It's not all that different to a fax machine, the way it's described in st.

You just need to be able to accurately scan and place atoms to achieve the 'teleportation' being discussed here.

Thinking about it even that is probably not possible, as you'd need to know both the position and momentum and state of every sub atomic particle in the body.

I felt like they hinted in some episodes that there was some rule of nature they were exploiting to get it to work. Like imagine trying to tell someone in the 11th century that humans made machines that can fly, they imagine some mechanical thing flapping wings. They imagine it because they don't know what air does when it passes over a fast moving surface. It isn't like the transporter really stores your pattern down to every particle, there was something that they found that made it a lot easier problem to solve.

Does quantum entanglement count? Probably depends on your definition of "teleportation", I'd assume.