  We prove that it is impossible to distill more entanglement from a single
copy of a two-mode bipartite entangled Gaussian state via LOCC Gaussian
operations. More generally, we show that any hypothetical distillation protocol
for Gaussian states involving only Gaussian operations would be a deterministic
protocol. Finally, we argue that the protocol considered by Eisert et al.
[quant-ph/0204052] is the optimum Gaussian distillation protocol for two copies
of entangled Gaussian states.
