Physics Asked by joelfischerr on April 29, 2021
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.
[Wiki]
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.
Answered by Chiral Anomaly on April 29, 2021
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