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arXiv:2602.06091

Entanglement Before Spacetime in Quantum-Gravity-Induced Interactions

Hollis Williams

quant-phSubmitted Feb 5, 2026• Announced Feb 6, 2026
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Abstract

Quantum-gravity-induced entanglement of massive systems (QGEM) is commonly approximated in the nonrelativistic static limit by a Newtonian interaction between spatially separated masses. In this work, we reformulate the gravitationally mediated interaction phase in a conformally invariant twistor framework in which no notion of spacetime distance is assumed. We show that the bilocal phase responsible for entanglement generation remains well-defined and non-factorizable even in the absence of spacetime geometry. The familiar Newtonian $1/r$ phase, relevant for QGEM protocols, arises only after the conformal invariance is broken by introducing the infinity twistor, which selects a particular spacetime representation of the underlying bilocal quantum interaction. Our results isolate the genuinely quantum content of QGEM protocols and clarify the contingent role played by spacetime geometry in mediating entanglement.

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Quantum-gravity-induced entanglement of massive systems (QGEM) is commonly approximated in the nonrelativistic static limit by a Newtonian interaction between spatially separated masses. In this work, we reformulate the gravitationally mediated interaction phase in a conformally invariant twistor framework in which no notion of spacetime distance is assumed. We show that the bilocal phase responsible for entanglement generation remains well-defined and non-factorizable even in the absence of spacetime geometry. The familiar Newtonian 1/r1/r1/r phase, relevant for QGEM protocols, arises only after the conformal invariance is broken by introducing the infinity twistor, which selects a particular spacetime representation of the underlying bilocal quantum interaction. Our results isolate the genuinely quantum content of QGEM protocols and clarify the contingent role played by spacetime geometry in mediating entanglement.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
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.
This work presents a model-independent analysis of gravity-mediated entanglement based on the geometric structure of interaction-induced phase evolution. Using a minimal two-body phase model inspired by recent gravity-mediated entanglement proposals, it is shown that quantum entanglement between initially separable systems arises if and only if the induced phase structure is non-factorable. The central result identifies a gauge-invariant plaquette phase as a necessary and sufficient operational condition for entanglement generation. When this plaquette invariant is nonzero, standard quantum information diagnostics—such as negativity, concurrence, and Bell–CHSH correlations—confirm the presence of entanglement. When the invariant is eliminated, entanglement vanishes identically, even when individual phase magnitudes remain nonzero. A comprehensive suite of falsification tests is applied, including local phase factorization, plaquette removal, deterministic and stochastic phase scrambling, permutation symmetry tests, LOCC protocols, causal reordering, and controlled noise injection. Across all tests, entanglement survives exclusively in the presence of non-factorable phase structure. Scaling analyses further demonstrate consistent dependencies on mass, interaction time, separation distance, and superposition size, yielding a distinctive interaction fingerprint incompatible with classical or semiclassical channels. The framework is fully operational and does not assume a specific theory of quantum gravity. Instead, it provides a concrete, experimentally accessible criterion for probing nonclassical aspects of gravity using near-term interferometric platforms. The results sharpen the interpretational foundations of gravity-mediated entanglement proposals by isolating the minimal structural feature responsible for entanglement generation.
The recently introduced quantum gravity-induced entanglement of masses (QGEM) protocol aims to test the quantum nature of gravity by witnessing the entanglement produced by the virtual exchange of a graviton between two spatially superposed masses. Shortly after the original proposal, further improvements upon the experiment were suggested, including the addition of a third mass, showing that three-qubit setups can be more resilient to higher rates of decoherence caused by the interaction of the system with the environment. In this work, we investigate the type of tripartite entanglement generated in these three-qubit QGEM experiments when considering the effects of decoherence. We show that the gravitational interaction between the qubits is able to generate genuine tripartite entanglement between them, studying the corresponding parameter spaces and comparing the performance of the possible experimental configurations of the three qubits at allowing for the detection of genuine entanglement via an entanglement witness.
Tests of gravity-induced entanglement have been proposed as a route to probing the quantum nature of gravity, but existing schemes rely on free-fall interferometry of massive spatial superpositions, imposing severe experimental constraints. We show that systems exhibiting effectively inertial dynamics in the short-time regime reproduce the same gravitational phase accumulation responsible for entanglement generation. Deviations from the free-fall phase enter at order (τ/T)2(τ/T)^2(τ/T)2, where τττ is the interaction timescale and TTT is the characteristic period of the constrained motion. We analyse a representative mechanically constrained implementation using carbon nanotube pendula and show that the resulting correction to the entangling phase remains small in experimentally relevant regimes, leading to a negligible modification of the interference visibility used to certify entanglement. These results demonstrate that gravity-induced entanglement protocols extend beyond free-fall implementations to a broader class of constrained dynamical systems, complementing existing proposals for experimental realisations of the Bose-Marletto-Vedral protocol.
We investigate the generation rate of quantum gravity induced entanglement of masses (QGEM) in setups with multiple quantum massive particles, among which only the gravity interaction due to the Newton potential is taken into account. When the distance between any two adjacent Stern-Gerlach devices is fixed, we consider all the possible configurations of the setup with the same number of particles. In particular, we systemically analyze the case of particle number n=4n=4n=4 and find that the prism setup with a massive particle at the center is the most efficient setup for the entanglement generation. This result can be extended to a system with multiple particles up to seven, where the entanglement efficiency is also enhanced in comparison with the setup with fewer particles. This work provides the strategy to construct the quantum gravity induced entanglement of masses setup with the best generation rate of entanglement.