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arXiv:2605.00967 · Physical Review A

Gravity-induced entanglement under constrained dynamics

Hollis Williams

quant-phSubmitted May 1, 2026• Announced May 4, 2026• 0 citations• Revised Aug 16, 2026 (v2)
v1 · May 1, 2026v2 · Aug 16, 2026
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Abstract

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 $(τ/T)^2$, where $τ$ is the interaction timescale and $T$ 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.

Journal reference
Phys. Rev. A 114, 032221 (2026)
DOI
10.1103/pg7l-f26t

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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.
No experimental test to date has provided conclusive evidence on the quantum nature of gravity. Recent proposals, such as the Bose-Marletto-Vedral experiment, suggest that generating entanglement could serve as a direct test. Motivated by these proposals, we study a system of three-harmonic oscillator system, with the mediator oscillator operating in two distinct parameter regimes: a heavy mediator regime and a light mediator regime. These regimes induce qualitatively different entanglement dynamics between the terminal oscillators. Crucially, distinguishing these regimes experimentally remains challenging when relying solely on entanglement measures. We demonstrate that the dynamical fidelity susceptibility offers a viable and sensitive probe to contrast the regimes in practice. Our results provide testable signatures for optomechanical and trapped-ion platforms simulating gravitational interactions, and provide new avenues to characterize quantum-gravity-inspired systems beyond entanglement-based protocols.
Gravity-induced entanglement (GIE) is widely regarded as key evidence of nonclassical gravity. Recent work, however, argues that a classical gravitational background can generate entanglement through virtual matter propagation between separated masses. Here we show that this mechanism is negligible once realistic matter dynamics is taken into account. For bound or condensed matter, the binding potential converts the claimed long-range matter-mediated interaction into an exponentially short-ranged one, with an attenuation length of only a few picometers for representative binding energies-well below atomic dimensions and therefore negligible under experimentally relevant distances. For unbound matter, the channel remains negligible before significant wave-packet overlap, while after overlap the packets no longer represent two spatially separated subsystems. Thus the proposed classical matter-mediated mechanism does not challenge the usual interpretation of GIE as evidence for nonclassical gravity once physical localization and finite-time matter dynamics are treated consistently.
Finding a feasible scheme for testing the quantum mechanical nature of the gravitational interaction has been attracting an increasing level of attention. Gravity mediated entanglement generation so far appears to be the key ingredient for a potential experiment. In a recent proposal [D. Carney et al., PRX Quantum 2, 030330 (2021)] combining an atom interferometer with a low-frequency mechanical oscillator, a coherence revival test is proposed for verifying this entanglement generation. With measurements performed only on the atoms, this protocol bypasses the need for correlation measurements. Here, we explore formulations of such a protocol, and specifically find that in the envisioned regime of operation with high thermal excitation, semiclassical models, where there is no concept of entanglement, also give the same experimental signatures. We elucidate in a fully quantum mechanical calculation that entanglement is not the source of the revivals in the relevant parameter regime. We argue that, in its current form, the suggested test is only relevant if the oscillator is nearly in a pure quantum state, and in this regime the effects are too small to be measurable. We further discuss potential open ends. The results highlight the importance and subtleties of explicitly considering how the quantum case differs from the classical expectations when testing for the quantum mechanical nature of a physical system.
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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.