  Satellite quantum communication is a promising way to build long distance
quantum links, making it an essential complement to optical fiber for quantum
internetworking beyond metropolitan scales. A satellite point to point optical
link differs from the more common fiber links in many ways, both quantitative
(higher latency, strong losses) and qualitative (nonconstant parameter values
during satellite passage, intermittency of the link, impossibility to set
repeaters between the satellite and the ground station). We study here the
performance of a quantum link between two ground stations, using a
quantum-memory-equipped satellite as a quantum repeater. In contrast with
quantum key distribution satellite links, the number of available quantum
memory slots m, together with the unavoidable round-trip communication latency
t of at least a few milliseconds, severely reduces the effective average
repetition rate to m/t -- at most a few kilohertz for foreseeable quantum
memories. Our study uses two approaches, which validate each other: 1) a simple
analytical model of the effective rate of the quantum link; 2) an event-based
simulation using the open source Quantum Internet Simulation Package (QuISP).
The important differences between satellite and fiber links led us to modify
QuISP itself. This work paves the way to the study of hybrid satellite- and
fiber-based quantum repeater networks interconnecting different metropolitan
areas.
