This paper investigates the performance advantages of Rydberg atomic quantum (RAQ)-based multiple-input multiple-output (MIMO) satellites for enhancing direct ground-to-space uplink access.We analytically evaluate the impact of Rydberg atoms on channel estimation by deriving closed-form expressions for the mean-square error (MSE) and normalized mean-square error (NMSE). Based on the estimated channels, we further derive lower bounds on the achievable data rates for maximum ratio combining (MRC) and zero-forcing (ZF) detection schemes. Rigorous analysis demonstrates that RAQ-MIMO outperforms conventional radio-frequency (RF) MIMO under both Rayleigh and satellite channel conditions. Specifically, compared with conventional MIMO, RAQR achieves a ``squaring" gain under Rayleigh fading, especially in long-distance transmission scenarios with stringent power constraints. In contrast, under line-of-sight (LoS)-dominated satellite channels, this gain saturates as channel-estimation benefits diminish, with the remaining improvement primarily arising from the normalized noise background. Monte Carlo simulations validate the analytical results and show that the performance gains of RAQ-MIMO satellites translate into smaller antenna apertures, lower transmit power, and longer communication ranges, thereby paving the way for next-generation satellite networks.