Gravity-Mediated Entanglement

Gravity-mediated entanglement proposals aim to use two initially separable quantum systems as witnesses of the interaction connecting them. If gravity is their only relevant interaction and a specified classical mediation model cannot create entanglement, observing entanglement would rule out that model. This is a conditional inference about mediation, not a direct observation of gravitons or a complete test of quantum gravity.

Branch-dependent Newtonian phases

Prepare each of two masses in a superposition of localized branches labeled $0,1$. Assume nonrelativistic, weak-field motion, approximately fixed branch separations $r_{ij}$ during a hold time $t$, and negligible transitions between branches. The Newtonian potential gives

$$\lvert\psi(t)\rangle= \frac12\sum_{i,j=0}^{1}e^{i\phi_{ij}}\lvert i,j\rangle, \qquad \phi_{ij}=\frac{Gm_Am_Bt}{\hbar r_{ij}}.$$

The positive phase follows from $U=e^{-iVt/\hbar}$ with attractive $V=-Gm_Am_B/r$. One-body phases can be removed locally. The invariant combination

$$\Phi=\phi_{00}+\phi_{11}-\phi_{01}-\phi_{10}$$

cannot generally be removed by separate operations on the two masses. For this ideal pure state, the concurrence is

$$C=2|c_{00}c_{11}-c_{01}c_{10}| =\left|\sin\frac{\Phi}{2}\right|.$$

Thus a nonadditive interaction phase can entangle initially product branch states. A measurable phase on each interferometer separately is insufficient; the nonlocal combination or an entanglement witness is needed.

From branch entanglement to a measured witness

In spin-based proposals, spin-dependent forces correlate a spin with each mass’s location. After the gravitational interaction, recombining the paths can transfer the phase correlations to spins, whose measurements are more accessible. The complete calculation must include imperfect splitting and recombination, motional overlap, spin dephasing, and environmental information about branches.

The proposals by Bose and collaborators and by Marletto and Vedral explain related routes to witnessing nonclassical mediation. Their model assumptions, including locality of coupling and what is meant by a classical mediator, are part of the conclusion.

What must be excluded?

A channel implemented solely by local operations and classical communication cannot entangle an initially separable state. An inference from entanglement therefore requires excluding pre-existing entanglement and unwanted nonlocal quantum channels. Electrostatic, magnetic, Casimir, and shared electromagnetic interactions must be quantitatively controlled before attributing the witness to gravity.

The theoretical conclusion also depends on the mediator description. Writing an instantaneous operator-valued two-body potential already supplies an entangling quantum interaction; identifying its physical mediator requires further assumptions. Tests target specified classical-channel or hybrid models, rather than every imaginable use of the word “classical.”

Claims of exceptions require the same care. Aziz and Howl propose matter-mediated entanglement in a classical gravitational field. Gundhi, Infantino, and Bassi challenge that interpretation, attributing the entanglement in the analyzed model to particle diffusion and the subsystem partition, including diffusion without a gravitational interaction. This mechanism is disputed, not an established counterexample to every mediator inference. The stable methodological lesson is to specify the subsystem partition, permitted communication channels, and interaction-dependent witness before drawing a conclusion about gravity.

The dated research assessment follows the competing analyses and experimental requirements, with explicit review dates and proposed checks.

A positive result would not by itself determine ultraviolet gravitational dynamics, establish spacetime discreteness, or observe individual gravitons. A null witness could result from decoherence or inadequate control. This page presents the stable proposal logic, not a claim that the required experiment has been completed.

Exercise

If $\phi_{00}=\phi_{11}=0$ and $\phi_{01}=\phi_{10}=\varphi$, find the concurrence. At what smallest positive $\varphi$ is it maximal?

Solution

Here $\Phi=-2\varphi$, so $C=|\sin\varphi|$. The first maximum occurs at $\varphi=\pi/2$. If instead every phase had the additive form $\phi_{ij}=a_i+b_j$, then $\Phi=0$ and no entanglement would be created.

References

• Aziz, J., and Howl, R., “Classical theories of gravity produce entanglement,” Nature 646, 813–817 (2025), doi:10.1038/s41586-025-09595-7 — a proposed field-theoretic mechanism whose interpretation is disputed.
• Bose, S., et al., “Spin entanglement witness for quantum gravity,” Physical Review Letters 119, 240401 (2017), arXiv:1707.06050 — spin-mediated readout proposal.
• Gundhi, A., Infantino, G., and Bassi, A., “Can classical theories of gravity produce entanglement?,” arXiv:2604.19696v3, revised 7 August 2026, preprint — a challenge based on diffusion and the choice of subsystem partition.
• Marletto, C., and Vedral, V., “Gravitationally induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity,” Physical Review Letters 119, 240402 (2017), arXiv:1707.06036 — mediator-witness reasoning.