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I am wondering if every contextual theory that reproduces QM is NON-local and reciprocally. Otherwise, when is contextuality equivalent to non-locality? And moreover, how much nonlocality is encoded into contextuality? Are every non-local quantum-like theory contextual?

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    $\begingroup$ What is a contextual theory? $\endgroup$ – Prahar Dec 30 '17 at 2:39
  • $\begingroup$ 1. Quantum contextuality (standard definition, I presume): quantum contextuality states that is NOT possible to assign results to experiments independently of the measurement procedure. That is, Contextuality: the results of measurements can depend on how we made the measurement, or what combination of measurements we chose to do. 2. Nonlocality and Contextuality are inescapable features of Quantum Mechanics! 3. Bohmian QM is surely nonlocal, but WHY it is contextual, or, more precisely, how much contextual bohmian QM is? $\endgroup$ – riemannium Dec 30 '17 at 11:10
  • $\begingroup$ QM mysteries: Is contextuality essential if QM is not the final microtheory? For instancie: Is contextuality of Bohmian QM relevant or necessary? $\endgroup$ – riemannium Dec 30 '17 at 11:10
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I believe the answers to your question can be found in Locality and realism in contextual theories by Dick Hoekzema. If I understand it correctly, the paper does show that contextual theories must be non local.

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