  There has been considerable interest recently in the generation of azimuthal
phase functions associated with photon orbital angular momentum (OAM) for
high-dimensional quantum key distribution (QKD). The generation of secure
quantum keys requires not only this pure phase basis, but also additional bases
comprised of orthonormal superposition states formed from the pure states.
These bases are also known as mutually unbiased bases (MUBs) and include
quantum states whose wave functions are modulated in both phase and amplitude.
While modulo 2\pi optical path control with high-resolution spatial light
modulators (SLMs) is well suited to creating the azimuthal phases associated
with the pure states, it does not introduce the amplitude modulation associated
with the MUB superposition states. Using computer-generated holography (CGH)
with the Leith-Upatnieks approach to hologram recording however, both phase and
amplitude modulation can be achieved. This paper presents a description of the
OAM states of a 3-dimensional MUB system and analyzes the construction of these
states via CGH with a phase modulating SLM. The effects of phase holography
artifacts on quantum-state generation are quantified and a prescription for
avoiding these artifacts by preconditioning the hologram function is presented.
Practical effects associated with spatially isolating the first-order
diffracted field are also quantified and a demonstration utilizing a liquid
crystal SLM is presented.
