  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.
