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Entanglement without quantum mechanics: Operational constraints on the quantum signature

Samuel Schlegel1,*, Borivoje Dakić1,2, and Flavio Del Santo1,3,4

  • 1Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna 1090, Austria
  • 2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, Vienna 1090, Austria
  • 3Group of Applied Physics, University of Geneva, Rue de l’École-de-Médecine 21, Geneva 1211, Switzerland
  • 4School of Science, Constructor University, Bremen, Germany

  • *Contact author: samuel.schlegel@univie.ac.at
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Phys. Rev. Research 8, 033313 – Published 14 September, 2026

DOI: https://doi.org/10.1103/xdz9-x3zj

Abstract

Quantum entanglement is defined as nonseparability of density operators, yet experimental phase-space statistics alone cannot distinguish classical from quantum sources, so classical data can be used to violate entanglement inequalities. Imposing uncertainty bounds, or full tomography, can map the same data onto positive, entangled density operators, yielding a hybrid regime in which classical and quantum models coincide. Thus, certifying genuine quantum entanglement requires additional tests, such as Wigner negativity, incompatibility beyond phase-space measurements, or nonlinear dynamics.

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Phys. Rev. Research 8, 033313– Published 14 September, 2026
  • Received 14 January 2026
  • Accepted 18 August 2026
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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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