No, classical gravity does not entangle quantized matter fields

TL;DR

The paper refutes a recent claim that classical gravity can generate entanglement between quantized matter fields, providing a non-perturbative proof of the impossibility.

Contribution

It offers a non-perturbative derivation demonstrating that classical gravity cannot entangle quantized matter, contradicting previous perturbative results.

Findings

Perturbative approach is inconsistent with exact non-perturbative derivation.

Classical gravity fundamentally cannot produce entanglement between quantum matter.

The result challenges claims that classical gravity can induce quantum entanglement.

Abstract

In their recent work, Nature, {\bf 646}, 813 (2025), Aziz and Howl claim that classical (unquantized) gravity can generate entanglement of quantized matter if matter is treated within quantum field theory which is, no doubt, our ultimate theory to use. We show that the perturbative result of Aziz and Howl in interaction picture is inconsistent with our exact and simple non-perturbative derivation in Heisenberg picture, that fundamentally precludes the claimed entanglement.