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arXiv:2507.13201 · Journal of Physics A Mathematical and Theoretical

Gravity-mediated entanglement via infinite-dimensional systems

Stefan L. Ludescher, Leon Loveridge, Thomas D. Galley, Markus P. Müller

Published Apr 28, 2026• 2 citations
arXivHTMLPDF

Abstract

Abstract There has been a wave of recent interest in detecting the quantum nature of gravity with tabletop experiments that witness gravitationally mediated entanglement. Central to these proposals is the assumption that any mediator capable of generating entanglement must itself be nonclassical. However, previous arguments for this have modeled classical mediators as finite, discrete systems such as bits, which excludes physically relevant continuous and infinite-dimensional systems such as those of classical mechanics and field theory. In this work, we close this gap by modeling classical systems as commutative unital C ∗ -algebras, arguably encompassing all potentially physically relevant classical systems. We show that these systems cannot mediate entanglement between two quantum systems A and B , even if A and B are themselves infinite-dimensional or described by arbitrary unital C ∗ -algebras (as in quantum field theory), composed with an arbitrary C ∗ -tensor product. This result reinforces the conclusion that the observation of gravity-induced entanglement would require the gravitational field to possess inherently non-classical features.

DOI
10.1088/1751-8121/ae65e7

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Abstract There has been a wave of recent interest in detecting the quantum nature of gravity with tabletop experiments that witness gravitationally mediated entanglement. Central to these proposals is the assumption that any mediator capable of generating entanglement must itself be nonclassical. However, previous arguments for this have modeled classical mediators as finite, discrete systems such as bits, which excludes physically relevant continuous and infinite-dimensional systems such as those of classical mechanics and field theory. In this work, we close this gap by modeling classical systems as commutative unital C ∗ -algebras, arguably encompassing all potentially physically relevant classical systems. We show that these systems cannot mediate entanglement between two quantum systems A and B , even if A and B are themselves infinite-dimensional or described by arbitrary unital C ∗ -algebras (as in quantum field theory), composed with an arbitrary C ∗ -tensor product. This result reinforces the conclusion that the observation of gravity-induced entanglement would require the gravitational field to possess inherently non-classical features.
We propose a general argument to show that if a physical system can mediate locally the generation of entanglement between two quantum systems, then it itself must be nonclassical. Remarkably, we do not assume any classical or quantum formalism to describe the mediating physical system: our result follows from general information-theoretic principles, drawn from the recently proposed constructor theory of information. This argument provides a broader theoretical basis for recently proposed tests of nonclassicality in gravity, based on witnessing gravitationally induced entanglement in quantum probes, making them applicable in the context where quantum theory may not apply.
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.
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.
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.
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
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.