Diagnosing quantum channel decoherence via vector coherent mode decomposition

High-dimensional quantum key distribution (HD-QKD) is limited by atmospheric turbulence, which scrambles the spatial modes used to encode information. A critical challenge is the lack of general methods to diagnose how this decoherence occurs. We apply the vector coherent mode decomposition (VCMD)-a numerical framework that represents a partially coherent beam as an incoherent superposition of its natural, orthogonal eigenmodes-as a powerful diagnostic engine for this problem. We simulate a qudit state propagating through a turbulent channel and use VCMD to quantify the decay of channel fidelity and reveal the exact spatial structure of the dominant error modes. This provides a complete modal fingerprint of the channel's decoherence mechanism. To establish the framework's credibility, we first validate its accuracy against a benchmark suite, including unmasking a deceptive "Masked Gaussian" beam and quantifying the purity of a decohered optical skyrmion. While the theory of vector coherence is established, this work consolidates it into a practical, basis-independent framework and applies it to discover the physical error modes of a turbulent quantum channel, a task for which conventional, basis-dependent methods are ill-suited.