Protecting single-photon entanglement with imperfect single-photon source

Photon noiseless linear amplification (NLA) is a powerful way to protect the single photon or single-photon entanglement (SPE) from photon loss. However, current NLA protocols for single photon or SPE usually require the local auxiliary single photon, but the ideal single-photon source is unavailable in current technology. In this paper, we investigate the NLA protocols for both single photon and SPE with imperfect single-photon source. We show that the quality of amplified quantum state greatly depends on the imperfect single-photon sources. The upper bound of the fidelity of the amplified quantum state is the fidelity of the single-photon source. In this way, in order to realize the amplification, we should require the fidelity of the single-photon source to be greater than the fidelity of the initial degraded state.