  Recent experimental breakthroughs in satellite quantum communications have
opened up the possibility of creating a global quantum internet using satellite
links. This approach appears to be particularly viable in the near term, due to
the lower attenuation of optical signals from satellite to ground, and due to
the currently short coherence times of quantum memories. The latter prevents
ground-based entanglement distribution using atmospheric or optical-fiber links
at high rates over long distances. In this work, we propose a global-scale
quantum internet consisting of a constellation of orbiting satellites that
provides a continuous, on-demand entanglement distribution service to ground
stations. The satellites can also function as untrusted nodes for the purpose
of long-distance quantum-key distribution. We develop a technique for
determining optimal satellite configurations with continuous coverage that
balances both the total number of satellites and entanglement-distribution
rates. Using this technique, we determine various optimal satellite
configurations for a polar-orbit constellation, and we analyze the resulting
satellite-to-ground loss and achievable entanglement-distribution rates for
multiple ground station configurations. We also provide a comparison between
these entanglement-distribution rates and the rates of ground-based quantum
repeater schemes. Overall, our work provides the theoretical tools and the
experimental guidance needed to make a satellite-based global quantum internet
a reality.
