Entanglement without Quantum Mechanics: Operational Constraints on the Quantum Signature

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 en- tanglement 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.

10 pages, 5 figures. Published version

arXiv:2512.14834 [quant-ph]

(or arXiv:2512.14834v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2512.14834 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. Research 8, 033313 (2026)

https://doi.org/10.1103/xdz9-x3zj Focus to learn more DOI(s) linking to related resources

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