Why would violation of the conservation of information be problematic for quantum theory? To build on that, do we have sufficient reason to claim that conservation of information is absolutely fundamental to quantum theory?
I understand (well enough, I think) that the equations of quantum theory are deterministic and time reversal symmetric, and conserve probability, and so conservation of quantum information is baked into the equations.
What I'm wondering about is this:
I'm not in physics so I just don't know this stuff, but it seems that any time we use equations of quantum theory, we are only ever applying them in very restricted, isolated systems/cases. If that's accurate, then do we have good reason to extrapolate that limited application to more complex phenomena (eg, the various theorized goings-on of the black hole information paradox), or to the entire universe? Is there a proof or direct observation that indicates this must hold everywhere or for every kind of interaction?