  The discrete Fourier transform (DFT) is of fundamental interest in photonic
quantum information, yet the ability to scale it to high dimensions depends
heavily on the physical encoding, with practical recipes lacking in emerging
platforms such as frequency bins. In this Letter, we show that d-point
frequency-bin DFTs can be realized with a fixed three-component quantum
frequency processor (QFP), simply by adding to the electro-optic modulation
signals one radio-frequency harmonic per each incremental increase in d. We
verify gate fidelity F > 0.9997 and success probability P > 0.965 up to d = 10
in numerical simulations, and experimentally implement the solution for d = 3,
utilizing measurements with parallel DFTs to quantify entanglement and perform
full tomography of multiple two-photon frequency-bin states. Our results
furnish new opportunities for high-dimensional frequency-bin protocols in
quantum communications and networking.
