I know how quantum non-locality is defined in Wikipedia

quantum nonlocality is a characteristic of some measurements made at a microscopic level that contradict the assumptions of local realism found in classical mechanics. Despite consideration of hidden variables as a possible resolution of this contradiction, some aspects of entangled quantum states have been demonstrated irreproducible by any local hidden variable theory

[Wiki] and how quantum contextuality is defined in Wikipedia

Quantum contextuality is a foundational concept in quantum mechanics stating that the outcome one observes in a measurement is dependent upon what other measurements one is trying to make. More formally, the measurement result of a quantum observable is dependent upon which other commuting observables are within the same measurement set.


I however can't grasp how they are related or even if they are related at all. Can anyone help me with a high level explanation?


Locality, specifically Bell locality, is the hypothesis that the outcome of a given measurement is pre-determined by information that was present within its past light-cone.

(Beware that the word "locality" is also used with different meanings, such as Einstein locality, which refers to the hypothesis that observables localized in spacelike-separated regions commute with each other. Quantum field theory satisfies Einstein locality but not Bell locality. Einstein locality is enough to preclude faster-than-light communication.)

Non-contextuality is the hypothesis that the outcome of one measurement does not depend on whatever else is also being measured.

(Bell) locality implicitly assumes non-contextuality for space-like separated measurements but not necessarily for others.

The CHSH inequality can be derived using either Bell locality or just non-contextuality. A derivation from non-contextuality is shown in https://physics.stackexchange.com/a/446977. Nature does not respect the CHSH inequality (or other Bell inequalities), and quantum theory correctly predicts the observed violations.

  • $\begingroup$ Following up on your statement "(Bell) locality can be regarded as a special case of non-contextuality": What about state-independent demonstrations of contextuality (e.g., Peres-Mermin square)? Since they're state independent, that would mean that even disentangled states could exhibit contextuality, and hence even nonlocality. But that surely can't be right. Am I misunderstanding something? $\endgroup$
    – Tfovid
    Oct 21 '20 at 20:41
  • $\begingroup$ @Tfovid After re-reading what I wrote, I think calling it a "special case" wasn't the right way to say it. I should have simply said that (Bell) locality assumes non-contextuality for space-like separated measurements but not necessarily for others. I edited the answer to fix the incorrect wording. Thanks! $\endgroup$ Oct 21 '20 at 23:50
  • $\begingroup$ Does this mean that, conversely, contextuality for space-like measurements implies nonlocality? (If so, the crux of my confusion lies with the fact that contextuality can be desmonstrated in a state-independent fashion, i.e., even with disentagled states. But surely, those can't exhibit nonlocality. Hence the paradox in my head.) $\endgroup$
    – Tfovid
    Oct 22 '20 at 5:25
  • $\begingroup$ @Tfovid Whatever "nonlocality" means, suppose that (1) contextuality for space-like measurements implies nonlocality, (2) that only entangled states can exhibit nonlocality, and (3) that Peres-Mermin is a state-independent demonstration of contextuality. I don't see any paradox here, because Peres-Mermin doesn't say anything about which observables are space-like separated. To get a paradox, we'd need to show that the Peres-Mermin observables can be arranged in space-time in such a way that makes those three statements contradict each other. Is that possible? $\endgroup$ Oct 22 '20 at 14:52
  • $\begingroup$ By "is that possible?", do you mean experimentally? My point is that the PM square is assembled from measurements at two (possibly space-like) points. If we use disentangled states, we'd then have (3) and hence (1), and thus finally contradicting (2). $\endgroup$
    – Tfovid
    Oct 22 '20 at 16:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.