Even if quantum mechanics involves the supersmall, what happens when you take the supersmall and put enough of it together, it's not small anymore. That's going to take a lot of work to figure out how to do it but it can and should be done. There's a way and someone will find it.
One argument is the improvement of communication. Quantum entanglement (the post was about entanglement specifically), allows data to be carried and read over massive distances instantaneously. So there is one logistical problem solved. Also, it can be used similarly to send data and enable teleportation of matter. The data can be recorded (this would take a supercomputer, but quantum mechanics will allow those soon enough) and sent via entangled particles to supply a distant vessel with supplies, equipment, and even personnel. Albeit, none of these directly improve space travel (there may be something I didn't think of, but oh well), but definitely get rid of some minor issues associated with it.
QM is currently understood to involve only the super small. I'm not sure what the current speculation is but I can't imagine what the applications might be. Most faster than light speculation revolves around Einstein's relativity, such as Warp theory, Wormhole theory, folding space etc. I think we are stuck at the realm of GR and SR for travel.
I don't know allot about the speculation for faster than light travel using QM. But as I understand it all QM phenomenon as of now is understood to be limited to the extremely small. Most idea's about faster than light travel are based on relativity; for instance Warp travel, wormholes, folding space etc.