Entanglement without Quantum Mechanics: Operational Constraints on the Quantum Signature

Abstract

Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum mechanics. If an observer is limited to a constrained set of measurements and transformations, certain classical phase-space distributions can mimic entanglement-like behaviours. Imposing positivity of the associated Hilbert space operator as a physicality requirement removes some of these representational artifacts, revealing a regime in which nonseparability is genuine but still reproducible by classical models. Only when the operational restrictions on the observer are lifted further--allowing operational tests of measurement incompatibility or other nonclassical signatures--does one obtain entanglement that can no longer be captured by any classical description. This operational hierarchy distinguishes classical artifacts, classically reproducible nonseparability, and genuine entanglement.