It seems, one could exploit the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates.
Obviously, relativity would preclude FTL information transfer, but as long as one did not try to measure the signal timing and impose an external reference frame of time, then there would be no violation of the speed of light limit, and would, in theory, be communicated instantaneously (presumably along an extra-dimensional Calabi-Yau surface/"brane").