Distillation and purification of symmetric entangled Gaussian states

We propose an entanglement distillation and purification scheme for symmetric two-mode entangled Gaussian states that allows to asymptotically extract a pure entangled Gaussian state from any input entangled symmetric Gaussian state. The proposed scheme is a modified and extended version of the entanglement distillation protocol originally developed by [Browne et al., Phys. Rev. A 67, 062320 (2003)]. A key feature of the present protocol is that it utilizes a two-copy de-Gaussification procedure that involves a Mach-Zehnder interferometer with single-mode non-Gaussian filters inserted in its two arms. The required non-Gaussian filtering operations can be implemented by coherently combining two sequences of single-photon addition and subtraction operations.