Optimization of Information Reconciliation for Decoy-State Quantum Key Distribution over a Satellite Downlink Channel

TL;DR

The paper tackles the challenge of information reconciliation in Decoy-State BB84 QKD over satellite downlinks with time-varying channels due to geometry and atmospheric scintillation. It introduces a detailed instantaneous channel model, including link-budget factors and scintillation dynamics, and uses this information to adapt LDPC-based information reconciliation. Key findings show that leveraging instantaneous QBER information can increase the secret-key length by approximately 3%, with the best approach using mean channel-capacity-based code selection and block-wise LLRs while excluding vacuum events. The work demonstrates a practical, hardware-light path to improve Sat-QKD performance and informs design choices for near-term satellite quantum-link deployments.

Abstract

Quantum key distribution (QKD) is a cryptographic solution that leverages the properties of quantum mechanics to be resistant and secure even against an attacker with unlimited computational power. Satellite-based links are important in QKD because they can reach distances that the best fiber systems cannot. However, links between satellites in low Earth orbit (LEO) and ground stations have a duration of only a few minutes, resulting in the generation of a small amount of secure keys. In this context, we investigate the optimization of the information reconciliation step of the QKD post-processing in order to generate as much secure key as possible. As a first step, we build an accurate model of the downlink signal and quantum bit error rate (QBER) during a complete satellite pass, which are time-varying due to three effects: (i) the varying link geometry over time, (ii) the scintillation effect, and (iii) the different signal intensities adopted in the Decoy-State protocol. Leveraging the a-priori information on the instantaneous QBER, we improve the efficiency of information reconciliation (IR) (i.e., the error correction phase) in the Decoy-State BB84 protocol, resulting in a secure key that is almost 3\% longer for realistic scenarios.

Figures (3)

• Figure 1: Simulated downlink end-to-end efficiency (i.e., link budget) for the reference satellite pass, including (solid, blue) and excluding (dashed, red) scintillation effects. Left: zoom-in of the first $100ms$ of the pass.
• Figure 2: On the $x$-axis are the indexes of the blocks used in IR, and on the $y$-axis are the corresponding IR rates, obtained via Eq. \ref{['eq:rate']} from the DLL output. (a) Mean channel capacity vs. mean QBER for code selection; in the following figures the mean channel capacity is always used for code selection. (b) Complete LLR knowledge vs. mean signal/decoy/vacuum vs. mean block-wise QBER; in the following figures complete LLR knowledge is used as baseline. (c) Baseline vs. bit position randomization strategy. (d) Baseline vs. noisy LLR information. (e) Baseline vs. complete LLR without vacuum states. (f) Baseline vs. mean signal/decoy without vacuum states.
• Figure 3: Comparison of the SKL obtained under the following strategies: a) no $\mathbf{llr}$; b) baseline (case (e)) with bit position randomization; c) noisy LLR estimation; d) LLR vector with mean QBER for code selection; e) LLR vector with mean channel capacity for code selection (baseline); f) three LLR values for signal/decoy/vacuum; g) two LLR values for signal/decoy, excluding vacuum events; h) baseline (case (e)), excluding vacuum events.