[kgwgk]

For a pure state a measurement doesn’t improve our knowledge about the state of the physical system, it changes it (and we get information about the new state). The Bayesian updating applies to mixed states, where there exists “classical” uncertainty while for a pure state the uncertainty is purely “quantum”.

"Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance."

https://www.perimeterinstitute.ca/personal/cfuchs/Oviedo.pdf

[nonbel]

Thanks, not what I was thinking it sounds like.