Topological State-Aware Simulation Framework for Inter-Satellite Twin-Field QKD Networks

Abstract

Inter-satellite links (ISLs) are the mandatory backbone for global quantum networks. While Twin-Field Quantum Key Distribution (TF-QKD) successfully surpasses linear rate-loss bounds, its extreme phase sensitivity makes it highly vulnerable to dynamic, non-IID (Independent and Identically Distributed) orbital environments. In composable finite-key analyses governed by the Generalized Entropy Accumulation Theorem (GEAT), traditional adaptive post-selection heuristics either violate strict independence conditions or incur massive second-order penalties that collapse the secret key rate. To overcome this, we introduce a reference-only topological post-selection oracle. By modeling the constellation as a Cellular Sheaf and applying Topological Data Analysis (TDA), our protocol derives a public acceptance event ($\Omega$) exclusively from classical beacon telemetry. To rigorously validate this mechanism, we develop a modular simulation framework equipped with stochastic noise injection and an explicit GEAT security ledger. Simulations across 2,000-5,000 km ISL separations compare the same Hodge-Koopman gate with TDA disabled and enabled. At 2,000 km, the median conditional candidate rates are $2.14 \times 10^{-6}$ and $5.87 \times 10^{-7}$ bit per emitted pulse, respectively; both configurations return zero at 3,000-5,000 km. TDA is active in all 4,788 evaluated windows, but does not extend the positive-candidate range in this scenario. These exported rates are conditional numerical candidates: the full protocol-level composable-security proof remains incomplete and the certified composable rate is therefore zero throughout.