What Is the Gravitational Field of a Mass in a Spatially Nonlocal Quantum Superposition?

The study of the gravitational field produced by a spatially nonlocal, superposed quantum state of a massive particle is an interesting and active area of research. One outstanding issue is whether the gravitational field behaves like the classical superposition of the gravitational field of two particles separated by a spatial distance with half the mass at each position. Alternatively, does the gravitational field behave as a quantum superposition with a far more interesting and subtle behavior than a simple classical superposition? Quantum field theory is ideally suited to probe exactly this kind of question.