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arXiv:2509.12426 · Journal of Physics Photonics

Mapping continuous-variable quantum states onto optical scalar beams

B. M. Rodríguez-Lara, Elohim Becerra

Published Dec 19, 2025• 0 citations
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Abstract

Abstract Optical scalar beams provide a platform to explore classical analogies to quantum mechanics. We introduce a Lie group-theoretic su ( 1 , 1 ) framework to construct optical beam analogs of continuous-variable (CV) quantum states, including one- and two-mode squeezing. Using Fourier methods and the optical Wigner distribution, we investigate how squeezing reshapes the spatial and spectral structure of these beams, and find that the achievable diffraction-limited spatial compression is bounded by the numerical aperture of the optical system. We construct an optical analog of the Duan–Simon inseparability criterion and use marginal optical Wigner distributions, which encode partial phase-space information, as witnesses of CV classical entanglement. Our framework provides a unified approach to quantum-inspired beam engineering with potential applications in optical imaging, metrology, and communication.

DOI
10.1088/2515-7647/ae2fa4

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Abstract Optical scalar beams provide a platform to explore classical analogies to quantum mechanics. We introduce a Lie group-theoretic su ( 1 , 1 ) framework to construct optical beam analogs of continuous-variable (CV) quantum states, including one- and two-mode squeezing. Using Fourier methods and the optical Wigner distribution, we investigate how squeezing reshapes the spatial and spectral structure of these beams, and find that the achievable diffraction-limited spatial compression is bounded by the numerical aperture of the optical system. We construct an optical analog of the Duan–Simon inseparability criterion and use marginal optical Wigner distributions, which encode partial phase-space information, as witnesses of CV classical entanglement. Our framework provides a unified approach to quantum-inspired beam engineering with potential applications in optical imaging, metrology, and communication.
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We propose an experimental scheme that has the potential for large-scale realization of continuous-variable (CV) cluster states for universal quantum computation. We do this by mapping CV cluster-state graphs onto two-mode squeezing graphs, which can be engineered into a single optical parametric oscillator (OPO). The desired CV cluster state is produced directly from a joint squeezing operation on the vacuum, using a multifrequency pump beam. This method has potential for ultracompact experimental implementation. As an illustration, we detail an experimental proposal for creating a four-mode square CV cluster state with a single OPO.
Continuous-variable (CV) qubits can be created on an optical longitudinal mode in which quantum information is encoded by the superposition of even and odd Schroedinger's cat states with quadrature amplitude. Based on the analogous features of paraxial optics and quantum mechanics, we propose a system to generate and detect CV qubits on an optical transverse mode. As a proof-of-principle experiment, we generate six CV qubit states and observe their probability distributions in position and momentum space. This enabled us to prepare a non-Gaussian initial state for CV quantum computing. Other potential applications of the CV qubit include adiabatic control of a beam profile, phase shift keying on transverse modes, and quantum cryptography using CV qubit states.
This paper establishes the Heisenberg's picture framework for seamless mmWave-to-photonic data transduction. Based on this framework, contactless modulation of continuous-variable (CV) quantum optical states with digitally modulated classical mmWave beams is shown for the first time. Our analysis reveals the direct influence of mmWave phase variation on the Wigner-space evolution of modulated optical coherent and squeezed states. Furthermore, the analysis indicates that classical mmWave phase not only governs the displacement but also modulates the quadrature uncertainty of squeezed states, revealing a novel technique for embedding information onto multiple quantum-optical degrees of freedom. This work builds the theoretical and analytical foundation for wireless conditioning of quantum light without conventional on-chip metallic interconnects and complex electronic control circuitry, thereby opening a key pathway toward seamless bridging of integrated quantum photonics with emerging mmWave or THz communication technology.