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

## TL;DR

This paper introduces a novel full-field mode sorter using two optimized phase elements, enabling efficient joint sorting of azimuthal and radial modes for high-dimensional quantum cryptography.

## Contribution

It presents a general, efficient mode sorting scheme based on two optimized phase transformations, advancing high-dimensional quantum measurement capabilities.

## Key findings

- Achieves high-fidelity joint sorting of azimuthal and radial modes.
- Demonstrates effectiveness through simulation in quantum cryptography.
- Uses evolutionary algorithms for optimizing phase elements.

## Abstract

High-dimensional encoding schemes have emerged as a novel way to perform quantum information tasks. For high dimensionality, temporal and transverse spatial modes of photons are the two paradigmatic degrees of freedom commonly used in such experiments. Nevertheless, general devices for multi-outcome measurements are still needed to take full advantage of the high-dimensional nature of encoding schemes. We propose a general full-field mode sorting scheme consisting only of up to two optimized phase elements based on evolutionary algorithms that allows for joint sorting of azimuthal and radial modes in a wide range of bases. We further study the performance of our scheme through simulations in the context of high-dimensional quantum cryptography, where high-fidelity measurement schemes are crucial.