  As Low Earth Orbit (LEO) satellite mega constellations continue to be
deployed for satellite internet and recent successful experiments in
satellite-based quantum entanglement distribution emerge, a natural question
arises: How should we coordinate transmissions and design scalable scheduling
policies for a quantum satellite internet? In this work, we consider the
problem of transmission scheduling in quantum satellite networks subject to
resource constraints at the satellites and ground stations. We show that the
most general problem of assigning satellites to ground station pairs for
entanglement distribution is NP-hard. We then propose four heuristic algorithms
and evaluate their performance for Starlink mega constellation under various
amount of resources and placements of the ground stations. We find that the
maximum number of receivers necessary per ground station grows very slowly with
the total number of deployed ground stations. Our proposed algorithms,
leveraging optimal weighted b-matching and the global greedy heuristic,
outperform others in entanglement distribution rate, entanglement fidelity, and
handover cost metrics. While we develop these scheduling algorithms, we have
also designed a software system to simulate, visualize, and evaluate satellite
mega-constellations for entanglement distribution.
