An invertible map between Bell non-local and contextuality scenarios
arXiv:2211.12550 · doi:10.1103/PhysRevLett.131.220202
Abstract
We present an invertible map between correlations in any bipartite Bell scenario and behaviours in a family of contextuality scenarios. The map takes local, quantum and non-signalling correlations to non-contextual, quantum and contextual behaviours, respectively. Consequently, we find that the membership problem of the set of quantum contextual behaviours is undecidable, the set cannot be fully realised via finite dimensional quantum systems and is not closed. Finally, we show that neither this set nor its closure is the limit of a sequence of computable supersets, due to the result MIP*=RE.
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- A bound on the quantum value of all compiled nonlocal games
- Certifying measurement incompatibility in prepare-and-measure and Bell scenarios
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- Failure of epistemic models to explain the antidistinguishability of quantum mixed preparations
- Optimal CHSH values for regular polygon theories in generalized probabilistic theories
- Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints
- Contextual advantages across two-state discrimination strategies
- Typicality of Contextuality
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- Probe of Generic Quantum Contextuality and Nonlocal Resources for Qubits