Compact entanglement distillery using realistic quantum memories

We adopt the beam-splitter model for losses to analyze the performance of a recent compact continuous-variable entanglement distillation protocol implemented using realistic quantum memories. We show that the decoherence undergone by a two-mode squeezed state while stored in a quantum memory can strongly modify the results of the preparatory step of the protocol. We find that the well-known method for locally increasing entanglement, phonon subtraction, may not result in entanglement gain when losses are taken into account. Thus, we investigate the critical number m_c of phonon subtraction attempts from the matter modes of the quantum memory. If the initial state is not de-Gaussified within m_c attempts, the protocol should be restarted to obtain any entanglement increase. Moreover, the condition m _c>1 implies an additional constraint on the subtraction beam-splitter interaction transmissivity, viz., it should be about 50% for a wide range of protocol parameters. Additionally, we consider the average entanglement rate, which takes into account both the unavoidable probabilistic nature of the protocol and its possible failure as a result of a large number of unsuccessful subtraction attempts. We find that a higher value of the average entanglement can be achieved by increasing the subtraction beam-splitter interaction transmissivity. We conclude that the compact distillation protocol with the practical constraints coming from realistic quantum memories allows a feasible experimental realization within existing technologies.