Summary: An increase in the dimension of state space for quantum key distribution (QKD) can decrease its fidelity requirements while also increasing its bandwidth. A significant obstacle for QKD with qudits $(d\ge 3)$ has been an efficient and practical quantum state sorter for photons whose complex fields are modulated in both amplitude and phase. We propose such a sorter based on a multiplexed thick hologram, constructed e.g. from photo-thermal refractive (PTR) glass. We validate this approach using coupled-mode theory with parameters consistent with PTR glass to simulate a holographic sorter. The model assumes a three-dimensional state space spanned by three tilted planewaves. The utility of such a sorter for broader quantum information processing applications can be substantial.