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We propose a scheme to perform basic gates of quantum computing and prepareentangled states in a system with cold trapped ions located in a single modeoptical cavity. General quantum computing can be made with both motional stateof the trapped ion and cavity state being qubits. We can also generatedifferent kinds of entangled states in such a system without state reduction,and can transfer quantum states from the ion in one trap to the ion in anothertrap. Experimental requirement for achieving our scheme is discussed.Comment: To appear in J. Opt.

Implementation of quantum gates and preparation of entangled states in cavity QED with cold trapped ions