Entangling quantum fields via a classical gravitational interaction

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that there are solutions for which two initially independent quantum fields evolve into an entangled state, even though their interaction occurs solely via a common classical gravitational field. Thus in contrast to recent suggestions, an observed generation of entanglement would not provide a definitive test of the nonclassical nature of gravity.