No, classical spacetime can’t produce entanglement

If spacetime is classical, it cannot mediate entanglement. This week’s Nature paper claiming it can "produce" entanglement is causing confusion. I "produce" entanglement when I turn on my laser...

A number of proposals for testing the quantum nature of spacetime (Bose et al.; Marletto–Vedral) aim to do so by producing gravitationally mediated entanglement (GME) between two masses. The logic is simple: creating entanglement between distant systems requires a quantum mediator like a photon or graviton. If gravity were only a classical field, it wouldn’t suffice to create entanglement.

This is already baked into the modern notion of entanglement as defined by Reinhard Werner. We may disagree on what entanglement exactly is, so we define entanglement as the thing, which cannot be created by Local Operations and Classical Communication (LOCC). A classical field counts as Classical Communication, so it can’t create entanglement while a quantum field can.

The local part (LO) is not actually that relevant here. If gravity is quantum, then it can create entanglement. Its interaction is a unitary (U) that depends on the relative configuration of two masses; A unitary generically entangles them. Take one mass in a spatial superposition and a second mass initially at a fixed location so that the total state is

\(|\psi\rangle=\frac{1}{\sqrt{2}}\left(|x_L\rangle+|x_R\rangle\right)\otimes |y\rangle\)

Because the interaction strength differs between the the two branches, the unitary of quantum gravity will accelerate the second mass by a different amount conditional on the location of the first particle and the state becomes entangled.

Likewise if gravity is classical, then it can’t create entanglement whether its local or non-local. Zach Weller-Davies and I showed this explicitly to be the case for any consistent classical field, but it’s been known from a formal point of view since the early days, just due to the definition of entanglement given by Werner. It’s even been shown to be formally true in the case of general probabilistic theories. Of course, entanglement can still arise through other quantum interactions (photons, spins, phonons), or through exotic nonlocal quantum effects (e.g. correlated decoherence, or Diósi–Penrose-type gravity models).

There has been debate regarding some subtleties to do with the Newtonian potential vs gravitons, but this was resolved by Danielson, Satishchandran, and Wald. Nonetheless, for reasons I don’t completely understand, there seems to be confusion in the field. At DICE 2024, the room was roughly split on whether classical gravity could generate entanglement.

So it’s unfortunate that this weeks Nature paper by Aziz and Howl adds to the confusion. And while I don’t want to be that guy, who stays up late because people are wrong on the internet, I’ve been getting a lot of questions about the article, including Nature News and I wanted to explain my comment there in a bit of detail.

It’s worth noting that the paper doesn’t claim that classical fields can mediate entanglement. It claims that classical fields can produce entanglement. But the word “produce” is doing a lot of work here! If a classical experimenter turns a knob on her laser to fire photons at another lab which creates entanglement, there is a sense in which she is “producing” entanglement, but it’s the photons that are mediating it. That’s pretty much what’s going on in Aziz and Howl’s example except the experimenter’s knob is replaced by the classical gravitational field, and the laser is replaced by a quantum field. The quantum field is mediating the entanglement, but it’s being turned on by changing the coupling constants of the quantum field locally.

UPDATE Nov 11, 2025

After this post appeared, Elizabeth Wilson and I teamed up with up with Chiara Marletto, and Vlatko Vedral (who wrote an overlapping analysis at the same time as this blog post), to put together this comment: https://arxiv.org/abs/2511.07348 We show that their model does not produce entanglement. Even if the model produced entanglement, it would be mediated by the quantised matter interaction, and not gravity.

What they actually do

Although much of the article discusses classical theories of gravity, they are essentially doing standard Quantum Field Theory (QFT) in curved space.

Quantum fields in curved space can mediate entanglement, and the relevant amplitudes can depend on the curvature of spacetime (here given by the Newtonian potential). That’s essentially what Aziz and Howl show.

Their result by itself is interesting, in the sense that the entanglement contains an imprint of the gravitational field [edit: we later found that this claim is incorrect, there is no entanglement], but the claim of their article is confusing. So, I’ll go into a bit of detail, and try to distill their argument. They consider the Hamiltonian of a quantum field in curved space, and write it as a piece which doesn’t contain gravity, and an interacting part which does

\(\begin{align}H&\approx\int d^3x \sqrt{g} \mathcal{H}^{(m)}\\ &\approx \int d^3x [1-2\Phi(x)]\mathcal{H}^{(m)}\\ &\equiv H_0+H_{int} \end{align}\)

g is the determinant of the metric which is the gravity part, ℋ is the Hamiltonian density of the matter (it usually also contains the metric, but never mind). So, if you start off with two distant particles in some approximate eigenstate of H₀ and then turn on the Newtonian potential Φ, the quantum field gets a kick and mediates the entanglement. But crucially it’s the quantum field that is producing the entanglement, it’s just that the coupling constants of the quantum field depend on the Newtonian potential. If in the GME experiment, the experimenters screen the interactions due to matter, the effect vanishes. And this is what leads Aziz and Howl to conclude that gravity is “responsible” for the entanglement. I guess that’s technically true, since it was gravity which turned on the quantum interaction. But crucially:

• The carrier of entanglement in their calculation is the quantum matter sector (the same virtual-matter exchange that entangles in ordinary QFT with (Φ=0)).

• The classical gravitational field contributes only the c-number prefactor (1-2Φ), which modulates the amplitude. It does not become a quantum mediator.

Turning off the gravitational interaction removes the particular amplitude they wrote down. But that doesn’t show that gravity mediates entanglement; it only shows their chosen amplitude depends on keeping that bookkeeping split (H=H₀ + H_int), and starting in an eigenstate of H₀. So this is not an effect which is restricted to quantum field theory. This effect exists every time experimenters (who we describe classically), turns on an interaction.

Now I think it’s interesting that this can be done without exciting on-shell particles, and the amplitude they write down is interesting in terms of its magnitude (which they calculate) and form (in terms of how it imprints the Newtonian potential). Aziz and Howl are right to compare effects like these, to GME, because the GME experiment requires understanding the possible ways that two masses can get entangled. And this makes the experiment very challenging. Zach Weller-Davies rightly emphasises this in his commentary, So, I think there is an interesting conversation to be had, I just wish it wasn’t about whether classical fields can entangle — we know they cannot.