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Regression Approach for the Reconstruction of Orbital Angular Momentum States

Danilo Zia, Riccardo Checchinato, Alessia Suprano, Taira Giordani, Emanuele Polino, Luca Innocenti, Alessandro Ferraro, Mauro Paternostro, Nicolò Spagnolo, Fabio Sciarrino

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We addressed the problem of decoding the information stored in Orbital Angular Momentum endowed beams with a machine-learning approach, extracting the coefficients of arbitrary superpositions via the combined use of dimensional reduction and regression algorithms.
DOI
10.1364/cleo_fs.2023.fm4a.3

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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 quantum walk dynamics. The high performance and versatility of the demonstrated approach make it an ideal tool to characterize high-dimensional states in quantum information protocols.
The capability to engineer and characterize high dimensional states has become a crucial request in the quantum information field. The quantum walk dynamics proved to be a suitable resource for developing general quantumstate engineering protocols. Here, we experimentally verified the flexibility of an engineering protocol based on a one-dimensional quantum walk in the Orbital Angular Momentum (OAM). Although this degree of freedom has found several applications in the quantum information field, extract the information stored in them appears to be difficult. Therefore, we employ machine learning protocols to classify and characterize particularly structured beams endowed with a not uniform distribution of the polarization on the transverse plane. Moreover, we prove that by modeling the engineering process through a refined model it is possible to improve the performances of measurement techniques such as holographic projection and machine-learning based classification. These results represent a further investigation in the manipulation and detection of OAM modes coupling the photonics platforms with machine-learning protocols.