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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!

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    $\begingroup$ Can you define specifically what you mean by "conservation of information" and specifically what you mean by "universal"? $\endgroup$ Feb 5, 2020 at 18:59
  • $\begingroup$ I'll do my best. "Conservation of information" is meant in the same way it's discussed in the black hole information paradox. Seemingly "quantum information is destroyed". Whatever that is, that's what I'm asking about. I unfortunately don't understand much beyond that. By "universal", does it hold for every interaction across any span of time at all places in the universe. It may be that quantum information is conserved when you shoot photons through a double slit (whatever the experimental situation is). But is there reason to believe it's therefore conserved universally? $\endgroup$
    – user22038
    Feb 6, 2020 at 14:24
  • $\begingroup$ Quantum mechanics is not "fundamentally time reversal symmetric". The evolution of free, isolated systems as described by the Schroedinger equation or by the equations of quantum field theory is. The measurement process as described by the Born rule, however, is fundamentally irreversible. $\endgroup$ Oct 7 at 16:31

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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.

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    $\begingroup$ "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")." I'm not sure I understand this. By Stinespring's dilation theorem, measurements are just unitary interactions between the measurement device and the system. This produces a classical probability distribution in the eigenvalues. The measurement problem is actually how the distribution actually results in an observation, AFAIK. $\endgroup$ Feb 5, 2020 at 20:24
  • $\begingroup$ that's not what the "measurement problem" is about. Any measurement is intrinsically non-unitary, as it must involve some collapse of the wavefunction and thus loss of information. $\endgroup$
    – glS
    Feb 6, 2020 at 14:13
  • $\begingroup$ @user2723984 Yes, you may be right. I might have to re-word that (or just remove the part about measurements entirely, as it's not related to the answer anyway). $\endgroup$ Feb 6, 2020 at 15:03
  • $\begingroup$ Measurement is related, in a way. Part of my question was about how we apply the wave equations in the first place. The wave function tracks the system evolution up to the point of measurement, but no further (right?). Interpretations about wave function collapse (or many worlds, etc) aside, are we able in principle to write out a wave function that follows the system's evolution beyond the point of "measurement" (wave function collapse, or whatever term you would ascribe to that - I'm sorry, I don't know all the actual lingo)? $\endgroup$
    – user22038
    Feb 6, 2020 at 22:40

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