke and Wendy Merritt. A Java version of the model has been coded by Dr. Claude Dietrich and Nick Ardlie, however this version has not been linked with the economic model as part of the fully integrated IWRAM-DSS

Filling minimality of Finslerian 2-discs

We prove that every Riemannian metric on the 2-disc such that all its geodesics are minimal, is a minimal filling of its boundary (within the class of fillings homeomorphic to the disc). This improves an earlier result of the author by removing the assumption that the boundary is convex. More generally, we prove this result for Finsler metrics with area defined as the two-dimensional Holmes-Thompson volume. This implies a generalization of Pu's isosystolic inequality to Finsler metrics, both for Holmes-Thompson and Busemann definitions of Finsler area.Comment: 16 pages, v2: improved introduction and formattin

Difficulty of distinguishing product states locally

Non-locality without entanglement is a rather counter-intuitive phenomenon in which information may be encoded entirely in product (unentangled) states of composite quantum systems in such a way that local measurement of the subsystems is not enough for optimal decoding. For simple examples of pure product states, the gap in performance is known to be rather small when arbitrary local strategies are allowed. Here we restrict to local strategies readily achievable with current technology; those requiring neither a quantum memory nor joint operations. We show that, even for measurements on pure product states there can be a large gap between such strategies and theoretically optimal performance. Thus even in the absence of entanglement physically realizable local strategies can be far from optimal for extracting quantum information.Comment: 5 pages, 1 figur

Sensitivity testing of a biophysical toolbox for exploring water resources utilisation and management options

This paper investigates the sensitivities of model outputs to model parameter values within a Biophysical Toolbox developed as part of a Decision Support System (DSS) for integrated catchment assessment and management of land and water resources in the highland regions of northern Thailand. The toolbox contains a hydrological module based upon the IHACRES rainfall-runoff model, a crop model (CATCHCROP), and an erosion model (USLE) modified to suit conditions in northern Thailand. Emphasis in the development of the individual models within the Biophysical Toolbox was placed upon limiting model complexity. Limited data availability commonly restricts the complexity of the model structure that can justifiably be used to model natural systems. The challenge under conditions with limited data is then to strike a balance in the model(s) between statistical rigour and model complexity. Once encompassed within the Biophysical Toolbox, linkages between the models increase the complexity of the system, despite the relative simplicity of the individual models. Consequently, the impacts of outputs from individual models on the outputs of other models deserve considerable attention. Understanding model sensitivity is of particular importance where there is a lack of data with which to support or adequately verify model behaviour. Sensitivity analysis potentially allows the identification of model components that require attention in terms of improved parameter estimation or improvement in model structure. Preliminary testing of the individual models within the Biophysical Toolbox has been reported previously within the literature and the Biophysical Toolbox as a whole has been described. This paper explores sensitivities within the Biophysical Toolbox, targeting in particular the identification of components of the toolbox in which sensitivities are propagated throughout the model

Maximum Confidence Quantum Measurements

We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state.Comment: 4 pages, 2 figure

On the conditions for discrimination between quantum states with minimum error

We provide a simple proof for the necessity of conditions for discriminating with minimum error between a known set of quantum states.Comment: 4 page

Ellipsometric study of Si(0.5)Ge(0.5)/Si strained-layer superlattices

An ellipsometric study of two Si(0.5)Ge(0.5)/Si strained-layer super lattices grown by MBE at low temperature (500 C) is presented, and results are compared with x ray diffraction (XRD) estimates. Excellent agreement is obtained between target values, XRD, and ellipsometry when one of two available Si(x)Ge(1-x) databases is used. It is shown that ellipsometry can be used to nondestructively determine the number of superlattice periods, layer thicknesses, Si(x)Ge(1-x) composition, and oxide thickness without resorting to additional sources of information. It was also noted that we do not observe any strain effect on the E(sub 1) critical point

Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009