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.

Highlights

  • Quantum contextuality, the phenomenon uncovered by Kochen and Specker (KS) [1], is at the core of the quantum departure from classicality and has recently been identified as a candidate for the resource behind the power of quantum computation [2]

  • We have derived KS inequalities as a consequence of the principle of no fine-tuning for causal models of phenomena that satisfy the no-disturbance conditions

  • This result unifies Bell nonlocality and KS contextuality as violations of classical causality

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Summary

INTRODUCTION

The phenomenon uncovered by Kochen and Specker (KS) [1], is at the core of the quantum departure from classicality and has recently been identified as a candidate for the resource behind the power of quantum computation [2]. A violation of a Bell inequality implies either a violation of relativistic causality or of one or more of the assumptions underlying this framework for causality, such as Reichenbach’s principle of common cause [12,13]. I bridge that gap and show that all classical causal models that reproduce the violation of Bell and KS inequalities violate a core principle of the causal-models framework: no fine-tuning. This unifies Bell nonlocality and KS contextuality as. VI with a summary of the results and a discussion of its relevance, drawbacks, and directions for further research

Causal models
Causal models and Bell’s theorem
Basic definitions
Main result
EXAMPLES
RELATION TO PREVIOUS WORK
CONCLUSION
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