  We present a quantum random number generator (QRNG) based on the random
outcomes inherent in projective measurements on a superposition of quantum
states of light. Firstly, we use multiplexed holograms encoded on a spatial
light modulator to spatially map down-converted photons onto a superposition of
optical paths. This gives us full digital control of the mapping process which
we can tailor to achieve any desired probability distribution. More
importantly, we use this method to account for any bias present within our
transmission and detection system, forgoing the need for time-consuming and
inefficient unbiasing algorithms. Our QRNG achieved a min-entropy of
$\text{H}_{\text{min}}=0.9991\pm0.0003$ bits per photon and passed the NIST
statistical test suite. Furthermore, we extend our approach to realise a QRNG
based on photons entangled in their orbital angular momentum (OAM) degree of
freedom. This combination of digital holograms and projective measurements on
arbitrary OAM combinations allowed us to generate random numbers with arbitrary
distributions, in effect tailoring the system's entropy while maintaining the
inherent quantum irreproducibility. Such techniques allow access to the
higher-dimensional OAM Hilbert space, opening up an avenue for generating
multiple random bits per photon.
