I understand that QM without observers is unitary and conserves information. My problem starts when there is a measurement. It is my understanding that the measurement problem has not been adequately resolved. But does any of the different interpretations of QM (which exist mostly to address the measurement problem) have satisfactorily answered it? Some people claim that there is no such thing as "the measurement problem", but I have not heard any comments from them about information conservation. Other interpretations, such as decoherence, do not seem to address the measurement problem itself, or that is what some experts in the field say. The only interpretation that seems to address this problem is the Born "interpretation", but I put it in quotes because it is not just an interpretation, it is a theory itself because it adds additional hidden variables that evolve deterministically before the "collapse", and these might in principle be measurable, something that standard QM does not allow if it is the ultimate description of reality.

Thus, the question is: what is the state of the art answer to how information is conserved in QM?

  • $\begingroup$ Actually, the measurement of quantum mechanics is very sutled, mathematically which is corresponding a projection process. So you just need a more postulate to determine how your quantum system evolve. $\endgroup$
    – Jack
    Jan 22, 2017 at 3:05
  • $\begingroup$ @Jack thanks, could you elaborate or give a reference $\endgroup$
    – user126422
    Jan 22, 2017 at 3:07
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    $\begingroup$ Maybe you could follow this link and see the lecture notes. pieter-kok.staff.shef.ac.uk/… $\endgroup$
    – Jack
    Jan 22, 2017 at 3:11
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    $\begingroup$ There was a question about this just recently Conservation of information and determinism? and an earlier one Is there conservation of information during quantum measurement? The short answer is no, in collapse interpretations information is not conserved, and in no-collapse ones it goes into unobservable/empty branches. $\endgroup$
    – Conifold
    Jan 22, 2017 at 3:13
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    $\begingroup$ And in decoherence it is conserved. Yes decoherence doesn't quite get you to the measurement, only partway. So there must still be an averaging with the different probabilities for large systems, and have it still be probabilistic for a single particle or a few. But when/why does it become large where you can average? But is this any different than Newtonian mechanics vs classical statistical mechanics? $\endgroup$
    – Bob Bee
    Jan 22, 2017 at 7:25