Ah, but that brings to light philosphical questions regarding the soul and consciousness.
It's actually philosophy 101 stuff. Am I a purely physical being (in which case if an exact molecular copy was made of me, it would BE me in terms of memories and personality) or is there a duality of being, the physical part and a spiritual part - the soul.
Digitizing as described by Tron (the movie) is reading the exact molecular makeup of an object and storing that as data while the actual molecules are suspended in the laser beam (which is preposterous, but hey it's fiction). Flynn's data describing him was enough to reproduce his consciousness in the computer. Since there's nothing to suggest that there is any kind of metaphysical transfer, we can assume that in the Tron universe a person is only a physical being. By that reasoning, I suppose if an exact copy of the user's data could be made, then that entity would effectively be the same person.
The obvious extention question is: could that copy then be brought into the real world? E.g. could digitization clone people? In the context of the universe I'd have to say no. In undigitization (wish I could think of a less awkward term) the laser isn't creating new molecules it's merely reusing the original molecules that were suspended in the beam. Nothing suggests laser can create molecules, so once one 'copy' is undigitized that's it.
That may all sound good, but there's still much more to explore here. Thorne 'died' in the computer, what happens to his physical molecules stored in suspension? What if someone tried to undigitize Thorne (when he was alive); his data is corrupted so would his molecules be reconstructed correctly? (Would he be a horrific pile of goo or would his molecules be reconstructed in a form paralleling his digital self). Indeed what if anything happens to my digital being (say I get a cut, or lose a limb or something) which is analgous to my data being altered, will it be reflected on my physical self when I'm undigitized?
Anyway there's definitely significant material for a low level philosophy paper. A lot of it would be things discussed in Matrix stuff, since the concepts are similar. I'd be interested in examining it more myself, but than I say #%@! that, it's fiction, I want to enjoy it not analyze it