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

• URL: http://arxiv.org/abs/2206.12897v3
• Date: Thu, 11 May 2023 14:38:14 GMT
• Title: Continuous-Variable Entanglement through Central Forces: Application to Gravity between Quantum Masses
• Authors: Ankit Kumar, Tanjung Krisnanda, P. Arumugam, and Tomasz Paterek
• Abstract summary: We show that entanglement in such experiments is sensitive to initial relative momentum only when the system evolves into non-Gaussian states. From a quantum information perspective, the results find applications as a momentum witness of non-Gaussian entanglement.
• Score: 4.362023116605902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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