# Quantum Entanglement Induced by Gravitational Potential

## TL;DR

This paper investigates how gravitational potential induces quantum entanglement between two masses, suggesting that entanglement is intrinsic to gravitational interactions and providing insights for quantum gravity theories.

## Contribution

It demonstrates through numerical analysis that the ground state of two masses interacting via gravity is inherently entangled, highlighting a fundamental link between gravity and quantum entanglement.

## Key findings

- Ground state of gravitationally interacting masses is entangled.
- Entanglement may be intrinsic to gravitational interactions.
- Provides insights for quantum gravity in weak-field, low-velocity regimes.

## Abstract

The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational potential. Through numerical calculation, we confirm that the ground state of such quantum system is an entangled state. This raises a question whether a quantum ground state describing masses interacting through gravity can ever be a separable state. Entanglement seems to be an intrinsic characteristic for the ground state when mutual gravitational interaction is involved. Although the study is in the context of non-relativistic quantum mechanics, it provides hints for a quantum gravity theory in the limit of very weak field and low relative velocity. The entanglement of the ground state of two masses seems intrinsically connecting to the curvature of spacetime they create.