  Continuous variable quantum key distribution (CV-QKD) offers
information-theoretic secure key sharing between two parties. The sharing of a
phase reference frame is an essential requirement for coherent detection in
CV-QKD. Due to the potential attacks related to transmitting the local
oscillator (LO) alongside quantum signals, there has been a focus on using
local LOs (LLOs) to establish a shared phase reference. In this work, we
develop a new noise model of a current state-of-the-art LLO scheme in the
context of the satellite-to-Earth channel. In doing this, we encapsulate
detailed phase-screen calculations that determine the coherent efficiency - a
critical parameter in free-space CV-QKD that characterizes the wavefront
aberrations caused by atmospheric turbulence. Using our new noise model we then
determine the CV-QKD key rates for the satellite-to-Earth channel, secure under
general attacks in the finite-size regime of the LLO scheme. Our results are of
practical importance for next-generation quantum-enabled satellites that
utilize multi-photon technology as opposed to single-photon technology.
