Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

APS Open Science

Speckle-learned regression for complete characterization of orbital angular momentum superposition states

Chayanika Sharma, Purnesh Singh Badavath, Vijay Kumar

Published Jul 7, 2026• 0 citations
Publisher

Abstract

Superpositions of orbital angular momentum (OAM) eigenstates form a continuous state space characterized by the complex coefficients of the constituent modes. When such OAM superposition states propagate through a random medium, they produce speckle patterns. The random granular speckle patterns encode the complete information of the original superposition states. This work demonstrates that the complex coefficients of an arbitrary OAM superposition can be retrieved from a single-shot speckle image. The extraction is performed using custom-designed regression model and is validated through both experimental measurements and numerical simulations. The method remains effective for superpositions of high-dimensional OAM eigenstates, including intensity-degenerate states, demonstrating that speckle can serve as a robust information carrier for state characterization.

DOI
10.1103/m8fm-gj1s

Related papers

High-fidelity orbital angular momentum spectrum reconstruction via sparse intensity measurements

Jingjing Zhang, Xiao Wang, Guangdong Ma +4 more

Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.

Optics Letters•Oct 20, 2025•0 citations

Regression Approach for the Reconstruction of Orbital Angular Momentum States

Danilo Zia, Riccardo Checchinato, Alessia Suprano +7 more

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.

•Jan 1, 2023•0 citations

Regression of high-dimensional angular momentum states of light

Danilo Zia, Riccardo Checchinato, Alessia Suprano +7 more

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.

arXiv:2206.09873•Physical Review Research•Feb 24, 2023•20 citations

Efficient phase measurement for orbital angular momentum comb through Poincaré-sphere-like representation

Zi-Mo Cheng, Shiyue Jia, Hao Sheng +5 more

Photons with a spiral phase will carry orbital angular momentum (OAM), which can serve as a valuable resource for constructing high-dimensional Hilbert spaces due to its orthogonality and unbounded dimensionality. However, the fast measurement of high-dimensional OAM spectra remains a challenge. While intensity detection is relatively straightforward, full characterization requires phase retrieval. Although quantum state tomography allows full reconstruction, it demands a number of measurements scaling quadratically with the d2 of dimension (d), leading to a “curse of dimensionality” as the dimension d increases. Thus, there is an urgent need for efficient and simple methods for extracting phase information from high-dimensional OAM spectra. Here, we propose a generalized Poincaré sphere model with analog Stokes-like parameters, enabling full phase measurement of a d-dimensional OAM spectrum using only 4d measurements, significantly reducing the data acquisition requirement. We experimentally validated the method by performing intensity and phase measurements on 8-, 16-, and 32-dimensional OAM comb spectra. The results show excellent agreement with theoretical predictions, with measured fidelities ranging from 0.9829 to 0.9965. This approach facilitates an efficient characterization of high-dimensional OAM spectra and contributes to advancing their practical applications.

APL Photonics•Feb 1, 2026•1 citation

Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval

Zhongzheng Lin, Jianqi Hu, Yujie Chen +2 more

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

arXiv:2206.12883•Advanced Photonics•Jun 12, 2023•37 citations

Revealing a high-dimensional orbital angular momentum complex spectrum under strong scattering

Chaozhou Xu, Qijian Xiong, Jingjing Wang +4 more

Optical vortex beams carrying orbital angular momentum (OAM) offer unique advantages in high-dimensional optical information processing. However, in the context of free-space links, the full reconstruction of high-dimensional OAM spectra remains challenging due to scattering-induced distortions. Here, we employ a residual convolutional neural network with a custom quantum-state-fidelity loss function (QLF-ResNet) that reconstructs and demultiplexes high-dimensional OAM light fields from a single distorted speckle pattern. Specifically, we achieve an average fidelity of 97.2% for nine-dimensional OAM states and maintain fidelity above 91.9% with only 6.25% of original data, illustrating resilience to information loss, thus enabling robust data encoding and multiplexing. For this, we employ high-dimensional OAM encoding to achieve efficient, high-fidelity transmission of RGB images under strong scattering conditions. These results underscore the promise of our current approach for precise OAM state reconstruction in intricate real-world environments, paving the way for advancements in next-generation optical communications.

Photonics Research•Jul 24, 2025•5 citations
Superpositions of orbital angular momentum (OAM) eigenstates form a continuous state space characterized by the complex coefficients of the constituent modes. When such OAM superposition states propagate through a random medium, they produce speckle patterns. The random granular speckle patterns encode the complete information of the original superposition states. This work demonstrates that the complex coefficients of an arbitrary OAM superposition can be retrieved from a single-shot speckle image. The extraction is performed using custom-designed regression model and is validated through both experimental measurements and numerical simulations. The method remains effective for superpositions of high-dimensional OAM eigenstates, including intensity-degenerate states, demonstrating that speckle can serve as a robust information carrier for state characterization.
Accurate reconstruction of the complex spectrum of orbital angular momentum (OAM) superposition states is crucial for their application in high-capacity optical communications and quantum information, yet existing methods are often constrained by system complexity, extensive data requirements, or incomplete information retrieval. Here, we propose and experimentally demonstrate an iterative algorithm that enables high-fidelity recovery of the complex OAM spectrum of high-dimensional superpositions from only a few sparsely sampled patterns. The method integrates the Laguerre-Gaussian (LG) modal basis as an a priori constraint, which enables the direct retrieval of spectral coefficients by circumventing intermediate field reconstruction. To validate its performance, we reconstructed a test field composed of a random superposition of 21 LG modes, achieving fidelities of 99.3% in simulation and 97.2% in experiment using only four sparse sampling patterns. This work provides an efficient and robust tool for characterizing high-dimensional structured light, with significant potential in optical communication and quantum science.
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.
Photons with a spiral phase will carry orbital angular momentum (OAM), which can serve as a valuable resource for constructing high-dimensional Hilbert spaces due to its orthogonality and unbounded dimensionality. However, the fast measurement of high-dimensional OAM spectra remains a challenge. While intensity detection is relatively straightforward, full characterization requires phase retrieval. Although quantum state tomography allows full reconstruction, it demands a number of measurements scaling quadratically with the d2 of dimension (d), leading to a “curse of dimensionality” as the dimension d increases. Thus, there is an urgent need for efficient and simple methods for extracting phase information from high-dimensional OAM spectra. Here, we propose a generalized Poincaré sphere model with analog Stokes-like parameters, enabling full phase measurement of a d-dimensional OAM spectrum using only 4d measurements, significantly reducing the data acquisition requirement. We experimentally validated the method by performing intensity and phase measurements on 8-, 16-, and 32-dimensional OAM comb spectra. The results show excellent agreement with theoretical predictions, with measured fidelities ranging from 0.9829 to 0.9965. This approach facilitates an efficient characterization of high-dimensional OAM spectra and contributes to advancing their practical applications.
Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.
Optical vortex beams carrying orbital angular momentum (OAM) offer unique advantages in high-dimensional optical information processing. However, in the context of free-space links, the full reconstruction of high-dimensional OAM spectra remains challenging due to scattering-induced distortions. Here, we employ a residual convolutional neural network with a custom quantum-state-fidelity loss function (QLF-ResNet) that reconstructs and demultiplexes high-dimensional OAM light fields from a single distorted speckle pattern. Specifically, we achieve an average fidelity of 97.2% for nine-dimensional OAM states and maintain fidelity above 91.9% with only 6.25% of original data, illustrating resilience to information loss, thus enabling robust data encoding and multiplexing. For this, we employ high-dimensional OAM encoding to achieve efficient, high-fidelity transmission of RGB images under strong scattering conditions. These results underscore the promise of our current approach for precise OAM state reconstruction in intricate real-world environments, paving the way for advancements in next-generation optical communications.