A demonstration that classical gravity does not produce entanglement

TL;DR

The paper argues that classical gravity, formulated as Newton-Cartan gravity, cannot mediate entanglement in proposed gravitationally induced entanglement experiments. It adopts a Newton-Cartan analysis to model gravity as a mediator within a tripartite system and shows that the entanglement phase arises from a classical work term, reducing to $m(\phi'-\phi)T$ and vanishing when the derivative operators coincide ($\nabla' = \nabla$). This key result invalidates entanglement generation by classical gravity in the Newtonian limit, clarifying that any observed entanglement would imply a non-classical mediator or other mechanisms. The work sharpens the interpretation of GIE experiments and reinforces the LOCC-based claims about classical mediators in quantum information contexts.

Abstract

Once again, dispute has arisen over the interpretation of proposed quantum information theory experiments to probe the quantum nature of gravity by testing for gravitationally induced entanglement (GIE) between two spatially separated massive particles ([1] vs. [11,12]; further contributions in [7,9]). The confusion appears to reside in interpreting applications of a Hamiltonian formalism. But classical gravity cannot mediate entanglement on independent grounds. A Newton-Cartan analysis shows that if gravity is classical, a mediator, and entanglement is observed as an outcome of performing a GIE experiment, something other than gravity must have supplied the (virtual) force needed during the experiment to produce the effect.