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

TL;DR

This paper demonstrates that classical causal models cannot faithfully explain Bell nonlocality or Kochen-Specker contextuality in any scenario, unifying these phenomena as violations of classical causality principles.

Contribution

It extends previous results to arbitrary scenarios, showing the fundamental limitations of classical causal models in explaining quantum contextuality and nonlocality.

Findings

Classical causal models cannot explain Bell nonlocality or Kochen-Specker contextuality in general scenarios.

The result applies to any number of parties or measurements, not just simple cases.

An explicit assumption about operational symmetries is identified as necessary for the models.

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.