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Ions, confined in a Paul trap and under influence of controlled laser fields provide one of the best controllable quantum mechanical systems up to date in which elements of quantum theory and quantum information theory can be realized and analyzed. In the framework of this work we realized a quantum random walk (QRW) with a single trapped ion. The difference of a QRW to a classical random walk is, that not a certain path is realized with a certain probability, but that all possible paths are realized at the same time – this leads to interference effects. We implemented the QRW in one motional degree of freedom of the ion. The steps of the QRW were fulfilled by applying a state-dependent optical dipole force. We used state-of-the-art techniques for preparation, manipulation and detection of the state of the ion and extended them to specialized methods for the implementation of the QRW. By theoretical investigations of the QRW in the special system of a trapped ion and extensive numerical analysis we developed a model that is suitable for the description of the QRW and that serves as a basis for further investigations. |