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

## TL;DR

This study experimentally assesses how adaptive optics improves the transmission of high-dimensional quantum states, like OAM, MUB, and SIC-POVM, in turbulent free-space channels, demonstrating basis-dependent correction effectiveness for secure quantum communication.

## Contribution

It provides the first experimental evaluation of high-speed adaptive optics correction for various spatial mode bases up to dimension 8 in turbulent conditions, informing optimal basis selection for QKD.

## Key findings

- OAM states are optimally corrected by AO due to cylindrical symmetry.
- MUB and SIC-POVM are more robust to turbulence but less corrected by AO.
- AO enables secure high-dimensional QKD by improving state fidelity in turbulence.

## Abstract

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.