Adaptive QKD link establishment for single- and dual-layer LEO quantum satellite networks

Satellite-based quantum key distribution (QKD), especially relying on low Earth orbit (LEO) satellites, overcomes the geographical limitations of fiber-based QKD and enables global secure communications. However, existing QKD link establishment schemes for LEO quantum satellite networks fail to fully consider practical scenarios (e.g., multi-layer constellations as well as heterogeneous satellite–ground and inter-satellite QKD links) along with realistic constraints (e.g., different illumination conditions and the need to avoid frequent link switching). To address this gap, this work focuses on the adaptive establishment of satellite–ground and inter-satellite QKD links in single- and dual-layer LEO quantum satellite networks. We describe the network structures of single- and dual-layer constellations, as well as formulate the corresponding network model, secret key rate model, and secret key volume model. To realize adaptive QKD link establishment, we develop two integer linear programming (ILP) models and design three heuristic algorithms. The two ILP models are denoted as ILP-G and ILP-R, respectively, where ILP-G aims to maximize the generated key volume, and ILP-R is dedicated to optimizing global key resource balance by prioritizing QKD links with lower remaining key volume. The three heuristic algorithms are designed based on maximum key rate (MaxKR), maximum generated key volume (MaxGKV), and minimum remaining key volume (MinRKV). Simulation results verify the applicability of the proposed approaches across single- and dual-layer LEO quantum satellite networks. Comparative evaluations against two benchmarks, i.e., random fit (RF) and first fit (FF), show that ILP-G and MaxGKV achieve the largest cumulative key volume, while ILP-R and MinRKV outperform the other approaches in key volume distribution, quantum satellite availability, and total number of established QKD links. Specifically, the cumulative key volume of ILP-G is 44.0% and 33.8% higher than that of RF in single- and dual-layer LEO quantum satellite networks, respectively. Furthermore, the dual-layer constellation generates more key resources, with the cumulative key volume reaching approximately five times that of the single-layer constellation. It also exhibits a more balanced global key resource distribution, where key resources are distributed across a broader set of node pairs rather than concentrated on a limited subset of nodes.