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The main topic of this thesis is linear optics and the implementation of quantum operations (measurements, quantum channels, and unitary rotations) on optical systems. In the opening chapter the basic notions needed to understand the rest of the thesis will be explained. These notions include defining a quantum state, measurement, quantum channel and the linear optics tool set. The work in this thesis takes both fundamental and practical approaches to studying linear optical networks. For instance in the first chapter a proof is provided that shows that any unitary on a single mode Fock state can be realised with linear optics. The proof is constructive, however the approach to realising the unitary is not suitable for experimental implementation because it requires complicated ancilla states. As in the KLM proposal the procedure works only stochastically however by allowing the size of the ancilla to grow the probability of failure can be made arbitrarly small. Furthermore we investigate the realisation of arbitrary channels in a specific encoding that we call a $d$-rail encoding. The only ancilla state that we allow is a vacuum ancilliary state and further restrictions were considered (e.g. photon counting). A proof is provided that using these resources only random unitaries can be applied deterministically using linear optics. An expression for the optimal probability of success for realising more general channels with these resources is also discussed. As a final topic we also investigate the realisation of a quantum non-demolition measurement onto the dual rail qubit space. The investigation is a blend of both fundamental and practical approaches. To begin we employ a modified KLM-like procedure and show that the scheme can be realised perfectly but stochastically. The probability that the proper measurement is made can be made arbitrarly close to one using a suitably large ancilla state. In addition we consider an existing scheme \cite{gisin10a} which uses practical sources (two single photon sources) to perform the measurement. The scheme does not realise the true measurement but instead has a free parameter in it which is the transmittiviy of a beamsplitter. The measurement will project onto a space that has a vacuum component. By adjusting the transmittivity of this beamsplitter the vacuum component can be made arbitrarly small but only at the expense of the probability of success of the procedure. In this thesis a modification that can be made to eliminate the vacuum component without changing the sources is introduced. The modification is surprisingly simple and only involves the addition of a single beamsplitter. In the proposal for the original amplifier it was used in simulations for DIQKD that included device imperfections. To show the improvement of our modification these DIQKD simulations are reproduced using the modified amplifier and its results are compared to the results of the original amplifier.

<p>This thesis deals with the design and implementation of some novel numerical methods for non-linear singular pertubations problems (NSPPs). It provide a survey of asymptotic and numerical methods for some NSPPs in the past decade. By considering two test problems, rigorous asymptotic analysis is carried out. Based on this analysis, suitable numerical methods are designed, analyzed and implemented in order to have some relevant results of physical importance. Since the asymptotic analysis provides only qualitative information, the focus is more on the numerical analysis of the problem which provides the quantitative information.</p>

In this thesis, a class of control and identification methods on a typical laboratory process - a ball and beam system - are discussed. The ball and beam is a common laboratory process which contains nonlinearity, a double integrator and time-delay. In our project, the hardware made by Wincon (Quanser SRV02 +BB01) is used. The main contribution of this work is the development of a variety of controller design methods, which together with suitable parameter identification techniques provide tools for rapid prototyping for real time control of processes within the laboratory, in preparation for industrial implementation of more complex schemes. The novelty of this work lies in the use of model predictive control (MPC) methods based on a non-minimal state space formulation, which permits the inclusion of process measurements and actuations in the state vector, leading to controller designs which are immediately ready for on-line implementation. A linear MPC controller based on a non-minimal state space model is based on an approximate linear model. The results from simulation and online experiment show that the linear MPC controller realizes a satisfying reference tracking in the face of nonlinearity and time-delay. In the following chapter, a nonlinear Hammerstein model is identified, which is a type of reliable structure for describing nonlinear plants. A nonlinear MPC scheme is developed based on the Hammerstein model. An inversion block is created to cancel the effect of the nonlinearity. The performance IS also tested in both simulation and experiment. Finally, MPC is combined with sliding mode control. The non-minimal state space model is also used here. In the first part of this chapter, the idea underlying sliding mode control contributes a method of modifying the definition of the cost function in MPC. In the second half, MPC is used to design the switching surface in sliding mode control. The performance of tests on the example (ball and beam system) illustrates that these are both valid methods for dealing with complex processes.

Thesis (Ph. D.)--Stanford University, 1987. / "June 1987." "Also numbered Classic-87-03"--Cover. "This research was supported by NASA Ames Consortium Agreement NASA NCA2-150 and Office of Naval Research Contracts N00014-86-K-0565, N00014-82-K-0335, N00014-75-C-1132"--P. vi. Includes bibliographical references (p. 125-129).

Thesis (M. Sc.)--University of Adelaide, Dept. of Statistics, 1993? / Includes bibliographical references (leaves 88-90).

Thesis (M.D.)--University of New South Wales, 2001. / Also available online.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 60-63). Also available via the Internet.

Thesis (M.S.)--Rochester Institute of Technology, 1992. / Typescript. Includes bibliographical references.