# Asymmetric Protocols for Mode Pairing Quantum Key Distribution with Finite-Key Analysis
###### Abstract  
The mode pairing quantum key distribution (MP-QKD) protocol has attracted considerable attention for its capability to ensure high secure key rates over long distances without requiring global phase locking. However, ensuring symmetric channels for the MP-QKD protocol is challenging in practical quantum communication networks. Previous studies on the asymmetric MP-QKD protocol have relied on ideal decoy state assumptions and infinite-key analysis, which are unattainable for real-world deployment. In this paper, we conduct a security analysis of the asymmetric MP-QKD protocol with the finite-key analysis, where we discard the previously impractical assumptions made in the decoy state method. Combined with statistical fluctuation analysis, we globally optimized the 10 independent parameters in the asymmetric MP-QKD protocol by employing our modified particle swarm optimization. Through further analysis, the simulation results demonstrate that our work achieves improved secure key rates and transmission distances compared to the strategy with additional attenuation. We further investigate the relationship between the intensities and probabilities of signal, decoy, and vacuum states with transmission distance, facilitating their more efficient deployment in future quantum networks. quantum key distribution; mode pairing; particle swarm optimization; finite-key analysis; asymmetric protocols +
Footnote †: journal:  
0000-0002-4001-558X/00/10/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/00002-4001-58X/0002-4001-58X/000  
Twin-field (TF) QKD [6] utilizes single-photon interference for key generation, surpassing the PLOB bound, while also retaining immunity to detector-side attacks. Nevertheless, in order to maintain the coherence between distant quantum states, TF-QKD requires the deployment of global phase locking technology [7, 8], leading to increased complexity and additional resource consumption within QKD systems. Fortunately, the recently proposed mode pairing (MP) QKD protocol [9, 10] eliminates the requirement for global phase locking while also surpassing the repeaterless bound. Given its exceptional performance in laboratory [11, 12] and field environments [13, 14], the MP-QKD protocol has established itself as a robust candidate for the future deployment of quantum communication networks. In scenarios involving geographical disparities (e.g., in star-shaped quantum communication networks [15]), or when the communicating parties ([PERSON] and [PERSON]) are situated in moving free spaces (e.g., drones, ships, satellites, etc. ), challenges are posed in achieving symmetric communication with the central node, [PERSON]. Introducing additional losses to compensate for channel asymmetry is a solution, but it results in suboptimal SKR [16]. Previous analyses of the asymmetric MP-QKD protocol [17, 18] required ideal decoy state assumptions and infinite-key, which are overly idealized and impractical. Thus, it is crucial to account for the finite-key size effects in the asymmetric MP-QKD protocol while considering practical decoy state deployment. In this paper, we evaluate the performance of the MP-QKD protocol with asymmetric channels. Through employing the practical decoy state method and the universally composable framework, we analyzed the security of the asymmetric MP-QKD protocol with finite-key size. By employing our modified particle swarm optimization (PSO) algorithm, we globally optimized the 10 independent parameters of the decoy state MP-QKD protocol. Our modified PSO algorithm is more suitable for asymmetric MP-QKD, as it does not rely on the specific form or gradient information of the SKR function, demonstrating robust global search capabilities.