Question about the principle that information is never lost

One thing I have trouble understanding in physics is the principle that information is never lost. Sean Carroll explains the principle like this:

Quote:

If you take an encyclopedia and toss it into a fire, you might think the information contained inside is lost forever. But according to the laws of quantum mechanics, it isn’t really lost at all; if you were able to capture every bit of light and ash that emerged from the fire, in principle you could exactly reconstruct everything that went into it, even the print on the book pages.

But as far as I can see you couldn't do this even in principle. If you could capture all the information every bit of light and ash and then work backwards, in principle, to reconstruct the encyclopedia it would imply that you could get that information, in principle, to an arbitrarily high precision.

But isn't it also a principle of physics that you can't, even in principle, get all of that information to an arbitrarily high precision?

So you can't take the remnants of the encyclopedia and reconstruct the encyclopedia, even in principle.

Carroll addresses the point by saying that the state is not given by a set of little bits of information, but by a single wave function, the evolution of which is completely reversible.

But I don't see how this helps you go from all the bits of ash and light back to the original encyclopedia. If you (or some supercharged version of Laplace's Demon) could know the wave function for the system and evolve it backwards they still wouldn't be able to pick out an individual encyclopedia which was the prior state of those bits of light and ash.

via International Skeptics Forum https://ift.tt/2BVJQ4E