This page is still in progress.

Exploring the quantum nature of the radial degree of freedom of a photon via Hong-Ou-Mandel interference. E. Karimi, D. Giovannini, E. Bolduc, N. Bent, F. Miatto, M. Padgett and R. Boyd in Phys. Rev. A 89:013829 (2014).  What the paper says!? (stub)

This work is specifically on the radial degree of freedom:

we aim at showing that radial modes can be successfully used to label distinct single-photon quantum states.

so for now I live it aside.

This page is still largely in progress.

Already their opening sentence is unclear to me:

Implementing quantum protocols and algorithms in highdimensional spaces requires engineering the interaction of several particles

They carry on with «A possible alternative»... But if there are alternatives, then this is not a requirement.

Radial and OAM provide two degrees of freedom in the transverse plane:

the transverse profile of a single photon supplies two unbounded Hilbert spaces [3], which in polar coordinates are labeled by discrete radial and orbital angular momentum (OAM) indice

For HOM interferences

any property that can help distinguish the photons leads to a positive contribution to the probability of the photons leaving from different ports.

What they do here:

we employed HOM interference to show experimentally that the radial DOF of single photons provides an additional unbounded discrete Hilbert space.