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High-dimensional encoding schemes have emerged as a novel way to performquantum information tasks. For high dimensionality, temporal and transversespatial modes of photons are the two paradigmatic degrees of freedom commonlyused in such experiments. Nevertheless, general devices for multi-outcomemeasurements are still needed to take full advantage of the high-dimensionalnature of encoding schemes. We propose a general full-field mode sorting schemeconsisting only of up to two optimized phase elements based on evolutionaryalgorithms that allows for joint sorting of azimuthal and radial modes in awide range of bases. We further study the performance of our scheme throughsimulations in the context of high-dimensional quantum cryptography, wherehigh-fidelity measurement schemes are crucial.

Full-field mode sorter using two optimized phase transformations for high-dimensional quantum cryptography