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PBS Spacetime recently released a video talking about 'why information is never destroyed in Quantum Mechanics'

I'm surprised to see this myth to persist even to this day. We know that unitarity and information conservation applies only as long as you do not measure anything never. Once you measure an eigenstate or a range of eigenstate, ALL the amplitudes of non-realised eigenstates are lost forever, even in principle. If we could in principle reconstruct that information, then we would have a contradiction with the No-Cloning theorem (The only way to avoid this conclusion is if the information is captured through some unknown or unaccounted non-unitary operations, but that is beyond the scope of traditional Quantum Mechanics).

Or is there anything to the claim that quantum information (specifically, amplitudes of non-realised eigenstates) can be recovered in principle? Can you avoid a contradiction with the No-Cloning theorem? As we know, decoherence only turns pure states into mixed states, so all it can explain per se is the loss of interference terms between probabilities, not how specific eigenvalues are realised from the classical probability distributions of mixed states

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    $\begingroup$ I quite like bob bee's answer here: "So if you want to determine classical observables, which means you have to measure and not simply let the quantum state go its own way, it produces the probabilistic results and has the quantum uncertainties given by the uncertainty principle for the different observable pairs. But it does not mean the state did not evolve In a perfectly unitary and causal way given by then laws of quantum theory." (+ preceding paragraph) $\endgroup$ – user12029 Jun 20 '18 at 23:20
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    $\begingroup$ For what it is worth, this paper claims that the no-cloning theorem actually derives from conservation of information: arxiv.org/abs/quant-ph/0306044 $\endgroup$ – Stéphane Rollandin Jun 21 '18 at 7:49
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    $\begingroup$ @moorephysics yes, quantum evolution is unitary if you include the observer even after a measurement. But unless you have VIP access across the multiverse, you cannot recover the amplitudes of non-realised states even in principle. Hence, quantum information is not conserved after a measurement from the point of view of physical observers that cannot peek into the multiverse $\endgroup$ – lurscher Jun 21 '18 at 11:11
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    $\begingroup$ the unexplained negative votes suggest that some people hold this wishy-washy belief very close to their hearts for some reason $\endgroup$ – lurscher Jun 22 '18 at 13:56
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    $\begingroup$ I downvoted because this is a complicated question with a complicated answer, and imprecise statements like "information is conserved" don't have a definite truth-value unless supplemented with careful technical definitions. It's not helpful to pose the question in a way that presupposes that an imprecise question has a precise answer, or that lots of people are foolish. $\endgroup$ – Ben Crowell Feb 1 at 18:59
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The black hole information paradox, which led to the understanding of blackhole thermodynamics, derives from applying exactly this conservation principle:

"a core precept of modern physics — that in principle the value of a wave function of a physical system at one point in time should determine its value at any other time" https://en.m.wikipedia.org/wiki/Black_hole_information_paradox

As far as I am aware this was the only serious challenge to it, and it is now almost universally accepted to have been resolved in favour of information in fact being conserved.

Conservation of information is associated with the https://en.m.wikipedia.org/wiki/Probability_current The developing generalisation of the strong statement of conservation of information is the 'axiom of purification' https://plus.maths.org/content/purifying-physics-quest-explain-why-quantum-exists This explains the arrow of time as emerging from otherwise reversible QM, as deriving from the flow towards increasingly mixed states.

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    $\begingroup$ How does that avoid the fact that information about a state is lost after a measurement? $\endgroup$ – lurscher Jun 21 '18 at 11:05
  • $\begingroup$ Taking a measurement joins the state of observer and observed. Entropy increase represents the evolution from unmixed to mixed states. $\endgroup$ – CriglCragl Jun 21 '18 at 11:16
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    $\begingroup$ as I said in a comment under the OP: yes, quantum evolution is unitary if you include the observer even after a measurement. But unless you have privileged access across the multiverse, you cannot recover the amplitudes of non-realised states even in principle. Hence, quantum information must not conserved after a measurement from the point of view of physical observers that cannot peek into the multiverse. If you can recover in principle, you can make many copies of quantum states and use them for FTL communication via entanglement $\endgroup$ – lurscher Jun 21 '18 at 11:17
  • $\begingroup$ @lurscher The 'in principle' is crucial, look for instance at the concrete difference between whether quantum events are truly random, or there are hidden variables. Conservation of information is a midern restatement of wgat we think causality is, at root. $\endgroup$ – CriglCragl Feb 5 at 17:12
  • $\begingroup$ if we insist in adhering to this myth of information conservation, we might do so "at our own peril", i.e. in the understanding that it departs from what is the potential set of physical experiences, as no observer looking at physical black holes might rely on the assertion of 'conservation of information' to make any prediction. Very unlike conservation of energy, charge or momentum, for example $\endgroup$ – lurscher Feb 6 at 1:12

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