Gravitationally-Induced Photon Entanglement in an FLRW Cosmological Background

Abstract: In order to detect the quantum nature of gravity, the quantum gravity induced entanglement of masses(QGEM) has been proposed both in flat and curved spacetime. In this paper we propose an analogous QGEM protocol using photons produced in astronomical processes as the quantum systems. Unlike massive particles, the gravitational interaction between photons-intrinsically relativistic particles-simultaneously satisfies both the event and system localities. So it can provide a clear test of whether the gravitational mediator must be nonclassical based on the Local Operations and Classical Communication (LOCC) principle. Although the gravitationally induced entanglement between massless relativistic photons is extremely small, our quantitative calculations clarify the characteristic features of the entanglement induced by the photon's own gravitational field in astronomical process and may inspire other photon entanglement experiments.