Overcoming Intensity Limits for Long-Distance Quantum Key Distribution

Abstract: Quantum Key Distribution (QKD) enables the sharing of cryptographic keys secured by quantum mechanics. The BB84 protocol assumed single-photon sources, but practical systems rely on weak coherent pulses vulnerable to photon-number-splitting (PNS) attacks. The Gottesman-Lo-L\"utkenhaus-Preskill (GLLP) framework addressed these imperfections, deriving secure key rate bounds under limited PNS scenarios. The Decoy-state protocol further improved performance by refining single-photon yield estimates, but still considered multi-photon states as insecure, thereby limiting intensities and constraining key rate and distance. More recently, finite-key security bounds for decoy-state QKD have been extended to address general attacks, ensuring security against adversaries capable of exploiting arbitrary strategies. In this work, we focus on a specific class of attacks, the generalized PNS attack, and demonstrate that higher pulse intensities can be securely used by employing Bayesian inference to estimate key parameters directly from observed data. By raising the pulse intensity to 10 photons, we achieve a 50-fold increase in key rate and a 62.2% increase in operational range (about 200 km) compared to the decoy-state protocol. Furthermore, we accurately model after-pulsing using a Hidden Markov Model and reveal inaccuracies in decoy-state calculations that may produce erroneous key-rate estimates. While this methodology does not address all possible attacks, it provides a new approach to security proofs in QKD by shifting from worst-case assumption analysis to observation-dependent inference, advancing the reach and efficiency of discrete-variable QKD protocols.