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In this talk I will outline the basic questions that are being studied in any theory of entanglement. Following a brief review of some of the main achievements of entanglement theory for finite dimensional systems such as qubits, I will then consider entanglement in infinite dimensional systems. Asking for a theory of entanglement in such systems under experimentally feasible operations leads to the development of the theory of entanglement of Gaussian states. Results of this theory are presented and the tools that have been developed for it are then applied to a number of interesting problems.
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