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A Field Cannot Both Broadcast and Entangle: The Quantum Darwinism of Gravity

Rolando P. Hong Enriquez

Published Jul 14, 2026• 0 citations

Abstract

In the Bose–Marletto–Vedral (BMV) proposal, two masses placed in superposition become entangled only if the gravitational field between them is quantum — a proposed table-top test of whether gravity is quantum. This paper reframes the question through quantum Darwinism. A mass's Newtonian field is a record of its position imprinted on nearby matter; a classical field is one that broadcasts that record objectively, whereas a genuinely quantum field can remain in superposition and refuses to copy a which-path record. The paper models exactly a source in superposition, its recording environment, and its partner mass, and proves an objectivity–entanglement monogamy: if the field records the position redundantly across many fragments, the entanglement it can generate is exponentially small in that redundancy — a field cannot both broadcast and entangle. Several results follow. The field record is extensive. A sharp classical-versus-quantum dichotomy is carried by an information measure that rises from zero to one bit as the field becomes classical. The source's position is the unique objective observable. And earlier black-hole decoherence results reappear as the single-fragment limit. A measured entanglement therefore bounds the field's objective redundancy from above. The results are finite-dimensional theorems with exact numerics reproduced by self-testing code, and two algebraic cores are additionally verified by proof-checking software; the gravitational couplings and decoherence rates are imported, not re-derived. In short: a field cannot both broadcast and entangle — so the entanglement a BMV experiment measures is precisely the price gravity pays for not being classical.

DOI: 10.5281/zenodo.21357416

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In the Bose–Marletto–Vedral (BMV) proposal, two masses placed in superposition become entangled only if the gravitational field between them is quantum — a proposed table-top test of whether gravity is quantum. This paper reframes the question through quantum Darwinism. A mass's Newtonian field is a record of its position imprinted on nearby matter; a classical field is one that broadcasts that record objectively, whereas a genuinely quantum field can remain in superposition and refuses to copy a which-path record. The paper models exactly a source in superposition, its recording environment, and its partner mass, and proves an objectivity–entanglement monogamy: if the field records the position redundantly across many fragments, the entanglement it can generate is exponentially small in that redundancy — a field cannot both broadcast and entangle. Several results follow. The field record is extensive. A sharp classical-versus-quantum dichotomy is carried by an information measure that rises from zero to one bit as the field becomes classical. The source's position is the unique objective observable. And earlier black-hole decoherence results reappear as the single-fragment limit. A measured entanglement therefore bounds the field's objective redundancy from above. The results are finite-dimensional theorems with exact numerics reproduced by self-testing code, and two algebraic cores are additionally verified by proof-checking software; the gravitational couplings and decoherence rates are imported, not re-derived. In short: a field cannot both broadcast and entangle — so the entanglement a BMV experiment measures is precisely the price gravity pays for not being classical.

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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.

We revisit the Bose-Marletto-Vedral (BMV) tabletop experimental proposal---which aims to witness quantum gravity using gravity-mediated entanglement---analyzing the role of locality in the experiment. We first carry out a fully quantum modeling of the interaction of matter and gravity and then show in what way gravity-mediated entanglement in the BMV experiment could be accounted for without appealing to quantum degrees of freedom of the gravitational field. We discuss what assumptions are needed in order to interpret the current BMV experiment proposals as a proof of quantum gravity, and also identify the modifications that a BMV-like experiment could have in order to serve as proof of quantum gravity without having to assume the existence of local mediators in the gravitational field.

We develop a low-energy, Newtonian-limit effective field theory (EFT) describing gravitationally induced decoherence arising from a classical stochastic gravitational channel. The framework is formulated as completely positive, Markovian Lindblad dynamics coupled to the mass-density operator with spatially correlated white noise. We derive scaling laws for single-mass superpositions and for two-mass Bose–Marletto–Vedral (BMV) configurations, identify four universal parametric regimes, and construct a model-independent testability window in the parameter space of noise strength and correlation length. Our results provide a direct operational link between laboratory-scale entanglement experiments and foundational questions concerning the quantum or classical nature of gravity.

Reconciling quantum mechanics and general relativity remains one of the most profound challenges in modern physics. The BMV (Bose-Marletto-Vedral) experiment can assess the quantum nature of gravity by testing whether gravitational interactions can generate entanglement between quantum systems. In this work, we show that entanglement can be generated by gravity without requiring spacetime superpositions or quantum spacetime degrees of freedom by using mediators that do not satisfy the usual property of local tomography when coupling to quantum matter. Specifically, we showcase how entanglement can be generated using three distinct toy models that display non-locally tomographic couplings between quantum matter and a locally classical gravitational mediator. These models include (i) fermionic systems with the parity superselection rule, (ii) non-Abelian anyonic systems, and (iii) a novel bit anti-bit model. Our results demonstrate a crucial point: a gravitational mediator which does not exhibit superpositions of its classical basis but still qualifies as non-classical via non-locally tomographic coupling mechanisms can generate entanglement through local interactions. This work also underscores the importance of relaxing local tomography in exploring the quantum-gravitational interface. It provides a novel perspective on the role of spacetime degrees of freedom in entanglement generation through local interactions.

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.