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  • Open Access

Quantum aberrations: Entangling photons with Zernike polynomials

H. Avetisyan*

G. Nikoghosyan

  • *Contact author: h.avetisyan@yerphi.am
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Phys. Rev. A 112, 043714 – Published 15 October, 2025

DOI: https://doi.org/10.1103/dbfr-f46b

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 disk, 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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Phys. Rev. A 112, 043714– Published 15 October, 2025
  • Received 27 May 2025
  • Accepted 23 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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