On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Micromachined 300GHz high Q resonant slot frequency selective surface filter

The design of a low loss quasi-optical beam splitter which is required to provide efficient diplexing of the bands 316.5-325.5 GHz and 349.5-358.5 GHz is presented. To minimise the filter insertion loss, the chosen architecture is a three-layer freestanding array of dipole slot elements. Floquet modal analysis and finite element method computer models are used to establish the geometry of the periodic structure and to predict its spectral response. Two different micromachining approaches have been employed to fabricate close packed arrays of 460 mm long elements in the screens that form the basic building block of the 30mm diameter multilayer frequency selective surface. Comparisons between simulated and measured transmission coefficients for the individual dichroic surfaces are used to determine the accuracy of the computer models and to confirm the suitability of the fabrication methods.

Dynamic Multivariate Statistical Process Control using Subspace Identification

This paper points out a serious flaw in dynamic multivariate statistical process control (MSPC). The principal component analysis of a linear time series model that is employed to capture auto- and cross-correlation in recorded data may produce a considerable number of variables to be analysed. To give a dynamic representation of the data (based on variable correlation) and circumvent the production of a large time-series structure, a linear state space model is used here instead. The paper demonstrates that incorporating a state space model, the number of variables to be analysed dynamically can be considerably reduced, compared to conventional dynamic MSPC techniques.

One-way quantum computing in a decoherence-free subspace

We introduce a novel scheme for one-way quantum computing (QC) based on the use of information encoded qubits in an effective cluster state resource. With the correct encoding structure, we show that it is possible to protect the entangled resource from phase damping decoherence, where the effective cluster state can be described as residing in a decoherence-free subspace (DFS) of its supporting quantum system. One-way QC then requires either single or two-qubit adaptive measurements. As an example where this proposal can be realized, we describe an optical lattice set-up where the scheme provides robust quantum information processing. We also outline how one can adapt the model to provide protection from other types of decoherence.