O(^√η) efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel

Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1) or even near-zero transmittance (η ≈ 0) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0. The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O(√η) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.