Investigating the Performance of Adaptive Optics on Different Bases of Spatial Modes in Turbulent Channels

Quantum key distribution (QKD) allows secure key exchange based on the principles of quantum mechanics, with higher-dimensional photonic states offering enhanced channel capacity and resilience to noise. Free-space QKD is crucial for global networks where fibres are impractical, but atmospheric turbulence introduces severe states distortions, particularly for spatial modes. Adaptive optics (AO) provides a pathway to correct these errors, though its effectiveness depends on the encoding basis. Here, we experimentally evaluate a high-speed AO system for orbital angular momentum (OAM) modes, mutually unbiased bases (MUB), and symmetric, informationally complete, positive operator-valued measures (SIC-POVM) up to dimension $d=8$ in a turbulent free-space channel. While OAM states are strongly distorted, their cylindrical symmetry makes them optimally corrected by AO, yielding error rates below QKD security thresholds. MUB and SIC-POVM exhibit greater intrinsic robustness to turbulence but are less precisely corrected, though their performance remains within protocol tolerances. These results establish AO as a key enabler of secure, high-dimensional QKD and highlight the role of basis choice in optimizing resilience and correction.