  High-dimensional quantum key distribution (QKD) offers higher information
capacity and stronger resilience to noise compared to its binary counterpart.
However, these advantages are often hindered by the difficulty of realizing the
required high-dimensional measurements and transformations. Here, we implement
a large-scale multi-plane light converter (MPLC) and program it as a
high-dimensional mode sorter of spatial modes for QKD. Using the MPLC, we
demonstrate five-dimensional QKD with six mutually unbiased bases and
25-dimensional QKD with two mutually unbiased bases in the same experimental
setup. Furthermore, we propose a construction of pairs of mutually unbiased
bases that are robust to experimental errors, with measurement complexity
scaling only with the square root of the encoded dimension. This approach paves
the way for QKD implementations in higher dimensions.
