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

J. C. Pearl and E. G. Cavalcanti

Centre for Quantum Dynamics, Griffith University, Gold Coast, QLD 4222, Australia

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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 $\textit{no fine-tuning}$. 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.

Bell nonlocality and Kochen-Specker contextuality are two classes of quantum phenomena where the departure from classicality becomes most striking. They have also been identified as key resources in powering quantum advantage over classical information processing. Nevertheless, many questions remain about their meaning and the precise relationship between these phenomena. On one hand, their formal similarity has led many to think of Bell nonlocality as nothing but a special case of Kochen-Specker contextuality. On the other hand, their conceptual basis is very distinct: whereas Bell nonlocality is now well understood as the quantum violation of classical causal constraints applied to a relativistic causal structure, K-S contextuality has not been traditionally understood in causal terms at all.

In this paper, based on a causal framework for contextuality introduced by EGC in Phys. Rev. X 8, 021018 (2018), we prove in full generality that both Bell and KS contextuality can be understood as the impossibility to simulate quantum correlations with any classical causal model satisfying a principle of no-fine-tuning – regardless of any assumptions about the causal structure. We conjecture that this opens a path to better understand the resource overheads required for the classical simulations of these key quantum phenomena. On the other hand, we identify the need for a slightly stronger notion of no-fine-tuning for KS contextuality than for Bell scenarios, requiring that certain operational symmetries in the phenomenon be reflected in the model. This clarifies a subtle but important distinction between the two types of scenarios.

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Cited by

[1] Jonathan Barrett, Robin Lorenz, and Ognyan Oreshkov, "Quantum Causal Models", arXiv:1906.10726.

[2] Eric G. Cavalcanti and Howard M. Wiseman, "Implications of Local Friendliness Violation for Quantum Causality", Entropy 23 8, 925 (2021).

[3] Ehtibar N. Dzhafarov, "Assumption-free derivation of the Bell criteria of contextuality/nonlocality", arXiv:2108.05480.

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