Is equivalence principle valid for quantum gravitational field?

Abstract

Entanglement can be generated through the gravitational interaction between two massive bodies that are initially in a product state. This shows that the gravitational field is quantum. When the third massive body is introduced and the gravitational interaction only between the third body with either one of the former two bodies is considered, we find that no entanglement is generated between the former two bodies up to the monopole approximation, even though the considered gravitational interaction is quantum. This resembles the behavior of two accelerating two-level atoms that is usually regarded as the Unruh–DeWitt detectors. By linking the acceleration to that generated by the gravitational field, we show that the equivalence principle is still valid even though the gravitational field is quantum.