A thought experiment about the nature of self (see details)- what do you think?

A book I read recently cited this thought experiment (proposed by a rather eccentric amateur philosopher who’s name I don’t recall)-

Suppose that someone finally invents the long-awaited teleportation machine. It’s a bit like Star Trek-style “beaming”, but it works on the following principle: the machine reads the precise physical state of a person at a given moment, down to the most minute atomic detail. This data would include the electrochemical state of every brain cell, along with any other information necessary to reconstruct every other cell in the body in exactly the same condition as at the precise moment of the reading. In order to do this, however, it must completely destroy the body, dispersing its atoms to the wind. This data is then transmitted to another location, where the exact same atomic constituents are assembled in precisely the same relationship, only seconds after the dissolution of the original body.

There’s a great deal more to the experiment, but just starting with this much, here’s a question: if you were to be “processed” by this machine, is it you that would emerge at the new location? What would make it you, or not-you?