Entanglement Model for Mode-Pairing Quantum Key Distribution

Abstract: Mode-pairing (MP) quantum key distribution (QKD) eliminates the requirements of phase locking and phase tracking compared with twin-field (TF) QKD while still surpassing the fundamental rate-distance limit of QKD. The complexity of the experimental implementation is reduced while the efficiency can still be guaranteed. In MP-QKD, two communication parties need to pair two effective rounds according to the announced results by the third party. Therefore, it is not intuitive how to provide an entanglement protocol equivalent to the prepare-and-measure protocol for proving security. At present, the security of MP-QKD is rigorously proven by examining the consistency of the states detailly between MP-QKD and the fixed-pairing scheme under all of Eve's possible interference to obtain the equivalence, and verifying the security of the latter. Here, we directly present an entanglement model for MP-QKD by proposing a free-pairing entanglement scheme that is equivalent to MP-QKD. This entanglement model simplifies the security proof and provides a clearer insight into the foundation of MP-QKD. Besides, it could provide a theoretical framework for the comprehensive analysis of MP-QKD, such as facilitating practical security analysis. Additionally, we propose an optimized pairing strategy based on the entanglement model. The simulation results show an enhancement of 163\% in pairing efficiency with a reasonable pairing interval $2 \times 10^5$.