Classical Gravity Cannot Create Quantum Entanglement

A fundamental question in physics is whether gravity, which we experience as a classical force in everyday life, must be described by quantum mechanics at its core. Recent experiments have been proposed to test this by looking for entanglement—a purely quantum phenomenon where particles become interconnected—between two masses interacting only through gravity. If entanglement is observed, it would suggest gravity itself has quantum properties. However, a paper published earlier this year by Aziz and Howl in Nature 2025 d this logic, arguing that even with a classical gravitational field, higher-order quantum processes in matter could generate entanglement, potentially muddying the interpretation of such experiments. Now, a critical analysis by Sienicki and Sienicki, building on work by Marletto, Oppenheim, Vedral, and Wilson, clarifies that classical gravity cannot mediate entanglement, reinforcing the original experimental premise.

The key finding from this analysis is that when the gravitational field is treated as purely classical, it cannot create entanglement between two initially separate quantum systems. This conclusion stems from a detailed examination of the Aziz and Howl model, which proposed that fourth-order perturbative processes in quantum field theory could mimic gravity-mediated entanglement. The critique shows that in the nonrelativistic limit actually used by Aziz and Howl, the interaction becomes ultra-local, meaning it reduces to independent terms for each mass. As a result, the time evolution factorizes into a product of local unitaries, which mathematically cannot turn a separable state into an entangled one. This factorization means the model does not generate entanglement under its own approximations, contrary to the original claim.

To reach this conclusion, the researchers employed a multi-faceted ology. First, they summarized the Aziz and Howl paper, noting its reliance on a semiclassical coupling where gravity responds to the expectation value of the stress-energy tensor while matter is treated fully quantum mechanically. Then, they analyzed the critique by Marletto et al., which identified three main issues: ultra-locality and factorization, inconsistent handling of spatial gradient terms, and perturbative artefacts. Specifically, the critique showed that in a consistent nonrelativistic treatment, the propagator between non-overlapping wave packets vanishes, eliminating the cross-term Aziz and Howl identified as entangling. Additionally, the researchers reformulated the problem using quantum channel theory, providing a model-independent argument that channels representing classical mediators are separable and thus incapable of generating entanglement from product states.

Of this analysis are clear and robust. The quantum channel formulation demonstrates that any genuinely classical gravitational mediator must implement a channel of the form E(ρ_AB) = Σ_c p(c) (U_A^(c) ⊗ U_B^(c)) ρ_AB (U_A^(c) ⊗ U_B^(c))†, which is a convex mixture of local unitaries and cannot create entanglement. This aligns with the specific from the Aziz and Howl model: under consistent approximations, the effective Hamiltonian reduces to H ≃ H_A ⊗ I_B + I_A ⊗ H_B, leading to a factorized unitary U(t) = U_A(t) ⊗ U_B(t). The researchers also distinguish between entanglement activation in already-quantum matter and genuine mediation by gravity, emphasizing that in the Aziz and Howl framework, any entanglement would arise from quantum matter resources controlled classically, not from the gravitational field itself. This separation clarifies that the nonclassical resource resides in matter, not gravity.

Of this work are significant for ongoing experimental efforts to test the quantum nature of gravity. Proposals like the BMV experiments, initiated by Bose et al. and Marletto-Vedral, aim to observe entanglement between masses coupled only via gravity. The analysis confirms that if such entanglement is detected, it would strongly indicate that gravitational degrees of freedom are nonclassical, as a purely classical mediator cannot achieve this. This restores confidence in the logical template underlying these experiments: entanglement via a mediator implies nonclassicality in that mediator. also relate to broader hybrid quantum-classical gravity models, reinforcing that consistency conditions in such models typically prevent entanglement generation by classical fields, making BMV-type experiments conceptually clean probes.

Despite these clarifications, the paper acknowledges limitations and ongoing debates. The analysis focuses on the specific nonrelativistic limit used by Aziz and Howl, and while the channel-theoretic argument is model-independent, it assumes the gravitational field is genuinely classical in the defined sense. The researchers note that the Aziz and Howl effect appears when constraints typical of hybrid models are relaxed non-uniformly, suggesting it may be an artefact of modelling choices rather than a robust prediction. Additionally, a note added in proof references independent work by Schneider, Huggett, and Linnemann using Newton–Cartan geometry, which complements these by showing gravitational phases vanish when classical geometry is shared, further supporting the conclusion. However, the broader question of how to fully unify quantum mechanics and gravity remains open, with this work addressing one specific aspect of the debate.