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arXiv:2512.17024

Subsystems (in)dependence in GIE proposals

Nicolas Boulle, Guilherme Franzmann

quant-phhep-thmath-phphysics.hist-phSubmitted Dec 18, 2025• Announced Dec 22, 2025• Revised Dec 22, 2025 (v2)

v1 · Dec 18, 2025 v2 · Dec 22, 2025

Abstract

Recent proposals suggest that detecting entanglement between two spatially superposed masses would establish the quantum nature of gravity. However, these gravitationally induced entanglement (GIE) experiments rely on assumptions about subsystem independence. We sharpen the theoretical underpinnings of such proposals by examining them through the lens of algebraic quantum field theory (AQFT), distinguishing distinct operational and algebraic notions of independence. We argue that state and measurement independence of subsystems, essential to the experimental logic, is nontrivial in the presence of gauge constraints and gravitational dressing. Using gravitationally dressed fields, we recall that commutation relations between spacelike separated observables are nontrivial, undermining strict Hilbert space factorization. We further explore the implications for entanglement witnesses, investigating the Tsirelson bound when subsystem algebras fail to commute, and showing that the Tsirelson bound persists for a suitably symmetrized CHSH observable even though the operational status of such "joint" observables becomes delicate when commensurability fails. Our analysis highlights how even within linearized covariant quantum gravity, violations of microcausality may affect both the interpretation, modelling, and design of proposed laboratory tests of quantum gravity, despite remaining negligible for current experimental regimes. Although we consider GIE-style protocols as a concrete case study, the subsystem-independence issues we highlight are generic to low-energy (perturbative) quantum gravity. Finally, we derive estimates for dressing-induced microcausality violations, which suggest a complementary avenue to current proposals: in principle, bounding dressing-induced microcausality violations themselves as a probe of the quantum nature of gravity.

Journal reference: Phys. Rev. D 114, 025015 (2026)
DOI: 10.1103/tgjx-y7hl
Comments: Minor revisions and references added. Comments are very welcome!

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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.

Probing the quantum nature of gravity is one of the most profound open challenges in physics. A promising direction is the Gravitationally Induced Entanglement (GIE) protocol, where two initially unentangled probes become entangled solely through local interactions with a mediator of interaction, the gravitational field. Such entanglement would imply that gravity must carry quantum features, namely, it must possess at least a couple of incompatible observables. This thesis further expands the GIE protocol and its Theory-Independent argument by introducing a general, dynamics-independent inequality: the quantum correlation gain between the probes is upper-bounded by the non-commutativity of the mediator’s observables and its Hilbert space dimension. This bound holds for arbitrary interactions and any finite-dimensional systems. A decoherence analysis shows the bound vanishes when the mediator becomes classical. These results provide a quantitative, operational tool for observing the non-classicality of mediators, thereby expanding the conceptual and experimental reach of GIE-based tests of gravity.

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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.

A Bell violation by material probes certifies nonlocal behavior, but it does not identify which internal subsystem carried or was measured to produce that behavior. We determine the additional information required to attribute such a violation to a gravitational field. For any setting-independent field-to-probe channel completed before the Bell settings are chosen, an entanglement-breaking channel makes all induced field measurements jointly measurable. A static Newtonian phase pickup belongs to this class, even with arbitrary adaptive probe control. Applied to a recent four-mass proposal, the claimed field-only measurements obey the stronger CHSH bound

\sqrt2

, whereas the Bell-active operation is the source-to-probe instrument that includes the coherent source herald. At the published parameters, the observed flagged behavior is at least

0.1630

from the claimed field-detector family, exceeding its

0.0898

distance from Bell locality. We then incorporate a common field slice, gravitational constraints, dressing, detector backreaction, and coherent references into a robust certification theorem. The result isolates the minimum missing information: field-only factorization and a local measurement- incompatibility witness on each wing. More precise phase data cannot replace either requirement.