Optimised finite key for satellite up-link entangled quantum key distribution
Entanglement-based quantum key distribution from ground to satellite has been proposed as a scalable primitive for global quantum networks and will be demonstrated as part of the imminent QEYSSat mission. Both theoretical studies and experimental emulations have shown that a significant asymptotic key rate can be expected. In this work we investigate this scenario with a more rigorous security analysis taking into account the finite size effects that arise from short block lengths common in satellite transmission. Our findings suggest a slight alteration of the optimal source operation when informed by finite statistics as opposed to the asymptotic regime, notably that the pump power should be slightly lowered. We quantify the annual key rate based on a dynamically optimised source operation for the Heriot-Watt ground station and several satellite parameters. We find an improved annual key rate when accumulating all raw key material before extracting a secure key instead of doing so for each overpass. We ultimately show that QEYSSat will be able to generate a significant secure annual key with both strategies.