Entanglement without Quantum Mechanics: Operational Constraints on the Quantum Signature

TL;DR

This paper demonstrates that entanglement-like phenomena can arise from classical correlations under limited measurement access, and clarifies the conditions under which genuine quantum entanglement can be distinguished from classical mimics.

Contribution

It introduces an operational hierarchy that differentiates classical artifacts, classical nonseparable correlations, and true quantum entanglement based on measurement constraints.

Findings

Classical correlations can mimic entanglement under restricted measurements.

Imposing physicality constraints filters out classical artifacts, revealing genuine nonseparability.

Full operational tests are necessary to confirm true quantum entanglement.

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.