This page is still in progress.Engineering two-photon high-dimensional states through quantum interference. Y. Zhang, F. S. Roux, T. Konrad, M. Agnew, J. Leach and A. Forbes in Science Advances 2:e1501165 (2016).  What the paper says!?

This reports the first observation of HOM interferences for high-dimensional OAM entangled states.

The text is well-written. It starts with the reminder of the correspondence between many objects in low-dimensional parameter spaces or few objects in high-dimensional ones (see my Wulfrunian lecture on that). High-dimensional entanglement works with «lesser number of particles that exist in high-dimensional state»

They rely on states with «both symmetric and antisymmetric contributions; this is achieved with Dove prisms»

When each of the two input ports of a 50:50 beamsplitter receives one photon, only the antisymmetric state component and not the symmetric one produces coincidence counts in the output ports. This has been demonstrated for incident pairs of photons prepared in symmetric and antisymmetric states involving two spatial modes (21–23).

Refs. 23 and 29-31 on HOM on spatial modes.

Check their Ref. 6 for the quantum state created at the output.

This needs to be studied in detail, this is a pioneering work.