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arXiv · 2206.12897

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

Ankit Kumar·Tanjung Krisnanda·P. Arumugam·Tomasz Paterek
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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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Ankit Kumar, Tanjung Krisnanda, P. Arumugam, Tomasz Paterek. 2023-05-11. Continuous-Variable Entanglement through Central Forces: Application to Gravity between Quantum Masses. https://doi.org/10.22331/q-2023-05-15-1008

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