  We examine the quantum gravitational entanglement of two test masses in the
context of linearized General Relativity with specific non-local interaction
with matter. To accomplish this, we consider an energy-momentum tensor
describing two test particles of equal mass with each possessing some non-zero
momentum. After discussing the quantization of the linearized theory, we
compute the gravitational energy shift which is operator-valued in this case.
As compared to the local gravitational interaction, we find that the change in
the gravitational energy due to the self-interaction terms is finite. We then
move on to study the quantum gravity induced entanglement of masses for two
different scenarios. The first scenario involves treating the two test masses
as harmonic oscillators with an interaction Hamiltonian given by the aforesaid
gravitational energy shift. In the second scenario, each of the test masses is
placed in a quantum spatial superposition of two locations, based on their
respective spin states, and their entanglement being induced by the
gravitational interaction and the shift in the vacuum energy. For these two
scenarios, we compute both the concurrence and the von Neumann entropy; showing
that an increase in the non-locality of the gravitational interaction results
in a decrease in both of these quantities.
