Continuous-variable entanglement distillation by cascaded photon replacement

We study the entanglement distillation in continuous-variable systems when a photon replacement protocol is employed. A cascaded protocol is studied and we find that the resultant entanglement increases by increasing the number of repetitions. Interestingly, the entanglement enhancement is not sensitive to the asymmetry of the protocol and gives the same result for any arrangement in the absence of loss. The non-Gaussianity of the outcome state is also studied and it is found that the non-Gaussianity of the state dramatically depends on the experimental arrangements. We also consider the case of imperfect detectors and show that the main results are valid provided high-efficiency detectors are employed. By providing practical information on photon replacement operation, this work is one step towards the realization of universal quantum computation; in particular, in setups where de-Gaussifying protocols are only applicable to one of the parties.