The concept of a teleporter is simple. Scan yourself at the subatomic level, as well as each particle’s energy patterns; convert all the matter into energy and send it to your destination to be reassembled. This is different from quantum teleportation, which is different and, of course, possible with modern technology. Quantum teleportation is lame compared to regular.
The paradox itself asks us if you are killed in the process of destruction and someone else is created who is indistinguishable from you.
The Ship of Theseus and Cutty Sark
This paradox is simple and will be used as an example for my argument. Imagine a sailboat made of wood. Every month on average you have to replace a plank of wood because it get damaged. After a while, every plank on the ship is replaced. Is it still the same ship? Most people answer yes.
Now imagine another ship, we’re going to call it the Cutty Sark. It eventually burns down, compromising all of the hull. It is rebuilt with the exact same design for historical purposes. Is it the same ship? Most people answer no.
These two ships have the same end result, yet are classified differently. You may ask why this is relevant. Here’s why: You are the Ship of Theseus. Your body is replacing every molecule, every atom constantly. If you use a teleporter like the one described above, your body is destroyed entirely then reassembled identically. This scenario is similar to that of the Cutty Sark.
Life is Like the Cutty Sark
This seems contradictory to what I said above, and it is. The above is the standard interpretation. Below is a more existential version.
Every moment of your existence, you are different than you were before. The act of living destroys your old existence, creating a new you, different from the old. As time passes, you learn more, mature (physically and mentally), so you are no longer the same person.
Teleportation is Danger-Free
Considering the danger of teleporting is better than that of driving (according to Star Trek. It may be harmful as a prototype in real life, but more advanced technologies should be safer), you have nothing to worry about. If it’s the break in conscience that bugs you, sleeping does the same daily. If you think the process destroys an immeasurable soul, physics recognizes an immeasurable property as non-existent. Have no fear, beam me up Scotty!