I apologize if I’ve somehow got you on a bad day and if this is not your usual self.
A faster than light drive is an idea. A detailed description of a working physical device that can propel a vehicle faster than light; with sufficient detail that experts can make the device from the description is a potentially patentable invention.
Leonardo da Vinci had the idea of a human powered flying machine. I pretty sure nobody would say that his sketches are an invention. On a second thought, there are so many people around, probably somebody would claim it.
The South Hampton University eventually made it happen centuries later in 1961.
Did they invent it or "just" built it? Probably they could patent parts of the final airplane. I didn't check if they did.