Simultaneously testing the Kochen-Specker and Bell theorems

[bohm2]

Kochen-Specker rules out non-contextual hidden variable theories and Bell's theorem rules out local theories. I thought this was an interesting paper, particularly the authors' conclusions:

Previous experiments have demonstrated, separately, the violation of Bell inequalities and KS paradoxes. Bell experiments consist of local measurements on composite systems prepared in quantum entangled states, KS experiments consist of sequential measurements on systems in arbitrary quantum states. Each type of experiments shows a fundamental property of nature: Bell experiments show non-locality, KS experiments show contextuality. Here we have presented the first experiment in which both Bell and the KS theorems are proven simultaneously. Our results show that nature's non-locality is indeed a consequence of of nature's contextuality, and pave the way towards a deeper understanding of quantum theory.

Simultaneously testing the Kochen-Specker and Bell theorems
http://arxiv.org/pdf/1308.6336.pdf

 

[S.Daedalus]

That non-locality is in some sense a consequence of contextuality has been the lore in the field for a long time, I think, with the usual argument being that the spatial separation employed in Bell tests is merely a way to guarantee the compatibility of observables, which is otherwise a problem in Kochen-Specker tests (basically, in real measurements, due to errors, you never have perfect compatibility; but for anything other than perfect compatibility, the notion of (non-)contextuality doesn't really make sense). Recall that Bell derived the Kochen-Specker theorem first, and then went on to prove the theorem that now bears his name, pretty much exactly because he thought that only the locality constraint can make sense of the assumption that the measurements shouldn't influence one another.

But what they're doing in the paper seems to be something different, some kind of set of Kochen-Specker measurements which 'combine' to a Bell test; I'll have to take a closer look to see how exactly that relates to the above, if it does.

In any case, I suppose the point of view that the main no-hidden-variables theorems, meaning Leggett-Garg in addition to Bell and Kochen-Specker, are really just different aspects of 'the same thing' is becoming more and more widespread; I think it was Arthur Fine who (late 70s? Early 80s?) first argued that this 'same thing' is the impossibility of finding a joint probability distribution whose marginals are capable of accounting for all experimentally observed correlations. From this point of view, the three theorems really just differ in how they attempt to ensure the independence of measurements---in the Bell case, it's locality, for Kochen-Specker, compatibility of measurements, and for Leggett-Garg, the 'noninvasiveness' of measurement.

 

[audioloop]

Interesting.





-------
and is every state that is nonlocal is contextual ?

because, every state that is contextual is nonlocal.


.

 

[S.Daedalus]

and is every state that is nonlocal is contextual ?

because, every state that is contextual is nonlocal.

Yes to the first part, but no to the second: every state in a quantum system of d > 3 is contextual, but only entangled states are nonlocal.

 

[audioloop]

Yes to the first part, but no to the second: every state in a quantum system of d > 3 is contextual, but only entangled states are nonlocal.

right

https://www.physicsforums.com/showthread.php?t=619905

mutually agree.
contextuality is broader, subsumes nonlocality.
same thing in quantum information (nonlocality is a generic feature of non-signaling).


Existence of two spin-1/2 states that are non-local yet non-contextual.
http://arxiv.org/pdf/1207.1952v1.pdf