Continuous-Variable Entanglement through Central Forces: Application to Gravity between Quantum Masses

We describe a complete method for precise study of gravitational interaction between two nearby quantum masses. Since the displacements these masses are much smaller than initial separation their centers, displacement-to-separation ratio is natural parameter in which potential can be expanded. show that entanglement such experiments sensitive to relative momentum only when system evolves into non-Gaussian states, i.e., expanded at least up cubic term. A pivotal role force gradient as dominant contributor position-momentum correlations demonstrated. establish closed-form expression gain, shows contribution from term proportional and quartic squared. From information perspective, results find applications witness entanglement. Our methods versatile apply any number central interactions order.