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Inspired by string theory ideas, we probe quantum entanglement from thegravitational potential energy. Concretely, we reconsider the study of quantumcorrections to the Newtonian potential energy by treating a massivetwo-particle system $m_{1}$ and $m_{2}$ with size dimensions $r_{1}$ ad $%r_{2}$ where the two particles separated by a distance $d$ are under only theirmutual classical gravitational interaction $V_{r}\left( r_{1}\text{, }%r_{2}\right) $. Exploring such a size-dependent gravitational behavior andtaking the limit $r_{1}$, $r_{2}\ll d$, we investigate the associated quantumbiparticle state and express its evolution after an interaction time $\tau $.Among others, we show that the two masses cannot be separable due to theinduced gravitational entanglement in terms of the accumulated quantum phase$\delta \phi =\delta V_{g}\tau /\hbar $. By analogy with the classical gravity,we derive the expression of the resulting extremely weak entanglement forcefrom the corresponding gravitational entanglement energy. Then, we providecertain entanglement diagnostics.

Probing Quantum Entanglement from Quantum Correction to Newtonian Potential Energy