I don't know how deeply their function has been explained, but I assume all of the information contained in the physical structure of a person--be it expressed as a wave function or whatever--can be determined, stored, communicated, and recreated in another location.

I can't think of a good reason, other than ethical considerations, that the original person needs to be "destroyed" in order to create the copy. I mean, there's ethical arguments on either side, really. Doesn't the original person have a right to life?

I would be very surprised if the Star Trek universe didn't contain a rogue scientist who creates copies of themself. They can't possibly have a non-crackable anti-duplication safeguard in every transporter device.