The Di\'osi-Penrose model of classical gravity predicts gravitationally induced entanglement

TL;DR

This paper demonstrates that the Di"osi-Penrose model of classical gravity can induce entanglement between particles' mechanical states, with potential experimental implications for testing quantum gravity theories.

Contribution

It shows that the DP model predicts gravitationally induced entanglement under certain conditions and explores experimental configurations to detect such effects, challenging the notion that GIE confirms quantum gravity.

Findings

Entanglement occurs only below a critical separation distance.

GIE can persist for over a day under realistic parameters.

Detection of GIE alone does not confirm quantum gravity.

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.