Theseus ship and teleportation

The act of teleportation is questionable. It might happen it may not. Some scientist believe it could take quadrillions of years to accurately beam a human being to another place in space (link). This problem alone makes the feat problematic since the universe isn't even a fraction of a quadrillion years old. Basically teleporting using current technology is like trying to download the entire Lost series over dial up internet
The idea behind teleportation is interesting. The process is to take the atoms that make up a person, pull them apart separately, then put them together again in a completely new location. Seems straight forward, but that brings up the philosophical issue; is rebuilding a person atom by atom creating the same person or just creating a copy. Is that copy the same person.

This problem first surfaced with philosopher Plutarch in a story called the ship of Theseus.

The ship of Theseus, also known as Theseus's paradox, is a paradox that raises the question of whether an object which has had all its components replaced remains fundamentally the same object. The paradox is most notably recorded by Plutarch in Life of Theseus from the late 1st century. Plutarch asked whether a ship which was restored by replacing all and every of its wooden parts, remained the same ship. Wiki Page

Just something to think about. Do you think a teleported person would be the same after transmission or would the current arrangement of atoms that make us up be lost in transmission?
This was inspired by Reddit: What are the most mindblowing recent advancements most people still don't know about?