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.
http://www.flyingmachines.org/davi.html
The South Hampton University eventually made it happen centuries later in 1961.
https://en.m.wikipedia.org/wiki/SUMPAC
Did they invent it or "just" built it? Probably they could patent parts of the final airplane. I didn't check if they did.