[jerf]

If you have a complicated qubit that collapses (by whatever mechanism) into a pure 1 or 0, you still have a qubit with a history in the world that is continuous. A complicated qubit doesn't carry any more information than the pure 1 or 0 in this particular sense.

The concern about black holes is that you toss a bunch of qubits (in the mass) in, and then there is a discontinuity; qubits with no particular relationship to anything that went in come off the surface as Hawking radiation. It isn't just that the qubits are really, really "scrambled"; thing getting too scrambled to put back into their original state in any feasible amount of work is a thing that happens all the time in the non-black-hole world anyhow. But there's still continuity, and the theoretical possibility of restoring the original state. The concern with black holes is that it isn't even theoretically possible to put together the original states. (It's going to be practically impossible either way.) There's a discontinuity in the qubits evolution, where they seem to entirely disappear from the universe at one place ("in" the black hole, for whatever exact definition of that ends up making sense; for this particular discussion, that's a complicated question!), and suddenly re-emerge with no relationship to any past state in the Hawking radiation. That discontinuity is the concern.

If I have this right.

(Stepping even further out of my comfort zone, I think part of the problem with this "discontinuity" is ultimately the same problems you learned about in calculus class with discontinuities in functions. Our understanding of QM is mostly expressed in differential equations. Those equations can't tell us about what happens if there are actually discontinuities in the world. In their own way they're as bad as the singularities that appear in relativity for black holes. It means "anything" could happen.)