  Engineering single-photon states endowed with Orbital Angular Momentum (OAM)
is a powerful tool for quantum information photonic implementations. Indeed,
thanks to its unbounded nature, OAM is suitable to encode qudits allowing a
single carrier to transport a large amount of information. Nowadays, most of
the experimental platforms use nonlinear crystals to generate single photons
through Spontaneous Parametric Down Conversion processes, even if this kind of
approach is intrinsically probabilistic leading to scalability issues for
increasing number of qudits. Semiconductors Quantum Dots (QDs) have been used
to get over these limitations being able to produce on demand pure and
indistinguishable single-photon states, although only recently they were
exploited to create OAM modes. Our work employs a bright QD single-photon
source to generate a complete set of quantum states for information processing
with OAM endowed photons. We first study the hybrid intra-particle entanglement
between the OAM and the polarization degree of freedom of a single-photon. We
certify the preparation of such a type of qudit states by means of the
Hong-Ou-Mandel effect visibility which furnishes the pairwise overlap between
consecutive OAM-encoded photons. Then, we investigate the hybrid inter-particle
entanglement, by exploiting a probabilistic two qudit OAM-based entangling
gate. The performances of our entanglement generation approach are assessed
performing high dimensional quantum state tomography and violating Bell
inequalities. Our results pave the way toward the use of deterministic sources
(QDs) for the on demand generation of photonic quantum states in high
dimensional Hilbert spaces.
