Estimation for bilinear stochastic systems

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Quantum information processing with space-division multiplexing optical fibres

The optical fibre is an essential tool for our communication infrastructure since it is the main transmission channel for optical communications. The latest major advance in optical fibre technology is spatial division multiplexing (SDM), where new fibre designs and components establish multiple co-existing data channels based on light propagation over distinct transverse optical modes. Simultaneously, there have been many recent developments in the field of quantum information processing (QIP), with novel protocols and devices in areas such as computing, communication and metrology. Here, we review recent works implementing QIP protocols with SDM optical fibres, and discuss new possibilities for manipulating quantum systems based on this technology.Comment: Originally submitted version. Please see published version for improved layout, new tables and updated references following review proces

Superconducting Quantum Metamaterials

Superconducting quantum metamaterials extend the idea of their classical counterpart to a regime where their constituent meta-atoms are quantum objects, which can hold their quantum coherence for longer than the propagation time of light through the medium. In this work, we have realized a quantum metamaterial consisting of eight individually controllable superconducting transmon qubits, which are coupled to the mode continuum of a one-dimensional coplanar waveguide. This system can be described within the framework of waveguide-quantum electrodynamics, which predicates that the mutual interaction of the qubits with the waveguide gives rise to long-range interactions of the qubits. In spectroscopic measurements we observe the formation of super- and subradiant collective metamaterial excitations, as well as the emergence of a polaritonic band gap and study their dependence on the number of participating resonant qubits. We utilize the collective Autler-Townes splitting of the metamaterial to demonstrate control over its band gap. Furthermore, we exploit the control over the band structure for a first realization of slowly propagating light in the metamaterial. Our findings show that superconducting quantum metamaterials are a suitable platform to study fundamental excitations in solids and pave way to applications in quantum information processing like quantum memories

Quantum holonomies in photonic waveguide systems

The thesis at hand deals with the emergence of quantum holonomies in systems of coupled waveguides. Several proposals for their realisation in arrays of laser-written fused-silica waveguides are presented, including experimental results. I develop an operator-theoretic framework for the photon-number independent description of these optical networks. Finally, quantum holonomies will be embedded into schemes for measurement-based quantum computation, with the aim of approximating Jones polynomials.Die vorliegende Arbeit untersucht die Konzipierung von Quantenholonomien in Systemen gekoppelter Wellenleiter. Eine Vielzahl möglicher Realisierungen mittels lasergeschriebener Wellenleiter in Quarzglas wird präsentiert und zugehörige experimentelle Ergebnisse erläutert. Die Entwicklung einer operatortheoretischen Darstellung für die photonenzahlunabhängige Beschreibung dieser optischen Netzwerke wird vorgenommen. Abschließend werden Quantenholonomien für die messinduzierte Quantenberechnung von Jones-Polynomen verwendet