Optimised finite key for satellite up-link entangled quantum key distribution

Introduction

Entanglement‑based quantum key distribution (QKD) from a ground station to a low‑Earth‑orbit satellite is a cornerstone of future global quantum networks. The upcoming QEYSSat mission will demonstrate this uplink scenario, and early theoretical work has predicted generous asymptotic key rates. However, satellite passes are short, leading to modest block sizes where statistical fluctuations become important. A recent study examines how finite‑size effects reshape the optimal source settings and overall key‑generation strategy.

Finite‑size effects and source optimisation

In the asymptotic regime the pump power of the entangled photon source is typically set to maximise the raw pair production rate while keeping multi‑pair emissions tolerable. When the total number of detected events per pass drops to the order of 10⁴–10⁵, the confidence intervals used in parameter estimation widen. The analysis shows that a modest reduction in pump power—on the order of a few percent—lowers the multi‑pair contribution enough to tighten the statistical bounds on the quantum bit error rate (QBER) and the phase error rate. This adjustment yields a higher finite‑key secret fraction despite a slight drop in raw count rate.

Aggregating raw key across passes

Two practical post‑processing strategies were compared:

1. Per‑pass extraction – a secure key is distilled after each individual overpass.
2. Batch extraction – raw detection events from many passes are accumulated before a single privacy‑amplification step.

Finite‑size analysis favours the batch approach. By pooling data, the effective block size grows, shrinking the statistical penalty in the secret‑key formula. Simulations for the Heriot‑Watt ground station, using realistic satellite elevation profiles and atmospheric loss models, indicate an annual key‑rate increase of roughly 20‑30 % when batch extraction is employed.

Quantitative outlook for QEYSSat

Applying the dynamically optimised pump power and batch processing to a year‑long operation scenario yields a secure key throughput that is comfortably above the threshold required for practical cryptographic applications (e.g., one‑time‑pad encryption of several gigabytes per year). The study presents tables summarising key rates for different satellite zenith angles, ground‑station telescope apertures, and detector efficiencies. Even under conservative assumptions—moderate detector dark counts and modest pointing jitter—the projected annual key volume remains significant.

Practical takeaways

• Tune pump power: Slightly lower pump settings improve finite‑size security margins without sacrificing overall throughput.
• Batch post‑processing: Accumulate raw detection events over multiple passes before privacy amplification to mitigate finite‑size penalties.
• Dynamic scheduling: Adjust source parameters in real time based on predicted link loss for each pass to maintain optimal performance.

Conclusion

Finite‑size considerations are essential for realistic satellite‑uplink QKD. By modestly reducing pump power and adopting a batch extraction workflow, the QEYSSat mission can achieve a robust annual secret‑key rate, reinforcing the viability of entanglement‑based global quantum communication. These insights will guide the design of future space‑based QKD systems where short transmission windows and limited photon budgets are the norm.