  For quantum communications, the use of Earth-orbiting satellites to extend
distances has gained significant attention in recent years, exemplified in
particular by the launch of the Micius satellite in 2016. The performance of
applied protocols such as quantum key distribution (QKD) depends significantly
upon the transmission efficiency through the turbulent atmosphere, which is
especially challenging for ground-to-satellite uplink scenarios. Adaptive
optics (AO) techniques have been used in astronomical, communication, and other
applications to reduce the detrimental effects of turbulence for many years,
but their applicability to quantum protocols, and their requirements
specifically in the uplink scenario, are not well established. Here, we model
the effect of the atmosphere on link efficiency between an Earth station and a
satellite using an optical uplink, and how AO can help recover from loss due to
turbulence. Examining both low-Earth-orbit and geostationary uplink scenarios,
we find that a modest link transmissivity improvement of about 3dB can be
obtained in the case of a co-aligned downward beacon, while the link can be
dramatically improved, up to 7dB, using an offset beacon, such as a laser guide
star. AO coupled with a laser guide star would thus deliver a significant
increase in the secret key generation rate of the QKD ground-to-space uplink
system, especially as reductions of channel loss have favourably nonlinear
key-rate response within this high-loss regime.
