That is a really excellent question! It goes straight to the heart of what is actually going on. I give a longer explanation of this in the last section of my paper, but here is the TL;DR: The way in which you get copyable classical information out of non-copyable quantum information is by discarding parts of the wave function. The mathematical description of this operation is called a trace. The classical information that comprises our classical reality is a proper subset of the quantum information in the universal wave function.

The next question people usually ask at this point is: isn't that just multiple-worlds? And the answer is: yes, it sort of is, but with one important difference: the MWI insists that all of the myriad multiple worlds are equally real. And if you take the "god's-eye point of view" and look at the universal wave function, this is true. But it is not possible to actually take the gods-eye view except in the abstract. In order to take any "point of view" at all, you have to be a classical entity. So nothing can actually take the god's-eye view, not even God! Only a classical entity can take a point of view, and that point of view is necessary bound to one particular universe, and so that universe -- your universe, and mine -- is privileged from our mortal's-eye point of view, which is the only point of view anything can ever actually take.