Security Analysis of Mode-Pairing Quantum Key Distribution with Flexible Pairing Strategy

Mode-pairing quantum key distribution (MP-QKD) is advantageous for long-distance secure communication, leveraging its simple implementation and quadratic scaling capacity. The post-measurement pairing in MP-QKD alleviates the photon-coincidence demands, which is essential for surpassing the fundamental limit to the key-rate transmission. In this work, we propose an improved decoy-state MP-QKD protocol featuring a flexible and efficient pairing strategy. We prove the security of the proposed scheme by presenting an entanglement model for decoy-state MP-QKD. The simulation results show that the secret key rate (SKR) can be enhanced among all distances. Notably, compared with the original scheme [Nature Communication 13, 3903 (2022)], the improvement of SKR is greater than 65\% within 375 km in the asymptotic case and greater than 50\% within 400 km in the finite case. And the achievable distance can be extended in the finite case, especially with a small block length. The simulation results demonstrate the high efficiency of the proposed scheme, which is expected to promote the practical applicability of MP-QKD. Furthermore, the entanglement model could provide a theoretical framework for further security and performance analysis of decoy-state MP-QKD.