Linear dynamic filtering with noisy input and output

Estimation problems for linear time-invariant systems with noisy input and output are considered. The smoothing problem is a least norm problem. An efficient algorithm using a Riccati-type recursion is derived. The equivalence between the optimal filter and an appropriately modified Kalman filter is established. The optimal estimate of the input signal is derived from the optimal state estimate. The result shows that the noisy input/output filtering problem is not fundamentally different from the classical Kalman filtering problem

Variational Characterisations of Separability and Entanglement of Formation

In this paper we develop a mathematical framework for the characterisation of separability and entanglement of formation (EoF) of general bipartite states. These characterisations are of the variational kind, meaning that separability and EoF are given in terms of a function which is to be minimized over the manifold of unitary matrices. A major benefit of such a characterisation is that it directly leads to a numerical procedure for calculating EoF. We present an efficient minimisation algorithm and an apply it to the bound entangled 3X3 Horodecki states; we show that their EoF is very low and that their distance to the set of separable states is also very low. Within the same variational framework we rephrase the results by Wootters (W. Wootters, Phys. Rev. Lett. 80, 2245 (1998)) on EoF for 2X2 states and present progress in generalising these results to higher dimensional systems.Comment: 11 pages RevTeX, 4 figure

Local unitary versus local Clifford equivalence of stabilizer states

We study the relation between local unitary (LU) equivalence and local Clifford (LC) equivalence of stabilizer states. We introduce a large subclass of stabilizer states, such that every two LU equivalent states in this class are necessarily LC equivalent. Together with earlier results, this shows that LC, LU and SLOCC equivalence are the same notions for this class of stabilizer states. Moreover, recognizing whether two given stabilizer states in the present subclass are locally equivalent only requires a polynomial number of operations in the number of qubits.Comment: 8 pages, replaced with published versio

Four qubits can be entangled in nine different ways

We consider a single copy of a pure four-partite state of qubits and investigate its behaviour under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four-qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to a seven parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single copy distillation protocol

ARGOS policy brief on semantic interoperability

Semantic interoperability requires the use of standards, not only for Electronic Health Record (EHR) data to be transferred and structurally mapped into a receiving repository, but also for the clinical content of the EHR to be interpreted in conformity with the original meanings intended by its authors. Accurate and complete clinical documentation, faithful to the patient’s situation, and interoperability between systems, require widespread and dependable access to published and maintained collections of coherent and quality-assured semantic resources, including models such as archetypes and templates that would (1) provide clinical context, (2) be mapped to interoperability standards for EHR data, (3) be linked to well specified, multi-lingual terminology value sets, and (4) be derived from high quality ontologies. Wide-scale engagement with professional bodies, globally, is needed to develop these clinical information standards

Model error estimation in ensemble data assimilation

A new methodology is proposed to estimate and account for systematic model error in linear filtering as well as in nonlinear ensemble based filtering. Our results extend the work of Dee and Todling (2000) on constant bias errors to time-varying model errors. In contrast to existing methodologies, the new filter can also deal with the case where no dynamical model for the systematic error is available. In the latter case, the applicability is limited by a matrix rank condition which has to be satisfied in order for the filter to exist. <br><br> The performance of the filter developed in this paper is limited by the availability and the accuracy of observations and by the variance of the stochastic model error component. The effect of these aspects on the estimation accuracy is investigated in several numerical experiments using the Lorenz (1996) model. Experimental results indicate that the availability of a dynamical model for the systematic error significantly reduces the variance of the model error estimates, but has only minor effect on the estimates of the system state. The filter is able to estimate additive model error of any type, provided that the rank condition is satisfied and that the stochastic errors and measurement errors are significantly smaller than the systematic errors. The results of this study are encouraging. However, it remains to be seen how the filter performs in more realistic applications

The Lorentz singular value decomposition and its applications to pure states of 3 qubits

All mixed states of two qubits can be brought into normal form by the action of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$. These normal forms can be obtained by considering a Lorentz singular value decomposition on a real parameterization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criterion is conjectured for a mixed state to be convertible into another specific one with a non-zero probability. Finally the formalism of the Lorentz singular value decomposition is applied to tripartite pure states of qubits. New proofs are given for the existence of the GHZ- and W-class of states, and a rigorous proof for the optimal distillation of a GHZ-state is derived