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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

Qmechanic
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lurscher
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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.

CriglCragl
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