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Physical Review Applied

Simple-Diffraction-Based Deep Learning to Reconstruct a High-Dimensional Orbital-Angular-Momentum Spectrum Via Single-Shot Measurement

Haoxu Guo, Xiaodong Qiu, Lixiang Chen

Published May 11, 2022• 22 citations
Publisher

Abstract

Orbital-angular-momentum (OAM) complex-valued spectrum reconstruction routinely necessitates the measurements of a complete set of observables, which is rather time consuming and inefficient for high-dimensional OAM superposition state. Here we break this barrier to realize the full reconstruction of a high-dimensional OAM complex-valued spectrum via only a single-shot measurement, which benefits from the use of a residual convolutional neural network for learning the diffraction behaviors. In our experiment, the high-dimensional OAM states are diffracted by a simple aperture of pentagram that breaks the OAM conjugate symmetry. We achieve fidelity over 97.8% and 92.1% for high-dimensional pure and mixed OAM states (up to $d=15$), respectively. We also confirm the excellent robustness under strong noise environment. Our method will find potential applications in high-dimensional information encoding, such as large-alphabet communications, quantum imaging, and real-time quantum sensing.

DOI
10.1103/physrevapplied.17.054019

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Orbital-angular-momentum (OAM) complex-valued spectrum reconstruction routinely necessitates the measurements of a complete set of observables, which is rather time consuming and inefficient for high-dimensional OAM superposition state. Here we break this barrier to realize the full reconstruction of a high-dimensional OAM complex-valued spectrum via only a single-shot measurement, which benefits from the use of a residual convolutional neural network for learning the diffraction behaviors. In our experiment, the high-dimensional OAM states are diffracted by a simple aperture of pentagram that breaks the OAM conjugate symmetry. We achieve fidelity over 97.8% and 92.1% for high-dimensional pure and mixed OAM states (up to d=15d=15d=15), respectively. We also confirm the excellent robustness under strong noise environment. Our method will find potential applications in high-dimensional information encoding, such as large-alphabet communications, quantum imaging, and real-time quantum sensing.
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.
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Abstract High‐dimensional (HD) entanglement of photonic orbital angular momentum (OAM) offers significant potential for enhancing channel capacity and improving noise resistance in quantum information processing. However, the challenge of achieving simple and rapid measurement has limited its practical applications. In this work, a quantum state tomography (QST) framework is demonstrated that utilizes convolutional neural networks to rapidly reconstruct the density matrix of OAM entanglement from only two coincidence measurements. The experimental results for a 5D OAM entangled state yield a fidelity of 0.973 ± 0.005. This method is also applicable to mixed OAM entangled states and scenarios with incomplete tomographic measurements. These findings represent a significant step toward implementing high‐speed QST for applications involving HD spatial mode quantum state, whether in free space or integrated systems.
Abstract High-dimensional (HD) entanglement of photonic orbital angular momentum (OAM) is pivotal for advancing quantum communication and information processing, but its characterization remains significant challenges due to the complexity of quantum state tomography and experimental limitations such as low photon counts caused by losses. Here, we propose a pre-trained physics-informed neural network (PTPINN) framework that enables efficient and rapid reconstruction of HD-OAM entangled states under low photon counts. Experimental results show that the fidelity of five-dimensional OAM entanglement reaches F = 0.958 ± 0.010 even with an exposure time as short as 50 ms. This highlights the capability of PTPINN to achieve high-precision quantum state reconstruction with limited photons, owing to its innovative designs, thus overcoming the reliance on high photon counts typical of traditional methods. Our method provides a practical and scalable solution for high-fidelity characterization of HD-OAM entanglement in environments with low photon numbers and high noise, paving the way for robust long-distance quantum information transmission.
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Orbital angular momentum (OAM), emerging as an inherently high-dimensional property of photons, has boosted information capacity in optical communications. However, the potential of OAM in optical computing remains almost unexplored. Here, we present a highly efficient optical computing protocol for complex vector convolution with the superposition of high-dimensional OAM eigenmodes. We used two cascaded spatial light modulators to prepare suitable OAM superpositions to encode two complex vectors. Then, a deep-learning strategy is devised to decode the complex OAM spectrum, thus accomplishing the optical convolution task. In our experiment, we succeed in demonstrating 7-, 9-, and 11-dimensional complex vector convolutions, in which an average proximity better than 95% and a mean relative error <6 % are achieved. Our present scheme can be extended to incorporate other degrees of freedom for a more versatile optical computing in the high-dimensional Hilbert space.