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We show that a signature of the quantum nature of gravity is the quantummechanical squeezing of the differential motion of two identical masses withrespect to their common mode. This is because the gravitational interactiondepends solely on the relative position of the two masses. In principle, thissqueezing is equivalent to quantum entanglement between the masses. Inpractice, detecting the squeezing is more feasible than detecting theentanglement. To that end, we propose an optical interferometric scheme tofalsify hypothetical models of gravity.

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