Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels

We study the multiplicativity of the output 2-norm for depolarized Werner-Holevo channels and show that multiplicativity holds for a product of two identical channels in this class. Moreover, it shown that the depolarized Werner-Holevo channels do not satisfy the entrywise positivity condition introduced by C. King and M.B. Ruskai, which suggests that the main result is non-trivial.Comment: 3 page

Quantization of Hall Conductance For Interacting Electrons on a Torus

We consider interacting, charged spins on a torus described by a gapped Hamiltonian with a unique groundstate and conserved local charge. Using quasi-adiabatic evolution of the groundstate around a flux-torus, we prove, without any averaging assumption, that the Hall conductance of the groundstate is quantized in integer multiples of e^2/h, up to exponentially small corrections in the linear size of the system. In addition, we discuss extensions to the fractional quantization case under an additional topological order assumption on the degenerate groundstate subspace.Comment: 28 pages, 4 figures, This paper significantly simplifies the proof and tightens the bounds previously shown in arXiv:0911.4706 by the same authors. Updated to reflect published versio

Entanglement in Finitely Correlated Spin States

We derive bounds for the entanglement of a spin with an (adjacent and non-adjacent) interval of spins in an arbitrary pure finitely correlated state (FCS) on a chain of spins of any magnitude. Finitely correlated states are otherwise known as matrix product states or generalized valence-bond states. The bounds become exact in the limit of the entanglement of a single spin and the half-infinite chain to the right (or the left) of it. Our bounds provide a proof of the recent conjecture by Benatti, Hiesmayr, and Narnhofer that their necessary condition for non-vanishing entanglement in terms of a single spin and the ``memory'' of the FCS, is also sufficient . Our result also generalizes the study of entanglement in the ground state of the AKLT model by Fan, Korepin, and Roychowdhury. Our result permits one to calculate more efficiently, numerically and in some cases even analytically, the entanglement of arbitrary finitely correlated quantum spin chains.Comment: PACS 03.67.Mn, 05.50.+q. Minor typos in v1 corrected. In v2: expanded Introduction and Discussion. Simplified proof of the main resul

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\mathcal{H}$ into a tensor product of factors, we consider a class of "redundancy-constrained states" in $\mathcal{H}$ that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.Comment: 37 pages, 5 figures. Updated notation, references, and acknowledgemen

The development of a forecasting method for mining house capital projects

Bibliography: pages 95-103.A broad description of a project is a single, non-repetitive enterprise which is undertaken to achieve planned results within a time limit and a cost budget. This description could equally well apply to fixing a punctured tyre, expanding an existing mine, the design of a computer system or the building of the pyramids. Modern civilisation is largely based on the successful completion of projects. It is surprising therefore, that it is only in the very recent future, since the 1950's say, that the effective management of projects has been considered worthy of academic attention. Today project management in in the process of becoming a management science in its own right. This need for the effective management of projects is further evidenced by the emergence in large organisations of departments whose function it is to control projects. Typically, a project control department would, in addition to other functions, be required to report to management regularly on the health of a project - is the project on schedule and on budget? If it is not, management clearly needs to be given an indication of where the project is heading. A number of techniques are in common use which claim to 'forecast' the final cost and completion date of a project. These techniques include the S-curve in its many forms and Critical Path Networking, amongst others. On close analysis however, it soon becomes apparent that although these techniques offer a wealth of useful information regarding the present state of the project, and give a qualitative idea of the direction the project is heading in, they do not give any quantitative indication of the final cost and completion date of a project. In other words these techniques are control methods rather than forecasting methods. Most forecasting tends, in fact, to be done by an expert judgemental process which is highly subjective. iii It was felt therefore that there was a need for the development of an objective forecasting method. An informal Industrial Opinion Survey was conducted which confirmed this belief. On the basis of this it was decided to attempt to develop an objective forecasting method and to determine whether it was more useful, reliable and accurate than existing subjective forecasts. An exhaustive Literature Survey was then carried out in an attempt to find past work in the field. It was found that most techniques in use were control techniques as described above, with the exception of the Resource Appraisement Model developed by Dr P.P. Pekar. This model (with three variations), provides a means of recalculating the complete project plan in terms of cost at each report period in the light of reported expenditures. However, the model assumes the same time phasing as the original project plan. In other words, it assumes that the project will end on schedule. This assumption limits considerably the practical use of the model. As a result, the Resource Appraisement Model was refined and modified somewhat to include the forecasting of time as well as cost. This was done by relating the two parameters independently to percent physical completion. The resulting model, known as the Generalised Resource Appraisement Model (GRAM), was then tested using a computer program and a case study project. The results of this evaluation were then compared to the forecasts which had been produced by the existing subjective method for the case study project. On the basis of this evaluation it was concluded that the GRAM was more accurate but as reliable as the existing method in forecasting final project cost. It was also found that the model was much quicker in informing management of general project trends (i.e. over or under budgeting). iv It was found however, that the model was too sensitive to large periodical fluctuations in expenditure which were not necessarily true reflections of changes in trend. There is reason to believe that this characteristic may be overcome with relatively minor refinements to the model. The objectives of the thesis were therefore attained adequately. Inevitably however there remains a great deal of work to be done before the technique could be used with confidence. Future work is indicated in taking the model less sensitive to large random fluctuations, and making the model a more flexible management tool by allowing the 'what if' type of investigation

A Computational Approach for the Estimation of Elastic Behavior of Metal Matrix Composites

Composite materials are being widely used in many industries for their properties and efficiency. The current work presents a computational approach that can estimate the elastic behavior of metal composites and porous materials using finite element models of representative volume elements (RVEs) which have been used to test and design particulate composite materials. The required size of the RVE for the determination of elastic properties, the effects of the elastic modulus fraction Einc/Emat on the homogenized elasticity and the convergence of the homogenized properties E11, E22 and E33 with the size of the RVE is explored.https://scholarsjunction.msstate.edu/fea/1000/thumbnail.jp

Persistence of locality in systems with power-law interactions

Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems.Comment: 5 pages, 4 figures, version accepted by PR