Quantum–classical analogy reveals the shared mathematical framework and dynamical physical behaviors between quantum and classical systems. This work reviews structured light as a versatile platform for realizing such analogies. Theoretical mappings between quantum states and optical modes are summarized, followed by representative cases including entanglement state, cat state, coherent state, and squeezed state, where quantum features are emulated through tailored amplitude, phase, and polarization structures. Applications in quantum-inspired communication, teleportation, random walks, and billiard are further discussed. This work provides a systematic overview of the connections between quantum phenomena and classical optics and offers methodological guidance for future photonic implementations.
Quantum–classical analogy reveals the shared mathematical framework and dynamical physical behaviors between quantum and classical systems. This work reviews structured light as a versatile platform for realizing such analogies. Theoretical mappings between quantum states and optical modes are summarized, followed by representative cases including entanglement state, cat state, coherent state, and squeezed state, where quantum features are emulated through tailored amplitude, phase, and polarization structures. Applications in quantum-inspired communication, teleportation, random walks, and billiard are further discussed. This work provides a systematic overview of the connections between quantum phenomena and classical optics and offers methodological guidance for future photonic implementations.
Quantum-classical analogy refers to the fact that quantum and classical phenomena share a similar mathematical description and exhibit analogous behaviors, which has advanced optical frontiers. In this work, the mechanism of the squeezed state is incorporated into classical structured light, constructing a novel kind of structured light, termed the squeezed geometric beam, that is, the squeezed coherent state of geometric beams, and revealing a novel quantum-classical analogy between the noise of quantum squeezed state and the beam size of squeezed geometric beams, both evolving with the same squeezing parameter. The presented method provides an inspirational extensible framework to reveal more structured light analogies of quantum states. In addition, it is demonstrated in theory and experiment that thanks to the unveiled squeezing mechanism, the squeezed geometric beam as an information carrier can effectively lower the modal crosstalk, thus boosting the communication capacity of spatial mode multiplexing.
Much of the richness in nature arises due to the connection between classical and quantum mechanics. In advanced science, the tools of quantum mechanics was not only applied in microscopic description but also found its efficacy in classical phenomena, broadening the fundamental scientific frontier. A pioneering inspiration is substituting Fock state with structured spatial modes to reconstruct a novel Hilbert space. Based on this idea, here we propose the classical analogy of squeezed coherent state for the first time, deriving classical wave-packets by applying squeezed and displacement operators on free space structured modes. Such a generalized structured light not only creates new degrees of freedom into structured light, including tunable squeezed degree and displacement degree but also exhibits direct correlation between quadrature operator space and real space. Versatile generalized classical squeezed states could be experimentally generated by a simple large-aperture off-axis-pumped solid-state laser. On account of its tunablity, we initially put forward a blueprint using classical structured light, an analogy of squeezed states to realize super-resolution imaging, providing an alternative way to beat diffraction limit as well as opening an original page for subsequent applications of high-dimensional structured light, such as high-sensitive measurement and ultra-precise optical manipulation.
Control of structured light is of great importance to explore fundamental physical effects and extend practical scientific applications, which has been advanced by accepting methods of quantum optics - many classical analogies of exotic quantum states were designed using structured modes. However, the prevailing quantum-like structured modes are limited by discrete states where the mode index is analog to the photon number state. Yet, beyond discrete states, there is a broad range of quantum states to be explored in the field of structured light -- continuous-variable (CV) states. As a typical example of CV states, squeezed state plays a prominent role in high-sensitivity interferometry and gravitational wave detection. In this work, we bring together two seemingly disparate branches of physics, namely, classical structured light and quantum squeezed state. We propose the structured light analogy of squeezed state (SLASS), which can break the spatial limit following the process of surpassing the standard quantum limit (SQL) with quantum squeezed states. This work paves the way for adopting methods from CV quantum states into structured light, opening new research directions of CV entanglement, teleportation, classical and quantum informatics of structured light in the future.
Vectorial modes of light, a type of structured light where the polarization varies across the beam profile, are a useful tool both in classical and quantum applications. In quantum communication, for instance, these modes enable rotational invariant protocols, therefore overcoming the requirement of a shared reference frame between users. Moreover, structured light can be a resource for enhanced sensing purposes as for instance in the “photonic gears” technique. This quantum inspired scheme enables a boost of sensitivity in mechanical displacements measurement thanks to a bidirectional mapping between the polarization state and a properly tailored vectorial mode of a paraxial light beam. Finally, we will discuss how quantum interference can be controlled and tailored for structured light modes, therefore providing a key ingredient for exploiting the full potential of complex light in the quantum domain.
Recent progress in meta-optics, particularly the development of metasurfaces, has enabled compact, tunable, and integrable control over the amplitude, phase, polarization, and wavefront of light, thereby allowing a paradigm shift in traditional optical science and engineering. In parallel, the ability to generate and precisely manipulate nonclassical light is central to quantum optics, enabling key functionalities in secure quantum communication, precision measurement, and scalable quantum computation. This review aims to bridge these two rapidly advancing fields by presenting recent progress in the application of structured materials to the manipulation of quantum states of light. We begin by introducing the concept of singular optics, followed by a discussion of various families of spatially and temporally structured beams that form the foundation for many of the phenomena explored in quantum photonics. Next, we revisit the theoretical framework of quantum optics, including the formalism of photon quantization and the principles governing quantum frequency conversion. We then examine how metasurfaces can be engineered to enable highly efficient nonlinear quantum processes, including both up-conversion and down-conversion, thereby offering new approaches for generating and controlling complex quantum states. Furthermore, we discuss the crucial role of structured materials in shaping the properties of quantum light and in applications such as quantum ghost imaging. The review concludes by identifying emerging directions for integrating meta-optical platforms with quantum systems, highlighting their potential for scalable manipulation of nonclassical light at the nanoscale.
The realization of hybrid entanglement between a microscopic (quantum) and a macroscopic (classical) system, in analogy to the situation of the famous Schrödinger's cat paradox, is an important milestone, both from the fundamental perspective and for possible applications in the processing of quantum information. The most straightforward optical implementation of this condition is that of the entanglement between a single-photon and a coherent state. In this work, we describe the first step towards the generation of this type of hybrid entanglement from the experimental perspective.