Probing the Quantum Nature of Gravity through Classical Diffusion

Abstract: The question of whether gravity is fundamentally quantum remains one of the most profound open problems in modern physics. A recently explored approach consists in testing gravity's ability to entangle quantum systems, which requires preparing and controlling large-mass quantum states-a formidable experimental challenge. We propose an alternative strategy that circumvents the need for quantum state engineering. We show that if gravity is classical in the sense of being a local operation and classical communication (LOCC) channel, it must necessarily introduce diffusion in the motion of quantum systems. We derive the master equation governing this diffusive dynamics and establish a lower bound on the noise that any classical gravitational interaction must induce. Next, we outline an experimental protocol based on a high-precision torsion pendulum at millikelvin temperatures, showing that the predicted diffusion, if present, is in principle detectable with near-term technology. Our approach offers a novel route to testing the classical vs quantum nature of gravity without requiring macroscopic quantum superpositions or high control of the quantum state of the system, significantly reducing the experimental complexity.