High-dimensional quantum Fourier transform of twisted light

The Fourier transform proves indispensable in the processing of classical information as well quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme $d$-dimensional acting on single photons is known that uses path encoding and requires $O(d \log d)$ optical elements. In this paper we present an alternative design orbital angular momentum a carrier needs only $O(\sqrt{d}\log elements, rendering path-encoded inefficient. advantageous scaling fact our approach conventional elements allows for 256-dimensional with existing technology. Improvements design, explicit setups low dimensions, are also presented.