Quantum Key Distribution Beyond Stationary Channels

In satellite-based Quantum Key Distribution (QKD), transmission channels are non-stationary, characterized by fluctuating losses and sparse detection events. Standard statistical methods for finite-key security proofs are either too loose for small sample sizes or highly sensitive to model inaccuracies. The authors seek to develop tighter, more robust concentration inequalities that remain valid for non-IID (independent and identically distributed) processes without requiring precise prior knowledge of the channel.

The researchers employ a mixture martingale technique. By constructing a martingale that depends on a tunable parameter and then averaging (mixing) over a range of these parameters, they create a bound that retains the sharpness of existing methods (like Kato bounds) while gaining robustness against model mismatch. This approach allows the statistical bounds to adapt to varying channel conditions without needing to be re-tuned for every specific pass or link-budget shift.

The study demonstrates that these mixture-martingale bounds are significantly more robust than traditional methods. In simulations of decoy-state BB84 protocols over LEO and GEO satellite links, the new bounds reduced the minimum number of transmitted signals required for positive-key extraction by up to 71% when the actual channel loss deviated from the expected design value. The bounds consistently track the performance of the theoretical binomial tail benchmark, confirming their near-optimal tightness.

Finite-key statistics are a primary bottleneck in practical QKD, particularly for satellite links where acquisition windows are short and unpredictable. By providing a robust, computationally efficient way to bound statistical uncertainty, this method allows for more reliable key generation in real-world, non-stationary environments. It effectively turns statistical robustness into a design parameter, enabling engineers to optimize link resources more effectively.