Classical Causal Models for Bell and Kochen-Specker Inequality Violations Require Fine-Tuning

Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they 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, a...

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Bibliographic Details
Published in:Physical review. X Vol. 8; no. 2; p. 021018
Main Author: Cavalcanti, Eric G.
Format: Journal Article
Language:English
Published: College Park American Physical Society 01.04.2018
Subjects:
Bell's inequality
Causality
Cryptography
Graphical representations
Incompatibility
Optical communication
Quantum computers
Quantum mechanics
Random variables
Relativistic effects
Relativity
Signaling
Violations
ISSN:2160-3308, 2160-3308
Online Access:Get full text
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Summary:Nonlocality and contextuality are at the root of conceptual puzzles in quantum mechanics, and they 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 signaling 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 spacelike-separated systems and already manifests in scenarios involving single systems.
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ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.8.021018