Regression of high dimensional angular momentum states of light

TL;DR

This paper introduces a low-cost, efficient method to reconstruct high-dimensional orbital angular momentum states of light from intensity measurements, enhancing quantum information applications.

Contribution

The authors develop a novel approach combining PCA and linear regression to reliably recover high-dimensional OAM states from intensity profiles, addressing symmetry issues.

Findings

Successfully reconstructed up to four-dimensional OAM states

Low computational cost during training and testing

Effective in a real photonic quantum walk setup

Abstract

The Orbital Angular Momentum (OAM) of light is an infinite-dimensional degree of freedom of light with several applications in both classical and quantum optics. However, to fully take advantage of the potential of OAM states, reliable detection platforms to characterize generated states in experimental conditions are needed. Here, we present an approach to reconstruct input OAM states from measurements of the spatial intensity distributions they produce. To obviate issues arising from intrinsic symmetry of Laguerre-Gauss modes, we employ a pair of intensity profiles per state projecting it only on two distinct bases, showing how this allows to uniquely recover input states from the collected data. Our approach is based on a combined application of dimensionality reduction via principal component analysis, and linear regression, and thus has a low computational cost during both training and testing stages. We showcase our approach in a real photonic setup, generating up-to-four-dimensional OAM states through a quantum walk dynamics. The high performances and versatility of the demonstrated approach make it an ideal tool to characterize high dimensional states in quantum information protocols.