Matter-Mediated Entanglement in Classical Gravity: Suppression by Binding Potentials and Localization

Abstract: Aziz and Howl [Nature 646 (2025)] argue that two spatially separated masses can become entangled even when gravity is treated as a classical field, by invoking higher-order "virtual-matter" processes in a QFT description of matter, which is non-LOCC (local operations and classical communication). We point out that the relevant mechanism is not intrinsically field-theoretic, but is essentially a quantum tunneling/evanescent matter channel, which is already captured within ordinary quantum mechanics. More importantly, the microscopic constituents of realistic macroscopic objects are bound and localized by strong potentials, introducing a large internal energy scale that suppresses coherent propagation between distant bodies. Including such binding/localization generically yields an exponential suppression, rendering the matter-mediated contribution negligible at the macroscopic separations relevant to gravitational-entanglement proposals. Consequently, the entanglement identified by AH diagnoses the presence of a coherent matter-exchange channel rather than the classical or quantum nature of gravity, and it does not undermine LOCC-based witness arguments in realistic bound-matter platforms.