  Using angular position-orbital angular momentum entangled photons, we propose
an experiment to generate maximally entangled states of $D$-dimensional quantum
systems, the so called qudits, by exploiting correlations of parametric
down-converted photons. Angular diffraction masks containing $N$-slits in the
arms of each twin photon define a qudit space of dimension $N^2$, spanned by
the alternative pathways of the photons. Due to phase-matching conditions, the
twin photons will pass only by symmetrically opposite angular slits, generating
maximally entangled states between these different paths, which can be detected
by high-order two-photon interference fringes via coincidence counts. Numerical
results for $N$ angular slits with $N = 2, 4, 5, 6, 10$ are reported,
corresponding to qudit Hilbert spaces of dimension $D=N^2=4,16,25, 36,100$,
respectively. We discuss relevant experimental parameters for an experimental
implementation of the proposed scheme using Spatial Light Modulators (SLMs),
and twin-photons produced by Spontaneouos Parametric Down Conversion (SPDC).
The entanglement of the qudit state can be quantified in terms of the
Concurrence, which can be expressed in terms of the visibility of the
interference fringes, or by using Entanglement Witnesses. These results provide
an additional means for preparing entangled quantum states in high-dimensions,
a fundamental resource for quantum simulation and quantum information
protocols.
