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arXiv · 2504.15765

Quantum Aberrations: Entangling Photons with Zernike Polynomials

Hakob Avetisyan·Gor Nikoghosyan
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Abstract

We introduce Zernike polynomials as a novel degree of freedom for encoding quantum information in the spatial structure of photons. Building on their orthogonality and completeness over the unit disc, we develop a framework for generating, manipulating, and detecting photons in Zernike modes, and propose methods for realizing single-photon and two-photon Zernike wave packets. We demonstrate analytically that two-photon states generated via spontaneous parametric down- conversion exhibit mode entanglement in the Zernike basis, with correlations arising from selection rules enforced by Clebsch-Gordan coefficients. Our results open a new pathway for structured spatial entanglement, complementary to schemes based on Laguerre-Gaussian or Hermite-Gaussian modes, and suggest practical experimental implementations based on holographic modulation and optical Fourier techniques.

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Hakob Avetisyan, Gor Nikoghosyan. 2025-04-22. Quantum Aberrations: Entangling Photons with Zernike Polynomials. https://doi.org/10.1103/dbfr-f46b

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