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I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a rabbit hole where these concepts are poorly distinguished (in terms of logical relations).

Can someone disentangle and contextualize (pun intended) how they all relate, e.g., in terms of which one implies/encompasses/overlaps with the other. It need not be a Venn diagram. A set of logical statements in plain English would be just as good.

PS: Although explanations of each of these individual concepts are certainly welcome, it is the logical relationships between them which I'm really interested in.

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  • $\begingroup$ These might be useful: arxiv.org/abs/quant-ph/0612147, arxiv.org/abs/0709.0390. (Non-)contextuality can be defined in single systems and in a sense contains the definition of (non-)locality when you extend the concept to more than one system. $\endgroup$
    – Karl Pilkington
    Commented Jun 22, 2021 at 23:20
  • $\begingroup$ Perhaps it is more correct to use the term local realism, or non-contextual realism, because it goes together with the premisses. So in a typical Bell inequality the premisses are both locality AND realism, so if an experiment violates the inequality the conclusion (via contra-positive) is that the system exhibits nonlocality OR non-realism. Non-signalling is usually assumed, even though there are signalling toy models in the literature. $\endgroup$
    – Karl Pilkington
    Commented Jun 22, 2021 at 23:20
  • $\begingroup$ @KarlPilkington How about realism and non-contextuality. I can't find any example where one would have contextuality without a violation or realism, which makes me think that the former is nothing but a consequence of the latter---and not a distinct phenomenon. $\endgroup$
    – Tfovid
    Commented Jun 26, 2021 at 10:43
  • $\begingroup$ in the case of non-contextual realistic arguments the premisses are two: (A)independence of context (aka, non-contextuality) and (B) realism, phrased as the possibility of classically assigning definite values to the outcome of observables - in older texts (B) is sometimes called functional consistency, but it is an equivalent way of imposing realism. A non-contextual inequality then assumes (A) and (B), and if an experiment violates the inequality it means that (A) or (B) is incorrect, or even both. You can check arxiv.org/abs/2102.13036 for more details. $\endgroup$
    – Karl Pilkington
    Commented Jun 26, 2021 at 18:04
  • $\begingroup$ @KarlPilkington My problem is why A and B are treated separately. To me, contextuality can only happen if realism is violated. Is there any counterexample to this, namely where we'd get contextuality without a violation of realism? $\endgroup$
    – Tfovid
    Commented Jun 27, 2021 at 12:19

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