Bounding quantum contextuality with lack of third-order intereference

Abstract

Recently many simple principles have been proposed that can explain quantum limitations on possible sets of experimental probabilities in nonlocality and contextuality experiments. However, few implications between these principles are known. Here it is shown that lack of irreducible third-order interference (a generalisation of the idea that no probabilistic interference remains unaccounted for once we have taken into account interference between pairs of slits in a $n$-sit experiment) implies the principle known as the E principle or Consistent Exclusivity (that, if each pair of a set of experimental outcomes are exclusive alternatives in some measurement, then their probabilities are consistent with the existence of a further measurement in which they are all exclusive). This is a step towards a more unified understanding of quantum nonlocality and contextuality, which promises to allow derivations of important results from minimal, easily grasped assumptions. As one example, this result implies that lack of third order interference bounds violation of the CHSH-Bell inequality to 2.883.

Explanatory comments on proofs, citations and comparisons with other results have been added, and other edits have been made. 5 pages

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• Higher-order interference in extensions of quantum theory
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• The computational landscape of general physical theories
• Thermodynamics and the structure of quantum theory
• Testing higher-order quantum interference with many-particle states
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Quantum correlations from simple assumptions
• General Bayesian theories and the emergence of the exclusivity principle
• Bell non-locality and Kochen-Specker contextuality: How are they connected?
• Graph-theoretic approach to Bell experiments with low detection efficiency
• On the origin of nonclassicality in single systems
• A no-go theorem for theories that decohere to quantum mechanics
• The problem of quantum correlations and the totalitarian principle
• Composing decoherence functionals
• Exclusivity principle and unphysicality of Garg-Mermin correlation
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