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.
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.
Abstract Distance evaluation between high-dimensional vectors is a fundamental computational primitive in classical machine learning, widely employed to quantify similarity, yet often demanding substantial computational resources. The quantum nearest-centroid classifier leverages the principle of superposition to encode data vectors, enabling direct distance evaluation through inner-product measurements in a high-dimensional state space. In this work, we propose and experimentally demonstrate a quantum-inspired optical nearest-centroid (ONC) classifier that leverages the spatial superposition of high-dimensional orbital angular momentum (OAM) modes in classical light to optically encode data vectors and perform distance evaluation. We first experimentally characterize the measurement accuracy of the core distance estimation module across 32 OAM modes. Subsequently, we demonstrate its performance on real-world data, achieving high-dimensional classification using the four-dimensional Iris data set and a 16-dimensional subset of the complex MNIST data set. Experimental results show excellent agreement with theoretical expectations. Our work demonstrates that classical OAM modes can efficiently emulate complex quantum-inspired algorithms, establishing a scalable optical platform for resource-efficient high-dimensional data processing.
Photons are an ideal candidate for encoding both classical and quantum information. Besides spin angular momentum associated with circular polarization, single photon can also carry other fundamentally new degree of freedom of orbital angular momentum related to the spiral phase structure of light. The key significance of orbital angular momentum lies in its potential in realizing a high-dimensional Hilbert space and in encoding a high-dimensional quantum information. Since Allen et al. [Allen L, Beijersbergen M W, Spreeuw R J C, Woerdman J P 1992 Phys. Rev. A 45 8185] recognized the physical reality of photon orbital angular momentum in 1992, rapidly growing interest has been aroused in orbital angular momentum (OAM) from both classical and quantum points of view. Here we present an overall review on the high-order orbital angular momentum of photon, including its preparation and manipulation based on some specific techniques and also its applications. The spatial light modulator is a commercial device that has been widely employed to generate the OAM beams. We make and identify the optical OAM superposition with very high quantum numbers up to l=360. Recently, the metallic spiral phase mirrors were also developed to produce high-order OAM beams up to l=5050. In addition, the Q-plates made of anisotropic and inhomogeneous liquid crystals were invented to generate high-order OAM beams in a polarization-controllable manner, and the OAM superposition of l=± 50 were achieved. Owing to high rotational symmetry, these high OAM beams have been found to have more and more important applications in the fields of high-sensitivity sensing and high-precision measurements. Two fascinating examples are discussed in detail. The first example is that the research group led by Prof. Zeilinger has prepared and observed the quantum entanglement of high orbital angular momenta up to l=±300 by the technique of polarization-OAM entanglement swapping, and they demonstrated that the angular resolution could be significantly improved by a factor of l. Their result was the first step for entangling and twisting even macroscopic, spatially separated objects in two different directions. The second example is that the research group led by Prof. Padgett has demonstrated an elegant experiment of rotational Doppler effects for visible light with l=±20 OAM superposition. They showed that a spinning object with an optically rough surface might induce a Doppler effect in light reflected from the direction parallel to the rotation axis, and the frequency shift was proportional to both the disk's angular speed and the optical OAM. The potential applications in noncontact measurement of angular speed and in significant improvement of angular resolution for remote sensing will be particularly fascinating.
Abstract The rich structure of transverse spatial modes of structured light has facilitated their extensive applications in quantum information and optical communication. The Laguerre–Gaussian (LG) modes, which carry a well-defined orbital angular momentum (OAM), consist of a complete orthogonal basis describing the transverse spatial modes of light. The application of OAM in free-space optical communication is restricted due to the experimentally limited OAM numbers and the complex OAM recognition methods. Here, we present a novel method that uses the advanced deep learning technique for LG modes recognition. By discretizing the spatial modes of structured light, we turn the OAM state regression into classification. A proof-of-principle experiment is also performed, showing that our method effectively categorizes OAM states with small training samples and the accuracy exceeds 99% from three-dimensional (3D) to fifteen-dimensional (15D) space. By assigning each category a classical information, we further apply our approach to an image transmission task, achieving a transmission accuracy of 99.58%, which demonstrates the ability to encode large data with low OAM number. This work opens up a new avenue for achieving high-capacity optical communication with low OAM number based on structured light.
Introduction In this chapter, we will be concerned with entangled states of light. Historically, quantum states of light, i.e., photons, have played a dominant role in the experimental study of quantum entanglement. For instance, the first Bell tests and the first realizations of quantum teleportation were performed using two-dimensional polarization-entangled twophoton states [3]. From an experimental point of view these states are readily prepared and manipulated using conventional polarization optics. Recently, however, both theoretical and experimental efforts have shifted towards entanglement in more than two modes , which is often referred to as high-dimensional entanglement. This is much richer than two-dimensional entanglement, as is, for instance, reflected in stronger violations of various measures of nonlocality which reveal the complexity of high-dimensional Hilbert spaces [4–7]. Also, from an applications perspective, it promises a larger channel capacity [8, 9] and improved security for quantum communication [10, 11]. There are several ways to implement high-dimensional two-photon entanglement. One can exploit the temporal [12], frequency [13], or spatial [14–18] degrees of freedom of the optical field. A promising way to implement high-dimensional two-photon entanglement is to use the orbital-angular-momentum (OAM) degree of freedom of light. Light beams that carry OAM have a helical wavefront that spirals around the optical axis during propagation [19]. The winding number m , which characterizes the OAM eigenmodes, can adopt any integer value between −∞ and ∞; since all coaxial OAM modes are orthogonal they can thus span a very high-dimensional Hilbert space.
High-dimensional quantum computing has emerged as a recent alternative to conventional qubit-based approaches, offering advantages such as an increased information density and enhanced robustness against noise. In this work, we explore the use of the orbital angular momentum (OAM) of light as a degree of freedom in which high-dimensional quantum gates can be implemented. We present a theoretical and experimental study of structured light beams carrying OAM, with emphasis on Laguerre–Gauss modes, as a natural basis for high-dimensional quantum computing. We then describe the generation of OAM beams using computer-generated holograms and spatial light modulators, detailing practical methods for encoding arbitrary phase profiles. Building on this framework, we analyze the implementation of high-dimensional quantum logic gates, focusing on the generalized Pauli Z_d and X_d operations. Optical setups based on Dove prisms, Sagnac interferometers, spiral phase plates, and parity sorters are proposed and theoretically validated. Finally, we report experimental results demonstrating the generation of Laguerre–Gauss beams, the transformation properties of Dove prisms, and the operation of a parity sorter, which constitutes a building block for realizing high-dimensional quantum gates. These results establish a solid foundation for future implementations of high-dimensional quantum information processing using the orbital angular momentum of light.
We present a compact scheme for the generation of high-dimensional states of light encoded in the transverse linear momentum of photons that carry orbital angular momentum (OAM). We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup, we are able to control, independently, the relative phases and amplitudes of the spatial superposition in addition to the topological charge of the OAM. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions d × m . Experimental results from the characterization of different generated states of dimensions up to 9 × 5 are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above 95%.