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arXiv:2401.07832 · Physical Review A

Newton's laws of motion generating gravity-mediated entanglement

Marta Maria Marchese, Martin Plávala, Matthias Kleinmann, Stefan Nimmrichter

Published Apr 4, 2025• 2 citations
arXivHTMLPDF

Abstract

The interface between quantum theory and gravity represents still uncharted territory. Recently, a tabletop experiment has been proposed for witnessing quantum features of gravity: Two masses in an initial superposition of spatially localized states interact only through gravity and it is measured whether the final state is entangled. Here we show that one can generate the same amount of entanglement in this setup by using the time evolution given by Newton's laws of motion. We argue that theories of quantum gravity that can be approximated by the Newtonian potential and time evolution given by Newton's laws of motion will generate gravity-mediated entanglement.

DOI
10.1103/physreva.111.042202

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The interface between quantum theory and gravity represents still uncharted territory. Recently, a tabletop experiment has been proposed for witnessing quantum features of gravity: Two masses in an initial superposition of spatially localized states interact only through gravity and it is measured whether the final state is entangled. Here we show that one can generate the same amount of entanglement in this setup by using the time evolution given by Newton's laws of motion. We argue that theories of quantum gravity that can be approximated by the Newtonian potential and time evolution given by Newton's laws of motion will generate gravity-mediated 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.
The gravity-mediated entanglement experiments employ concepts from quantum information to argue that if entanglement due to gravitational interaction is observed, then gravity cannot be described by a classical system. However, the proposed experiments remain beyond our current technological capability, with optimistic projections placing the experiment outside of the short-term future. Here we argue that current matter-wave interferometers are sufficient to indirectly prove that gravitational interaction creates entanglement between two systems. Specifically, we prove that if we experimentally verify the Schrödinger equation for a single delocalized system interacting gravitationally with an external mass, then, under one of two reasonable assumptions, the time evolution of two delocalized systems will lead to gravity-mediated entanglement.
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 revisit the Bose-Marletto-Vedral (BMV) tabletop experimental proposal---which aims to witness quantum gravity using gravity-mediated entanglement---analyzing the role of locality in the experiment. We first carry out a fully quantum modeling of the interaction of matter and gravity and then show in what way gravity-mediated entanglement in the BMV experiment could be accounted for without appealing to quantum degrees of freedom of the gravitational field. We discuss what assumptions are needed in order to interpret the current BMV experiment proposals as a proof of quantum gravity, and also identify the modifications that a BMV-like experiment could have in order to serve as proof of quantum gravity without having to assume the existence of local mediators in the gravitational field.
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.
Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. However, the lack of empirical evidence has lead to a debate on whether gravity is a quantum entity. Despite varied proposed probes for quantum gravity, it is fair to say that there are no feasible ideas yet to test its quantum coherent behavior directly in a laboratory experiment. Here, we introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. We show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. We provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple spin correlation measurements.