Presumably zero. Patents are only permitted for "useful" subject matter. Useful is a term of art: you can still patent silly things like Slinkies: http://www.google.com/patents/US2415012?printsec=drawing – but whatever you patent has to actually function as advertised. So while the Slinky is objectively useless, it does what the patent says it does. A warp drive would be objectively useful, but when you build it, it won't do what the patent says it does; therefore, it's not patentable.

Though not quite in practice of course. I cannot substantiate my claim with data, but have come across several (approved) patents which are actually not even correct -- the described does not function as advertized.