If warp drives are impossible, maybe faster-than-light communication is still on the table?

I'm sure many readers of Universe Today are, like me, fans of the science fiction genre. From the light sabers of "Star Wars" to the neuralyzer of "Men in Black," science fiction has crazy inventions aplenty and once science fiction writers dream it, scientists and engineers try and create it. Perhaps the holy grail of science fiction creations is the warp drive from "Star Trek" and it is fair to say that many have tried to work out if it is even possible to travel faster than the speed of light. To date, alas, to no avail but if the warp drive eludes us, what about faster-than-light communication.