| Summary: | The research presented in this thesis is divided into three topics, all of which are related to different areas of Information Theory. Firstly I have worked with my supervisor Professor Mike Payne on proposals for the implementation of two different types of quantum measurements of single photons, namely generalized measurements and weak measurements. This research belongs to the field of Quantum Information Theory. My second area of research has been Molecular Dynamics. With Gabor Csanyi I have worked on the development of a new way of constructing empirical potentials, which are needed for the large-scale simulation of atomic systems. Until now the construction of such potentials has been a laborious task and highly specific to the particular species of atoms involved. Our method, which employs a fitting technique known as Gaussian Processes, aims to provide a comparatively simple and very general way of constructing empirical potentials, using data from quantum-mechanical methods, such as Tight-Binding schemes. In this thesis I present results which demonstrate the feasibility of fitting a function in the configuration space of atomic neighbourhoods. My third research topic has been the analysis of biological data series using algorithmic information theory, together with Thomas Fink of the Institut Curie in Paris. By calculating a bound on the Algorithmic Information Content (AIC) of a given data curve we are able to identify biologically significant curves, thus providing a tool for biological data analysis.
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