Continuous-variable entanglement through central forces: application to gravity between quantum masses

• Main Authors: Kumar, Ankit, Krisnanda, Tanjung, Arumugam, P., Paterek, Tomasz
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2024
• Subjects: Physics; Continuous-variable entanglement; Quantum masses
• Online Access: https://hdl.handle.net/10356/173610
• Institution: Nanyang Technological University

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