Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

Bose et al. and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schrödinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton-Schrödinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by Döner and Grossardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.