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arXiv:2604.22593

Stability Thresholds for Gravitationally Induced Entanglement in Shielded Setups

Jan Bulling, Marit O. E. Steiner, Julen S. Pedernales, Martin B. Plenio

quant-phcond-mat.mes-hallSubmitted Apr 24, 2026• Announced Apr 27, 2026
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Abstract

Proposed experiments for gravitationally induced entanglement (GIE) typically suppress direct electromagnetic interactions between two massive particles by inserting a conducting Faraday shield. For superconducting particles, their large diamagnetism requires additional magnetic shielding to screen magnetic dipolar interactions. Here, we analyze the effect of residual particle-shield interactions and show that both Casimir and magnetic-dipole interactions can severely limit GIE tests by imprinting large phases. We quantify how run-to-run positional and orientational fluctuations of the setup elements, including the shield, trapping potentials, and detectors, convert these phases into effective decoherence, strongly reducing the detectable bipartite entanglement. In particular, we show that magnetic interactions between the particles and a superconducting shield constitute a major noise source, especially relevant for levitated superconducting particles. Treating the vibrational modes of the shield quantum mechanically, we further find that thermal vibrations generate persistent particle-shield correlations and can even mediate particle-particle entanglement that can mimic a gravitational signal. Finally, we derive quantitative thresholds on the maximum tolerable positional and orientational fluctuations of the setup elements required to observe entanglement, and propose mitigation strategies including geometry optimization and shield cooling to preserve a genuine GIE signature.

Comments
33 pages, 16 figures

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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.
We develop a quantum field-theoretic model of gravitationally induced entanglement (GIE) between two massive objects in spatial superposition. The masses are described as excitations of a scalar field in an external harmonic potential, allowing for a well-defined notion of relativistic coherent states. Using linearized quantum gravity in the static limit, we derive an effective Hamiltonian that induces entanglement between the field modes occupied by the masses. To probe this entanglement, we construct an observable from field operators that corresponds to the probability density of detecting the center of mass of one of these massive objects. Using this, we compute the fringe visibility in the overlap region and find that gravitationally induced entanglement leads to a decrease in visibility, consistent with previous nonrelativistic results. Additionally, we identify relativistic corrections that accelerate the decay of fringe visibility. These results provide a framework for studying weakly relativistic quantum field systems and their gravitational interactions in tabletop experiments.
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