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arXiv:2512.13675

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

Ziqian Tang, Chen Yang, Zizhao Han, Zikuan Kan, Yulong Liu, Hanyu Xue

quant-phSubmitted Dec 15, 2025• Announced Dec 16, 2025• 0 citations• Revised Dec 18, 2025 (v2)
v1 · Dec 15, 2025v2 · Dec 18, 2025v3 · Aug 31, 2026v4 · Sep 1, 2026
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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.

Comments
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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.
A recent paper by Aziz and Howl (Nature 2025) argues that, once quantum matter is described at the level of quantum field theory and coupled to a classical gravitational field, higher order processes can generate entanglement between two spatially separated masses. A contemporaneous critical note (Marletto, Oppenheim, Vedral, Wilson, arXiv:2511.07348v1) shows that, in the actual nonrelativistic limit employed there, the interaction becomes ultra local, the total unitary factorizes, and no entanglement is generated from a product input. In this comment we (i) restate the core point of that critique, (ii) give a channel theoretic reformulation that makes the conclusion model independent, and (iii) clarify the distinction between activation of entanglement in already quantum matter and genuine mediation of entanglement by a classical field. Once these clarifications are in place, the standard BMV inference that observation of gravity mediated entanglement strongly indicates nonclassical gravitational degrees of freedom remains intact.
Once again, dispute has arisen over the interpretation of proposed quantum information theory experiments to probe the quantum nature of gravity by testing for gravitationally induced entanglement (GIE) between two spatially separated massive particles ([2] vs. [16, 17]; further contributions in [11, 13]). The confusion appears to reside in interpreting applications of a Hamiltonian formalism. But classical gravity cannot mediate entanglement on independent grounds. A Newton-Cartan analysis shows that if gravity is classical, a mediator, and entanglement is observed as an outcome of performing a GIE experiment, something other than gravity must have supplied the (virtual) force needed during the experiment to produce the effect.
Gravity-induced entanglement (GIE) experiments have been proposed as a theory-independent test of the quantum nature of gravity, on the strength of several no-go theorems concluding that GIE detection implies the gravitational interaction is either nonlocal or nonclassical. This is in apparent tension with a growing number of papers claiming that theories with a classical gravitational field do predict GIE. This article resolves the tension by reviewing the assumptions of the no-go theorems and highlighting the information-theoretic, rather than spatiotemporal, nature of the locality assumption. This makes violating locality not particularly problematic. Indeed, quantum electrodynamics and perturbative quantum gravity are nonlocal in the sense of the theorems. Thus, simple detection GIE is not sufficient to rule out a classical gravitational field and we will need quantitative comparison of theoretical predictions in the low-energy quantum gravity regime to test whether the gravitational field is quantum or classical.
This note studies the role of a quantum mediator in gravitationally induced entanglement and decoherence using an exactly solvable dynamical mediator model. Two masses in spatial superposition interact through a mediator mode described by a displaced-oscillator Hamiltonian. The model provides a unified description of two regimes: when the mediator returns to its original state, it leaves behind pure entanglement between the masses through virtual excitation; when the mediator carries which-path information, it becomes a physical record that reduces coherence and suppresses entanglement. The work proves an exact record–decoherence relation: the loss of coherence of each subsystem equals the information stored in the rest of the universe, combining entanglement generation and decoherence into a single information budget. The paper also establishes a classical-channel dichotomy. A measure-and-feedforward channel calibrated to reproduce the same interaction produces no entanglement, while introducing additional noise. This provides an exact solvable distinction between a genuinely quantum mediator and a classical communication channel. The causal structure of mediation is studied in a multi-mode chain, where entanglement appears only after the mediator excitation reaches the relevant region, establishing a finite propagation constraint in the model. The work also proves analytically the separability boundary for partially coherent sources, including the condition relating source coherences required for entanglement generation. The results provide an exactly solvable framework connecting gravitationally induced entanglement, mediator quantum information, which-path records, decoherence, and quantum versus classical mediation. The declared limits are finite models, linear mediator coupling, and no claim of a complete theory of dynamical quantum gravity. Verification and reproducibility materials are included.
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Aziz and Howl argued that a classical gravitational field can generate quantum entanglement through a quantum-field-theoretic channel mediated by virtual matter propagation. However, their claimed channel is more naturally and accurately understood as semiclassical wavepacket motion in an external gravitational field, rather than as a distinctively quantum-field-theoretic entangling effect. Moreover, the result of their perturbative computation is incorrectly magnified: they selected a discontinuous wavefunction with infinite kinetic energy as the initial state and simultaneously treated it as stationary. Once a correct treatment using Gaussian wavepacket is adapted, the resulting effect will be negligibly small.