Gravity-mediated entanglement between oscillators as quantum superposition of geometries

Protocols for observing gravity induced entanglement typically comprise the interaction of two particles prepared either in a superposition of two discrete paths or in a continuously delocalized (harmonic oscillator) state of motion. An important open question has been whether these two different approaches allow one to draw the same conclusions on the quantum nature of gravity. To answer this question, we use a path-integral approach to analyze a setup that contains both features: a superposition of two highly delocalized center of mass states. In both cases the appearance of entanglement, within linearized quantum gravity, is due to gravity being in a superposition of distinct geometries.