# Proposal for Automated Operations for Single-Photon Multipath Qudits

## TL;DR

This paper introduces a programmable, automated method for implementing complex state transformations on single-photon multipath qudits using spatial light modulators and diffraction gratings, enhancing capabilities in high-dimensional quantum information processing.

## Contribution

It presents a novel approach combining spatial phase modulation and interferometric merging to perform versatile, automated transformations on multipath qudits, surpassing previous SLM-only methods.

## Key findings

- Method enables complex transformations on multipath qudits.
- Analysis of losses and effects of SLM pixelation.
- Potential to expand applications in quantum information and fundamental studies.

## Abstract

We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths with a stable interferometric network, and filtering out the unwanted diffraction orders. The automated feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyse how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than it is possible with an SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.