[Orlanthai]

Measurement is not just the same as entanglement. If you try that you get paradoxes and you don't match actual observations.

If you treat a measurement as entanglement then by the Kochen-Specker theorem you can't condition on the measurement outcome. However we seem to be able to do this in actual experiments.

Thus measurement is not entanglement alone, but also the elimination of other bases.

[mgraczyk]

I interpret KS backward from what you're saying. From my understanding, KS says that there is no sense in which the experiment involves an objective revelation of hidden state.

After the experiment, the experimenter did not "learn" or "reveal" some objective fact about reality, ie that the true state was UP rather than DOWN. Instead, after the experiment the experimenter becomes entangled with the UP/DOWN system in such a way that the experimenter measured both UP and DOWN, but all observables relating to the experimenter are either wholly consistent with UP or wholly consistent with DOWN.

[Orlanthai]

The lack of noncontextual hidden variables is the main implication of the Kochen-Specker theorem from which the inability to condition follows. It's not "backward" from the conclusion of no noncontextual hidden state, it's just another consequence there of.

So the Kochen-Specker theorem says there was no pre-existent noncontextual state for the particle. However that doesn't in any way imply the particle was both UP and DOWN or that the device measured both UP and DOWN. Especially for the device as the Kochen-Specker theorem is proved in a context where observable outcomes are assumed to be single-valued.

However in real practice we can condition on the states of our devices following measurement, hence they don't seem to be susceptible to a Kochen-Specker result when viewed as the system for some "super"-observational device. Which they would be if they simply entered an entangled state. Thus the assumption of measurement as simple entanglement does not match actual observed reality. This is a point made in many texts such as those of Schlosshauer, Omnès, Peres and at a very rigorous level in the theory of C* algebras and Category theory by Fröhlich and Landsman respectively.