Entanglement purification of Gaussian continuous variable quantum states in quantum optics

Presented is an entanglement purification scheme which generates maximally entangled states in finite Hilbert spaces from the continuous two-mode squeezed states. With high probabilities, one gets a more entangled state, and the entanglement in the continuous partially entangled state is transferred to the maximally entangled states with high efficiency. Furthermore, in several practical cases this purification protocol can be readily extended to distill maximally entangled states from the mixed Gaussian continuous states. One knows that a two-mode squeezed states with inevitably evolve into a mixed Gaussian continuous state due to the unavoidable loss in light propagation. A small alternation of the protocol also provides a method for preparing free Greenberger-Horne-Zeilinger states in high dimensional Hilbert spaces. The purification scheme relies on a local quantum non-demolition measurement of the total excitation number of several entangled pairs. Possible experimental implementations of the scheme is discussed.