High-dimensional quantum Fourier transform of twisted light

TL;DR

This paper introduces a more efficient method for implementing high-dimensional quantum Fourier transforms using orbital angular momentum, reducing the number of optical elements needed and enabling practical realization with current technology.

Contribution

The authors propose a novel design for high-dimensional quantum Fourier transforms that significantly reduces optical complexity compared to existing path-encoded schemes.

Findings

Achieves 256-dimensional Fourier transform with existing optical technology.

Uses only conventional optical elements, simplifying implementation.

Provides explicit setups for low-dimensional cases.

Abstract

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