# Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning

## TL;DR

This paper explores how violations of Bell and Kochen-Specker inequalities challenge classical causal models, showing that such violations require fine-tuning and can occur even in single-system scenarios, thus deepening understanding of quantum nonlocality and contextuality.

## Contribution

It demonstrates that Bell inequalities can be derived without measurement independence assumptions and shows all classical models for Kochen-Specker violations require fine-tuning.

## Key findings

- Bell inequalities derived from no-signalling and no-fine-tuning assumptions
- Classical models for Kochen-Specker violations require fine-tuning
- Quantum violations occur even in single-system scenarios

## Abstract

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlations and the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextuality as violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no-fine-tuning of the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextuality scenarios within causal models and show that all classical causal models for violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causality goes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.