Laser communications from small satellite platforms empowers the establishment of quantum key distribution (QKD), relying on quantum superposition states of single photons to realize unconditional security between distant parties at a global scale. Although recent breakthrough experiments have demonstrated the feasibility of satellite-to-ground QKD links, the underlying statistical characteristics of quantum atmospheric channels have not been well-understood and experimentally verified in the literature. In this paper, we highlight that classical atmospheric statistical models can be applied for describing random fluctuations of the quantum channels. To verify this fact, we report a statistical verification study of quantum atmospheric channels from the world’s first low-Earth orbit (LEO) 50-kg-class microsatellite-to-ground quantum-limited communication experiment. The verified statistical model is then applied to numerically investigate the quantum bit-error rate (QBER) and secret-key length (SKL) of a decoy-state efficient Bennett-Brassard 1984 (BB84) QKD protocol with optimized parameters considering finite-key effects, implemented over a LEO 6-unit (6U)-CubeSat-to-ground link. Important insights of the physical channel effects including pointing errors and atmospheric turbulence on the QBER and SKL are then revealed. Finally, we present a study using a deep-learning-based long short-term memory (LSTM) recurrent neural network (RNN) for predicting photon-count fluctuations over quantum atmospheric channels.