Study of the 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 which show 2-undistillability in a region of the state space which was previously conjectured to be undistillable. We also introduce bases which yield interesting expressions for the {\em distillability witnesses} and for a tensor product of Werner states with arbitrary number of copies.Comment: 16 pages, 2 figure

Spatio-temporal bivariate statistical models for atmospheric trace-gas inversion

Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a data-assimilation flavour, which implicitly consider univariate statistical models with the flux as the variate of interest. This univariate approach typically assumes that the flux field is either a spatially correlated Gaussian process or a spatially uncorrelated non-Gaussian process with prior expectation fixed using flux inventories (e.g., NAEI or EDGAR in Europe). Here, we extend this approach in three ways. First, we develop a bivariate model for the mole-fraction field and the flux field. The bivariate approach allows optimal prediction of both the flux field and the mole-fraction field, and it leads to significant computational savings over the univariate approach. Second, we employ a lognormal spatial process for the flux field that captures both the lognormal characteristics of the flux field (when appropriate) and its spatial dependence. Third, we propose a new, geostatistical approach to incorporate the flux inventories in our updates, such that the posterior spatial distribution of the flux field is predominantly data-driven. The approach is illustrated on a case study of methane (CH$_4$) emissions in the United Kingdom and Ireland.Comment: 39 pages, 8 figure

A study on the variability of ionospheric total electron content over the East African low-latitude region and storm time ionospheric variations

The variation of total electron content (TEC) derived from the International Global Navigation Satellite Systems Service receiver (formerly IGS) over the East African low-latitude region from up to 12 observation stations for the period 2012 was analyzed. The diurnal and annual TEC contour plots generated from data over the region show that the equatorial anomaly crests manifest remarkable seasonal variations. The crest of the equatorial ionization anomaly is fully formed and yields the maximum values of TEC during the equinoxes (March/April and September/October) and minimum in the solstice (June/July and November/December). The results of this observation show that the crest develops between 12:00 and 16:00 LT and is greatly dependent on the time when the ionosphere is uplifted at the dip equator via the E × B drift force. The postsunset TEC enhancements at stations away from dip equator depict the ionospheric plasma density diffusion (flow) from the dip equator leading to the formation of ionization anomaly crests that lasts for few hours after the sunset local time. The ionospheric response to the strong geomagnetic storm of the March 2015 has also been examined. The ionospheric response to the geomagnetic storms has shown a strong thermosphere-ionosphere coupling. The negative storm effect that occurred over the anomaly crest region is more likely due to the composition disturbances associated with high energy deposits

Verifying linearizability on TSO architectures

Linearizability is the standard correctness criterion for fine-grained, non-atomic concurrent algorithms, and a variety of methods for verifying linearizability have been developed. However, most approaches assume a sequentially consistent memory model, which is not always realised in practice. In this paper we define linearizability on a weak memory model: the TSO (Total Store Order) memory model, which is implemented in the x86 multicore architecture. We also show how a simulation-based proof method can be adapted to verify linearizability for algorithms running on TSO architectures. We demonstrate our approach on a typical concurrent algorithm, spinlock, and prove it linearizable using our simulation-based approach. Previous approaches to proving linearizabilty on TSO architectures have required a modification to the algorithm's natural abstract specification. Our proof method is the first, to our knowledge, for proving correctness without the need for such modification

Diurnal Variation of TEC and S 4 Index During the Period of Low Geomagnetic Activity at Ile-Ife, Nigeria

Ile-Ife lies on the equatorial anomaly region where the ionospheric current is greatly influenced by the existence of the equatorial electrojet. The dual frequency SCINDA NovAtel GSV 4004B GPS receiver recently installed at Ile-Ife [on geographical latitude 7°33′N and longitude 4°33′E and geomagnetic dipole (coordinate) of latitude 9.84°N and longitude 77.25°E] is currently operational and recording data from the available global positioning system satellites. The receiver provides the data on total electron content (TEC) and the scintillation index (S[subscript 4]). This paper presents the first sets of results from this station. Data records for the month of February 2010 were analyzed using the WinTec-P software program and these were interpreted to discuss the diurnal variation of the TEC and S[subscript 4] index during the period considered, as having low geomagnetic activity. The vertical TEC in this study showed that the values vary widely from as low as 0 TECu about sunrise to about 35 TECu during the day. Depletion in TEC was also noticed about sunset and marked by the occurrence of scintillations with a maximum index value of 0.3. Results of the IRI models and the observed TEC differ considerably; hence, there is the need to improve IRI models for its adaptability to the Africa ionospheric conditions

Bell's inequalities in the tomographic representation

The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be the most natural one to compare the predictions of classical and quantum theory. Examples of inequalities for two qubits an two qutrits are considered in the tomographic probability representation of spin states.Comment: 11 pages, comments and references adde

Optimal Unravellings for Feedback Control in Linear Quantum Systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state-based) control problems (the stationary Linear-Quadratic-Gaussian class), this question is a semi-definite program. Moreover, the answer also applies to Markovian (current-based) feedback.Comment: 5 pages. Version published by Phys. Rev. Let

Modelling an energetic tidal strait:investigating implications of common numerical configuration choices

Representation of the marine environment is key for reliable coastal hydrodynamic models. This study investigates the implications of common depth-averaged model configuration choices in sufficiently characterising seabed geometry and roughness. In particular, applications requiring a high level of accuracy and/or exhibiting complex flow conditions may call for greater detail in marine environment representation than typically adopted in coastal models. Ramsey Sound, a macrotidal strait in Pembrokeshire, Wales, UK is considered as a case study. The site contains various steeply inclined bathymetric features, including a submerged pinnacle named Horse Rock and a rocky reef called “The Bitches”. The available energy in Ramsey Sound’s tidal currents has attracted attention from tidal energy developers. There is interest in accurately modelling the energetic hydrodynamics surrounding its pronounced bathymetry. The coastal flow solver Thetis is applied to simulate the flow conditions in Ramsey Sound. It is shown that notable prominent bathymetric features in the strait influence localised and, most importantly, regional hydrodynamic characteristics. “The Bitches” consistently accelerate flow in the strait while Horse Rock induces a notable wake structure and flow reversals. The model is calibrated against bed- and vessel-mounted Acoustic Doppler Current Profiler (ADCP) observations, by altering seabed roughness parameterisations. A spatially variable and locally scaled Manning coefficient based on diverse seabed classification observations is found to improve model performance in comparison to uniformly applied constants, the latter a more common approach. The local impact of altering the Manning coefficient configuration is found to be greatest during spring flood periods of high velocity currents. Meanwhile, the effect of coarsening the computational mesh around bathymetric features towards values more typically applied in coastal models is investigated. Results indicate severe misrepresentation of seabed geometry and subsequent wake hydrodynamics unless refined to a mesh element size that adequately represents Horse Rock and “The Bitches”

Strategies for Real-Time Position Control of a Single Atom in Cavity QED

Recent realizations of single-atom trapping and tracking in cavity QED open the door for feedback schemes which actively stabilize the motion of a single atom in real time. We present feedback algorithms for cooling the radial component of motion for a single atom trapped by strong coupling to single-photon fields in an optical cavity. Performance of various algorithms is studied through simulations of single-atom trajectories, with full dynamical and measurement noise included. Closed loop feedback algorithms compare favorably to open-loop "switching" analogs, demonstrating the importance of applying actual position information in real time. The high optical information rate in current experiments enables real-time tracking that approaches the standard quantum limit for broadband position measurements, suggesting that realistic active feedback schemes may reach a regime where measurement backaction appreciably alters the motional dynamics.Comment: 12 pages, 10 figures, submitted to J. Opt. B Quant. Semiclass. Op