# Phase Matching Quantum Key Distribution based on Single-Photon Entanglement

## TL;DR

This paper introduces SEPM-QKD, a novel phase-matching quantum key distribution protocol based on single-photon entanglement, which achieves high key rates and avoids detection loopholes, advancing secure long-distance quantum communication.

## Contribution

It proposes SEPM-QKD, a new phase-matching QKD scheme based on single-photon entanglement, with a security proof and theoretical demonstration of its advantages.

## Key findings

- Achieves key rate bound of O(√η) with respect to transmittance
- Secure against all collective and beam-splitting attacks
- Eliminates detection loopholes in long-distance DI-QKD

## Abstract

Two time-reversal quantum key distribution (QKD) schemes are the quantum entanglement based device-independent (DI)-QKD and measurement-device-independent (MDI)-QKD. The recently proposed twin field (TF)-QKD, also known as phase-matching (PM)-QKD, has improved the key rate bound from $O\left( \eta \right )$ to $O\left( \sqrt {\eta} \right )$ with $\eta$ the channel transmittance. In fact, TF-QKD is a kind of MDI-QKD but based on single-photon detection. In this paper, we propose a different PM-QKD based on single-photon entanglement, referred to as single-photon entanglement-based phase-matching (SEPM)-QKD, which can be viewed as a time-reversed version of the TF-QKD. Detection loopholes of the standard Bell test, which often occur in DI-QKD over long transmission distances, are not present in this protocol because the measurement settings and key information are the same quantity which is encoded in the local weak coherent state. We give a security proof of SEPM-QKD and demonstrate in theory that it is secure against all collective attacks and beam-splitting attacks. The simulation results show that the key rate enjoys a bound of $O\left( \sqrt {\eta} \right )$ with respect to the transmittance. SEPM-QKD not only helps us understand TF-QKD more deeply, but also hints at a feasible approach to eliminate detection loopholes in DI-QKD for long-distance communications.