Mapping continuous-variable quantum states onto optical scalar beams

Abstract Optical scalar beams provide a platform to explore classical analogies to quantum mechanics. We introduce a Lie group-theoretic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi>su</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> 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.