How to Test Bell Nonlocality for Gravity?

Testing the quantum nature of gravity remains a fundamental challenge in physics. While previous proposals—such as the Quantum Gravity-Induced Entanglement of Masses (QGEM)—aim to show that gravity can mediate entanglement between masses, they do not definitively prove that the gravitational field itself is quantum. This paper addresses this gap by asking whether gravitational curvatures can exhibit Bell nonlocality, the strongest operational signature of quantumness.

The authors propose a four-mass setup to test the nonclassicality of gravity. Two source masses, each with an embedded entangled spin, are placed outside each other's light cones to ensure a locality-loophole-free environment. These spins are coupled to the motion of the masses to create spatial superpositions, effectively entangling the gravitational curvatures of the two source masses. Two additional probe masses are then introduced to interact locally with the gravitational fields of the source masses. By performing local measurements on the probe spins after they have interacted with the gravitational fields, the researchers can test for violations of the Bell-CHSH inequality.

The study demonstrates that if gravity is quantum, the gravitational fields will exhibit correlations that violate the Bell-CHSH inequality, thereby ruling out all local-realist descriptions of gravity. The protocol is designed to be fully device-independent, meaning it does not rely on assumptions about the internal workings of the measurement apparatus. The authors provide representative parameter sets, suggesting that the experiment is feasible with current or near-future technologies, such as levitated micro-diamonds with NV-center spins and satellite-based entanglement distribution.

This proposal moves beyond existing tests by providing a method to directly witness entangled gravitational curvatures. By combining the principles of Bell nonlocality with gravitational physics, this experiment offers a definitive way to distinguish between quantum and classical theories of gravity in a laboratory setting, potentially providing the first empirical evidence for the quantum nature of spacetime itself.