Amendable Gaussian channels: Restoring entanglement via a unitary filter

We show that there exist Gaussian channels which are amendable. A channel is amendable if when applied twice is entanglement breaking while there exists a unitary filter such that, when interposed between the first and second action of the map, prevents the global transformation from being entanglement breaking [Phys. Rev. A 86, 052302 (2012)]. We find that, depending on the structure of the channel, the unitary filter can be a squeezing transformation or a phase shift operation. We also propose two realistic quantum optics experiments where the amendability of Gaussian channels can be verified by exploiting the fact that it is sufficient to test the entanglement breaking properties of two mode Gaussian channels on input states with finite energy (which are not maximally entangled).