Gaussian Transformations and Distillation of Entangled Gaussian States

We prove that it is impossible to distill more entanglement from a single copy of a two-mode bipartite entangled Gaussian state via local Gaussian operations and classical communication. 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. [preceding Letter, Phys. Rev. Lett. 89, 137903 (2002)] is the optimum Gaussian distillation protocol for two copies of entangled Gaussian states.

Figure 1

Setup for implementation of a deterministic LOCC Gaussian CP map that is for a single fixed input Gaussian state equivalent to a given probabilistic LOCC Gaussian CP map.

Figure 2

Optimal distillation protocol for two copies of two-mode entangled Gaussian states.