Spatial qubit entanglement witness for quantum natured gravity

Abstract Witnessing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Both non-Gaussian and Gaussian protocols have been shown to be useful for this purpose. In non-Gaussian protocols the complete 1/r gravitational interaction can in principle be utilized for entanglement generation, as long as quantum superpositions of a spatial splitting ∆x comparable to the distance d between two masses can be generated. In practice, however, all non-Gaussian protocols proposed to date rely on embedded qubits -typically spins -to read out the entanglement: spin correlations are used to witness the entanglement developed between the masses during interferometry. Here we show that if superpositions of distinct spatially localized states of each mass can be created, then a spinless version of the non-Gaussian protocol is possible: simple position correlation measurements alone can yield a spatial qubit witness of the entanglement between the masses. We find that the principal new requirement for the viability of this protocol is a position squeezing of the wavefunction by approximately seven orders of magnitude, applied at a specific stage of the experiment.