On the one hand yes, it would be a different “person” but IF it could be done, as Erasmus wrote, the new version would not know that. Let's say that in your sleep someone came in, drugged you so that you did not wake up in the process, downloaded your memories, and then uploaded them into an identical body that had whatever was in it's brain wiped clean. This new “you” was placed, sleeping, in an identical bedroom built in lab elsewhere, with curtains drawn exactly the same, etc. For sake of argument “you” sleep alone, without spouse, pet, or roommate in the house. The lab personnel then provide an identical stimulus to wake both versions of “you” at the same time, say a car alarm going off outside. At that time would not both entities feel exactly the same, until such time as the copied “you” found out the bedroom was located in a lab somewhere?
As for Quantum Physics, why does that prohibit copying a mind? If our memories are bits of code in electrical impulses in brain cells, why could they not some day be replicated?
I saw The Prestige, by the way.
Here’s one from The Outer Limits right along those lines. It’s pretty good:
“Captain Cotter McCoy (Lou Diamond Phillips) is the first of a new breed of soldier. As part of a top secret program overseen by Dr. Greg Olander (Robert Joy), General Langston Chase (Dale Wilson), and Cotter’s friend, Colonel Pete Butler (Scott Kraft), the contents of McCoy’s brain can be temporarily transferred into an android version of himself. This process creates a virtually indestructible fighting machine with the smarts and experience of a human being.
“But, one day something goes wrong. During the transfer, the real McCoy’s body is blasted with electricity, stopping his heart, inflicting serious brain damage and leaving Cotter’s mind trapped in the android body...”
http://www.tv.com/shows/the-outer-limits/identity-crisis-21493/
I suspect that the ultimate processes of the brain are mediated by quantum effects. If this is true, then any attempt to "read out" the exact state of the brain would unavoidably scramble those quantum states.
My analogy with the proposed quantum-secure communications is that any attempt to intercept the data stream alters it and renders it undecipherable; in addition, it gives the legitimate receiver indication that there was an attempted interception. The single exception is if the interceptor happens to have chosen the exact correct decoding sequence, which would be astronomically improbable.