Classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in arbitrary scenarios

Abstract

In a recent work, it was shown by one of us (EGC) that Bell-Kochen-Specker inequality violations in phenomena satisfying the no-disturbance condition (a generalisation of the no-signalling condition) cannot in general be explained with a faithful classical causal model -- that is, a classical causal model that satisfies the assumption of no fine-tuning. The proof of that claim however was restricted to Bell scenarios involving 2 parties or Kochen-Specker-contextuality scenarios involving 2 measurements per context. Here we show that the result holds in the general case of arbitrary numbers of parties or measurements per context; it is not an artefact of the simplest scenarios. This result unifies, in full generality, Bell nonlocality and Kochen-Specker contextuality as violations of a fundamental principle of classical causality. We identify, however, an implicit assumption in the former proof, making it explicit here: that certain operational symmetries of the phenomenon are reflected in the model, rather than requiring fine-tuned choices of model parameters. This clarifies a subtle but important distinction between Bell nonlocality and Kochen-Specker contextuality.

13 pages, 10 figures

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• Quantum Nonlocality: how does Nature do it?
• Assumption-free derivation of the Bell-type criteria of contextuality/nonlocality
• Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning
• Implications of Local Friendliness violation for quantum causality
• Connecting extended Wigner's friend arguments and noncontextuality
• Twenty years of quantum contextuality at USTC
• A de Finetti theorem for quantum causal structures
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises