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Quantum correlations in three-beam symmetric Gaussian states accessed via photon-number-resolving detection and quantum universal invariants

Jan Peřina, Jr.1,*, Nazarii Sudak2, Artur Barasiński2,†, and Antonín Černoch3

  • 1Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
  • 2Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204 Wrocław, Poland
  • 3Joint Laboratory of Optics, Institute of Physics of CAS, 17. listopadu 50a, 779 00 Olomouc, Czech Republic

  • *Contact author: jan.perina.jr@upol.cz
  • †Contact author: artur.barasinski@uwr.edu.pl
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Phys. Rev. Research 7, 043292 – Published 15 December, 2025

DOI: https://doi.org/10.1103/vd3h-4pts

Abstract

Quantum correlations of symmetric three-beam Gaussian states are analyzed using their quantum universal invariants. These invariants, one-, two-, and three-beam purities, are expressed in terms of the beams’ intensity moments up to sixth order. The three-beam symmetric Gaussian states with varying amounts of the noise are experimentally generated using entangled photon pairs from down-conversion, their invariants are determined, and their quantum correlations are quantified. The coexistence of bipartite and tripartite entanglement and genuine tripartite entanglement is observed in these states that resemble the noisy GHZ/W states.

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Phys. Rev. Research 7, 043292– Published 15 December, 2025
  • Received 21 January 2025
  • Accepted 25 November 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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