Surpassing the currently achievable distance of quantum key distribution based on sending-or-not-sending approach

Protocols based on the sending-or-not-sending (SNS) principle have been intensively studied in recent years and have been shown to enable the longest transmission distances in quantum key distribution (QKD). In this work, we propose a sending-or-not-sending phase-matching QKD protocol (SNS-PM-QKD) that improves tolerance to phase mismatch, thereby extending the achievable transmission distance. We present a security analysis of SNS-PM-QKD in the asymptotic (infinite-key) regime under collective attacks. The performance of the proposed protocol is compared with that of standard phase-matching QKD, theoretical SNS-type twin-field QKD protocols (SNS-TF-QKD), and an experimental SNS-TF-QKD operated over transmission distances of up to 1002km. Our results show that SNS-PM-QKD achieves greater transmission distances than these existing protocols, highlighting its potential for long-distance quantum communication.

💡 Research Summary

This paper introduces a novel quantum key distribution (QKD) protocol called sending‑or‑not‑sending phase‑matching QKD (SNS‑PM‑QKD) that surpasses the transmission distance limits of existing protocols based on the sending‑or‑not‑sending (SNS) principle. Traditional SNS‑TF‑QKD has achieved record distances (≈910 km theoretically, ≈1002 km experimentally) by exploiting the fact that key generation can be made independent of certain error sources through a “send‑or‑not‑send” decision. However, its performance is still constrained by phase drift, dark counts, and the need for precise interference.

SNS‑PM‑QKD integrates the SNS idea into a phase‑matching (PM) framework. Each party (Alice and Bob) prepares two coherent pulses per round: a signal pulse and a reference (secondary) pulse, both with identical intensity and phase. They independently decide, with probability ε, whether to actually send each pulse to an untrusted intermediate node (Charlie). Charlie first interferes the signal pulses at coupler C_s and the reference pulses at coupler C_r. Both couplers are designed to impose a π phase shift on one input, guaranteeing that two identical‑phase pulses interfere destructively. Consequently, in the ideal loss‑only scenario only the “send‑not‑send” (sns) or “not‑send‑send” configurations produce a click at detector D⁻, while “send‑send” (ss) and “not‑send‑not‑send” (nn) produce no click.

In realistic channels, dark counts and phase misalignment cause occasional clicks in all configurations. The protocol mitigates this by employing outcome post‑selection: only detection events corresponding to destructive interference (D⁻ clicks) are kept for key generation. This dramatically reduces the quantum bit error rate (QBER) compared with standard SNS‑TF‑QKD, improving the key‑rate‑to‑error‑rate ratio and allowing longer distances for the same channel loss.

Security is proved in the asymptotic (infinite‑key) regime against collective attacks, following the framework of Ref.