Spatial Qubit Entanglement Witness for Quantum Natured Gravity

Abstract: Evidencing the quantum nature of gravity through the entanglement of two masses has recently been proposed. Proposals using qubits to witness this entanglement can afford to bring two masses close enough so that the complete 1/r interaction is at play (as opposed to its second-order Taylor expansion), and micron-sized masses separated by 10-100 microns (with or without electromagnetic screening) suffice to provide a 0.01-1 Hz rate of growth of entanglement. Yet the only viable method proposed for obtaining qubit witnesses so far has been to employ spins embedded in the masses, whose correlations are used to witness the entanglement developed between masses during interferometry. This comes with the dual challenge of incorporating spin coherence-preserving methodologies into the protocol, as well as a demanding precision of control fields for the accurate completion of spin-aided (Stern-Gerlach) interferometry. Here we show that if superpositions of distinct spatially localized states of each mass can be created, whatever the means, simple position correlation measurements alone can yield a spatial qubit witness of entanglement between the masses. We find that a significant squeezing at a specific stage of the protocol is the principal new requirement (in addition to the need to maintain spatial quantum coherence) for its viability