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Summary form only given. Quantum communication is hampered by the difficulty to generate maximally entangled states between distant nodes. Due to loss and decoherence, in reality we can only generate partially entangled states. Entanglement purification techniques are needed to concentrate maximally entangled states from partially entangled states. Here we present an entanglement purification scheme with the following properties: (i) For pure two-mode squeezed states it reaches the maximal allowed efficiency in the asymptotic limit (when the number of pairs of modes goes to infinity); (ii) It can be readily extended to distill maximally entangled states from a relevant class of mixed Gaussian states which result from losses in the light transmission. Furthermore, we propose and analyze a scheme to implement this protocol experimentally using high finesse cavities and cross-Kerr nonlinearities.