Structured photons often serve as physical realizations of high-dimensional quantum states beneficial to quantum information. One popular way of discretizing the space is through Laguerre-Gaussian modes that can have twisted phase front and, thus, orbital angular momentum (OAM).
We demonstrate that using multi-plane light-conversion techniques enables the performance of complex unitary transformations between multiple input-modes and output-modes in the quantum regime. We demonstrate various complex two-photon interferences observed in spatial modes, thereby realizing a linear optical network along a single beam path. Finally, we show that using this ability allows the generation of spatial-mode NOON-states, which offer angular super-sensitivity.
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