Two massive particles in a superposition of positions should become entangled through gravity, but realistic conditions sharply limit this. A new theoretical paper shows that the finite width of wave packets and residual forces narrow the useful windows for violating Bell inequalities and for quantum teleportation.
A group of researchers led by Saeed Haddadi studied a two-branch "gravitational cat" model with Gaussian wave packets. They averaged the Newtonian interaction over the finite width of the packets and added phenomenologically correlated dephasing. The work was published as a preprint on arXiv on 15 October 2026.
Instead of point-like branches, the authors considered blurred probability clouds. Imagine two blurred shadows on a wall: their gravitational attraction is averaged over the entire area rather than concentrated at a single point. This averaging weakens the phase needed for useful entanglement.
The team checked whether the state remains operationally useful. They calculated the violation of Bell inequalities, teleportation fidelity, coherent information, and state distinguishability. It turned out that the windows in which the state is simultaneously Bell-nonlocal and suitable for teleportation narrow as the packet width increases or dephasing strengthens.
The residual electrostatic interaction has a particularly strong effect: it can coherently cancel the gravitational phase and completely suppress the signal. Thus, even weak extraneous forces can mask gravitational entanglement.
The results define specific bounds on packet width and the permissible level of electrostatic interference that must be taken into account in future experiments testing the quantum nature of gravity. According to the preprint, these limits show how delicate the interface between quantum mechanics and gravity is under realistic conditions.
