I was out looking for something, and happened on this - long story short. I'll also point people to physforum.com, where there is or was a similar discussion. I registered just to post this, because it's useful - I won't be back, so don't expect replies.
20 or more years ago I read an article by a physicist about this very topic. He didn't even get to the things discussed here, or the things on physforum (souls, cloning....) He just said something more fundamental, and also showed much of his proof, which I do not remember - I also might be misremembering it in detail. Anyway: Using today's technology (20 years ago, but we still use the same essential methods), to put each atom of the human body into a single memory address would require all the matter in the known universe. You could argue that he's wrong by half, which means only 1/2 of the known universe. And yes, methods of computer storage will certainly evolve. That means an order of quadrillions cubed and cubed again to get to the point of storing it in the size of the Earth, much less a server the size of a desk. And of course that doesn't include mapping or algorithms for doing the actual process, since we don't know that stuff yet, anyway. Just thought I'd put it out there...... He simply figured the number of atoms in the body, which is roughly known (though I don't know that number) and how much disk it takes to store data, and that's what he came up with, in essence. No real mystery, just arithmatic.