Multipartite entanglement and quantum state exchange

We investigate multipartite entanglement in relation to the process of quantum state exchange. In particular, we consider such entanglement for a certain pure state involving two groups of N trapped atoms. The state, which can be produced via quantum state exchange, is analogous to the steady-state intracavity state of the subthreshold optical nondegenerate parametric amplifier. We show that, first, it possesses some 2N-way entanglement. Second, we place a lower bound on the amount of such entanglement in the state using a measure called the entanglement of minimum bipartite entropy.

Utility functions on locally connected spaces

We investigate the role of local connectedness in utility theory and prove that any continuous total preorder on a locally connected separable space is continuously representable. This is a new simple criterion for the representability of continuous preferences, and is not a consequence of the standard theorems in utility theory that use conditions such as connectedness and separability, second countability, or path-connectedness. Finally we give applications to problems involving the existence of value functions in population ethics and to the problem of proving the existence of continuous utility functions in general equilibrium models with land as one of the commodities. (C) 2003 Elsevier B.V. All rights reserved.

Experimental characterization of continuous-variable entanglement

We present an experimental analysis of quadrature entanglement produced from a pair of amplitude squeezed beams. The correlation matrix of the state is characterized within a set of reasonable assumptions, and the strength of the entanglement is gauged using measures of the degree of inseparability and the degree of Einstein-Podolsky-Rosen (EPR) paradox. We introduce controlled decoherence in the form of optical loss to the entangled state, and demonstrate qualitative differences in the response of the degrees of inseparability and EPR paradox to this loss. The entanglement is represented on a photon number diagram that provides an intuitive and physically relevant description of the state. We calculate efficacy contours for several quantum information protocols on this diagram, and use them to predict the effectiveness of our entanglement in those protocols.

Stationary two-atom entanglement induced by nonclassical two-photon correlations

A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulae describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon correlations and nonzero collective decay. It is shown that nonidentical atoms are a better source of stationary entanglement than identical atoms. We discuss the optimal physical conditions for creating entanglement in the system; in particular, it is shown that there is an optimal and rather small value of the mean photon number required for creating entanglement.

Entangling two atoms via spontaneous emission

We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r(12) and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.

Detecting multipartite entanglement

We discuss the problem of determining whether the state of several quantum mechanical subsystems is entangled. As in previous work on two subsystems we introduce a procedure for checking separability that is based on finding state extensions with appropriate properties and may be implemented as a semidefinite program. The main result of this work is to show that there is a series of tests of this kind such that if a multiparty state is entangled this will eventually be detected by one of the tests. The procedure also provides a means of constructing entanglement witnesses that could in principle be measured in order to demonstrate that the state is entangled.

Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation

Recently, there have been several suggestions that weak Kerr nonlinearity can be used for generation of macroscopic superpositions and entanglement and for linear optics quantum computation. However, it is not immediately clear that this approach can overcome decoherence effects. Our numerical study shows that nonlinearity of weak strength could be useful for macroscopic entanglement generation and quantum gate operations in the presence of decoherence. We suggest specific values for real experiments based on our analysis. Our discussion shows that the generation of macroscopic entanglement using this approach is within the reach of current technology.

Distillability of Werner states using entanglement witnesses and robust semidefinite programs

We use robust semidefinite programs and entanglement witnesses to study the distillability of Werner states. We perform exact numerical calculations that show two-undistillability in a region of the state space, which was previously conjectured to be undistillable. We also introduce bases that yield interesting expressions for the distillability witnesses and for a tensor product of Werner states with an arbitrary number of copies.

Mud, algae or seagrass: An assessment of remote sensing techniques for mapping inter-tidal seagrass cover and composition in turbid tropical environments

Large areas of tropical sub- and inter-tidal seagrass beds occur in highly turbid environments and cannot be mapped through the water column. The purpose of this project was to determine if and how airborne and satellite imaging systems could be used to map inter-tidal seagrass properties along the wet-tropics coast in north Queensland, Australia. The work aimed to: (1) identify the minimum level of seagrass foliage cover that could be detected from airborne and satellite imagery; and (2) define the minimum detectable differences in seagrass foliage cover in exposed intertidal seagrass beds. High resolution spectral-reflectance data (2040 bands, 350 – 2500nm) were collected over 40cm diameter plots from 240 sites on Magnetic Island, Pallarenda Beach and Green Island in North Queensland at spring low tides in April 2006. The seagrass species sampled were: Thalassia hemprechii, Halophila ovalis, Halodule uninerivs; Syringodium isoetifolium, Cymodocea serrulata, and Cymodoea rotundata. Digital photos were captured for each plot and used to derive estimates of seagrass species cover, epiphytic growth, micro- and macro-algal cover, and substrate colour. Sediment samples were also collected and analysed to measure the concentration of Chlorophyll-a associated with benthic micro-algae. The field reflectance spectra were analysed in combination with their corresponding seagrass species foliage cover levels to establish the minimum foliage projective cover required for each seagrass to be significantly different from bare substrate and substrate with algal cover. This analysis was repeated with reflectance spectra resampled to the bandpass functions of Quickbird, Ikonos, SPOT 5 and Landsat 7 ETM. Preliminary results indicate that conservative minimum detectable seagrass cover levels across most the species sampled were between 30%- 35% on dark substrates. Further analysis of these results will be conducted to determine their separability and satellite images and to assess the effects epiphytes and algal cover.

Admissible monetary aggregates for the Euro area

We use the Fleissig and Whitney (2003) weak separability test to determine admissible levels of monetary aggregation for the Euro area. We find that the Euro area monetary assets in M2 and M3 are weakly separable and construct admissible Divisia monetary aggregates for these assets. We evaluate the Divisia aggregates as indicator variables, building on Nelson (2002), Reimers (2002), and Stracca (2004). Specifically, we show that real growth of the admissible Divisia aggregates enter the Euro area IS curve positively and significantly for the period from 1980 to 2005. Out of sample, we show that Divisia M2 and M3 appear to contain useful information for forecasting Euro area inflation.

Admissible monetary aggregates for the euro area

We use the Fleissig and Whitney [Fleissig, A.R., Whitney, G.A., 2003. A new PC-based test for Varian's weak separability conditions. Journal of Business and Economics Statistics 21 (1), 133–144] weak separability test to determine admissible levels of monetary aggregation for the Euro area. We find that the Euro area monetary assets in M2 and M3 are weakly separable and construct admissible Divisia monetary aggregates for these assets. We show that real growth of the admissible Divisia aggregates enters the Euro area IS curve positively and significantly for the period from 1980 to 2005. Out of sample, we show that Divisia M2 and M3 appear to contain useful information for forecasting Euro area inflation.

Almost Separable Data Aggregation by Layers of Formal Neurons

Information extraction or knowledge discovery from large data sets should be linked to data aggregation process. Data aggregation process can result in a new data representation with decreased number of objects of a given set. A deterministic approach to separable data aggregation means a lesser number of objects without mixing of objects from different categories. A statistical approach is less restrictive and allows for almost separable data aggregation with a low level of mixing of objects from different categories. Layers of formal neurons can be designed for the purpose of data aggregation both in the case of deterministic and statistical approach. The proposed designing method is based on minimization of the of the convex and piecewise linear (CPL) criterion functions.

Manifold learning and the quantum Jensen-Shannon divergence kernel

The quantum Jensen-Shannon divergence kernel [1] was recently introduced in the context of unattributed graphs where it was shown to outperform several commonly used alternatives. In this paper, we study the separability properties of this kernel and we propose a way to compute a low-dimensional kernel embedding where the separation of the different classes is enhanced. The idea stems from the observation that the multidimensional scaling embeddings on this kernel show a strong horseshoe shape distribution, a pattern which is known to arise when long range distances are not estimated accurately. Here we propose to use Isomap to embed the graphs using only local distance information onto a new vectorial space with a higher class separability. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Circumarctic wetland dataset based on ENVISAT ASAR Global Monitoring Mode with links to geotiff image and NetCDF files (2005-01 to 2011-12)

A circumpolar representative and consistent wetland map is required for a range of applications ranging from upscaling of carbon fluxes and pools to climate modelling and wildlife habitat assessment. Currently available data sets lack sufficient accuracy and/or thematic detail in many regions of the Arctic. Synthetic aperture radar (SAR) data from satellites have already been shown to be suitable for wetland mapping. Envisat Advanced SAR (ASAR) provides global medium-resolution data which are examined with particular focus on spatial wetness patterns in this study. It was found that winter minimum backscatter values as well as their differences to summer minimum values reflect vegetation physiognomy units of certain wetness regimes. Low winter backscatter values are mostly found in areas vegetated by plant communities typically for wet regions in the tundra biome, due to low roughness and low volume scattering caused by the predominant vegetation. Summer to winter difference backscatter values, which in contrast to the winter values depend almost solely on soil moisture content, show expected higher values for wet regions. While the approach using difference values would seem more reasonable in order to delineate wetness patterns considering its direct link to soil moisture, it was found that a classification of winter minimum backscatter values is more applicable in tundra regions due to its better separability into wetness classes. Previous approaches for wetland detection have investigated the impact of liquid water in the soil on backscatter conditions. In this study the absence of liquid water is utilized. Owing to a lack of comparable regional to circumpolar data with respect to thematic detail, a potential wetland map cannot directly be validated; however, one might claim the validity of such a product by comparison with vegetation maps, which hold some information on the wetness status of certain classes. It was shown that the Envisat ASAR-derived classes are related to wetland classes of conventional vegetation maps, indicating its applicability; 30% of the land area north of the treeline was identified as wetland while conventional maps recorded 1-7%.

The Accuracy and Reliability of Traditional Surface Flow Type Mapping: Is It Time for A New Method of Characterising Physical River Habitat?

Surface flow types (SFT) are advocated as ecologically relevant hydraulic units, often mapped visually from the bankside to characterise rapidly the physical habitat of rivers. SFT mapping is simple, non-invasive and cost-efficient. However, it is also qualitative, subjective and plagued by difficulties in recording accurately the spatial extent of SFT units. Quantitative validation of the underlying physical habitat parameters is often lacking, and does not consistently differentiate between SFTs. Here, we investigate explicitly the accuracy, reliability and statistical separability of traditionally mapped SFTs as indicators of physical habitat, using independent, hydraulic and topographic data collected during three surveys of a c. 50m reach of the River Arrow, Warwickshire, England. We also explore the potential of a novel remote sensing approach, comprising a small unmanned aerial system (sUAS) and Structure-from-Motion photogrammetry (SfM), as an alternative method of physical habitat characterisation. Our key findings indicate that SFT mapping accuracy is highly variable, with overall mapping accuracy not exceeding 74%. Results from analysis of similarity (ANOSIM) tests found that strong differences did not exist between all SFT pairs. This leads us to question the suitability of SFTs for characterising physical habitat for river science and management applications. In contrast, the sUAS-SfM approach provided high resolution, spatially continuous, spatially explicit, quantitative measurements of water depth and point cloud roughness at the microscale (spatial scales ≤1m). Such data are acquired rapidly, inexpensively, and provide new opportunities for examining the heterogeneity of physical habitat over a range of spatial and temporal scales. Whilst continued refinement of the sUAS-SfM approach is required, we propose that this method offers an opportunity to move away from broad, mesoscale classifications of physical habitat (spatial scales 10-100m), and towards continuous, quantitative measurements of the continuum of hydraulic and geomorphic conditions which actually exists at the microscale.