Bounds on quantum communication via Newtonian gravity
  Newtonian gravity yields specific observable consequences, the most striking of which is the emergence of a $1/r^2$ force. In so far as communication can arise via such interactions between distant particles, we can ask what would be expected for a theory of gravity that only allows classical communication. Many heuristic suggestions for gravity-induced decoherence have this restriction implicitly or explicitly in their construction. Here we show that communication via a $1/r^2$ force has a minimum noise induced in the system when the communication cannot convey quantum information, in a continuous time analogue to Bell's inequalities. Our derived noise bounds provide tight constraints from current experimental results on any theory of gravity that does not allow quantum communication. 
D. Kafri, G. J. Milburn, J. M. Taylor
quant-ph