  Future quantum networks will be hybrid structures, constructed from complex
architectures of quantum repeaters interconnected by quantum channels that
describe a variety of physical domains; predominantly optical-fiber and
free-space links. In this hybrid setting, the interplay between the channel
quality within network sub-structures must be carefully considered, and is
pivotal for ensuring high-rate end-to-end quantum communication. In this work,
we combine recent advances in the theory of point-to-point free-space channel
capacities and end-to-end quantum network capacities in order to develop
critical tools for the study of hybrid, free-space quantum networks. We present
a general formalism for studying the capacities of arbitrary, hybrid quantum
networks, before specifying to the regime of atmospheric and space-based
quantum channels. We then introduce a class of modular quantum network
architectures which offer a realistic and readily analysable framework for
hybrid quantum networks. By considering a physically motivated, highly
connected modular structure we are able to idealize network performance and
derive channel conditions for which optimal performance is guaranteed. This
allows us to reveal vital properties for which distance-independent rates are
achieved, so that the end-to-end capacity has no dependence on the physical
separation between users. Our analytical method elucidates key infrastructure
demands for a future satellite-based global quantum internet, and for hybrid
wired/wireless metropolitan quantum networks.
