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On restricted unitary Cayley graphs and symplectic transformations modulo n Nail de Beaudrap Quantum Information Theory Group Institute f r Physic UND Astronomic, University t Potsdam u a Submitted:
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Nail de Beaudrap Quantum Information Theory Group Institute f r Physic UNIVERSITY POSTAL Potsdam, Germany f r Physical UND UNIVERSITY POTSDAM, GERMANY u a Submitted: Feb 11, 2010; Accepted: Apr 27, 2010; Published: May 7, 2010, Physics Subject Classification: 02Y5, 02Z13, 01P05, 03N3, 08C23 Abstract Mathematical methods can be used to study interactions between quantum particles and their environment. An example is the case of quits (one-time quantum states); in such systems, quantum states are associated with their associated measurements. We describe our experiments with the BESS detector and show that in some sense, these measurements can be made with classical particles. In particular, we use an alternative basis for a classical measurement to measure two quits simultaneously, which gives a better guarantee in some applications. We consider many additional applications, and present numerical results. The article is aimed at graduate and undergraduate physicists and their advisers, with particular emphasis placed on those with a background in non-classical electrodynamics. This is a book that will be useful to all levels of graduate students and experts, and anyone interested in quantum information theory and related topics. It has the following aims: First, to introduce the basic concepts of quantum information theory and to sketch the key issues in the relevant literature. Second, to review our recent experiments employing the BESS detector. Third, to show that, while in general methods for studying interactions between classical particles and their environment are suitable for the description of experiments with quits, certain properties can be preserved only in certain particular circumstances with the aid of classical measurements. A specific example of this preservation is that the measured state can be decoupled from the initial state (decoherence), for example to obtain an interference pattern. Fourth, to discuss the generalization of this generalization to a whole range of systems such as, for example, in a quantum-mechanical system in a BESS detector or in the quits that make up a two-qubit quantum computer. The book is intended for readers with some or no background in quantum information theory. The book gives several examples illustrating the application of quantum statistical physics, including an experiment from which the methods discussed in the text were developed and an experiment where the same results are obtained using a modified basis for measurements than that used in the original experiments.

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