The Diósi-Penrose model of classical gravity predicts gravitationally induced entanglement

Abstract: We show that the dynamics of the Di\'osi-Penrose (DP) model of classical gravity can entangle the mechanical degrees of freedom of two separate particles. For standard experiments of gravitationally induced entanglement (GIE), we find that entanglement can be generated if and only if the particles are separated by a distance smaller than some limiting value $d_c$, proportional to the only free parameter of the DP model. Greater distances can be achieved through new experimental configurations, where the initial wave functions of the particles are allowed to spread perpendicularly to the separation axis. Although the DP dynamics asymptotically drives the system to a separable state, we observe that, for reasonable experimental parameters, GIE can survive for more than a day. Our results therefore imply that GIE detection is not enough to validate quantum gravity. Experimental tests of GIE dynamics have nonetheless the potential to falsify the DP model.