A Bell's theorem vs Kochen–Specker theorem

[PreposterousUniverse]

I know of Bell's theorem. Kochen-Specker theorem is supposed to be a complement to Bell's theorem. I tried to understand it by reading the Wikipedia article. But I couldn't fully grasp the essential feature of this theorem, in what way it complements Bell's theorem. What are the main implications of Kochen-Specker's theorem, which Bell's original theorem did not address?

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[PeterDonis]

Kochen-Specker theorem is supposed to be a complement to Bell's theorem.

Can you give a reference for this claim? It's hard to answer your question without knowing what this claim is based on.

 

[Demystifier]

In short, Kochen-Specker theorem says that, in general, the values of observables found by measurement could not have been the same before measurement. Either (i) the system before measurement didn't have any sharp values of observables at all (non-realist interpretation), or (ii) it did have some sharp values (realist interpretation) but the act of measurement somehow changed them. That's called contextuality, where (i) and (ii) are two interpretations of contextuality. The Bell theorem says that, for some special quantum states and under certain reasonable additional assumptions, the change in (ii) cannot be described by any local law.

Note that the Bell theorem does not assume contextuality, it proves contextuality in a different way by itself. So why do we need the Kochen-Specker theorem if the Bell theorem proves it as well, in a technically much simpler way? The difference is that the Bell theorem proves it only for some special quantum states, while the Kochen-Specker does not depend on the state (in a Hilbert space of dimension larger than two).

For the relation of two theorems see also
https://arxiv.org/abs/1802.10119