Signatures of the quantum nature of gravity in the differential motion of two masses

We show that a signature of the quantum nature of gravity is the quantum mechanical squeezing of the differential motion of two identical masses with respect to their common mode. This is because the gravitational interaction depends solely on the relative position of the two masses. In principle, this squeezing is equivalent to quantum entanglement between the masses. In practice, detecting the squeezing is more feasible than detecting the entanglement. To that end, we propose an optical interferometric scheme to falsify hypothetical models of gravity.