Is conservation of quantum information universal? 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?
Thank you!
 A: It is a postulate of quantum mechanics that all physical processes except measurement are unitary, and thus, reversible. However, it is also a postulate that there are non-unitary measurement operations. Whether a non-unitary measurement interaction can be expressed as unitary for a larger composite system is an open question (typically referred to as the "measurement problem", and for which different proposed answers are called "interpretations of quantum mechanics"). 
Now, if we just take measurement out of the equation, then all quantum mechanic processes are unitary by assumption of the theory. That makes information conservation universal, according to quantum mechanics. (Any quantum state from the past is retrievable, in principle.)
If information crossing a black hole's event horizon is irretrievable (if the interaction truly is non-unitary) then quantum mechanics does not adequately describe this interaction, because the unitarity postulate is hard-boiled into QM. So either the process of crossing the event horizon is unitary, or quantum mechanics is the wrong theory to describe this process. Whichever one it is (or whether it's both) is an open question.
