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We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover, it allows us to find a pure product-state decomposition of any given separable Gaussian state. We also show that all bipartite Gaussian states with nonpositive partial transpose are distillable.
Giedke et al. (Mon,) studied this question.