Abstract
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.
7 More- Received 6 October 2017
- Revised 19 January 2018
DOI:https://doi.org/10.1103/PhysRevX.8.021018
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Two key features distinguish the quantum world from our everyday experience. One is nonlocality, the ability of separated particles to act as if they instantly know about each other’s quantum state. The other is contextuality, which refers to the impossibility of specifying the outcome of a measurement independently of other compatible measurements that may be performed with it. Contextuality provides quantum computers with an unprecedented advantage over their traditional counterparts; nonlocality is a critical resource for other quantum technologies such as communication and cryptography. While there is a generally agreed upon theoretical basis for describing nonlocality, comparable frameworks for describing contextuality remain controversial. In this work, I put nonlocality and contextuality on equal theoretical footing by describing both as violations of classical causality.
The work builds upon the classical theory of causal models, which represents causal structure as a graph, with nodes representing random variables and arrows representing cause-and-effect relationships. In the traditional nonlocality scenario, the causal graph is motivated by special relativity, which prohibits faster-than-light communication. I show that no causal model (with relativistic causal structure or otherwise) can explain nonlocality or contextuality without violating a fundamental principle of the theory of causal models: the principle of no fine-tuning. This means that any classical model for those quantum correlations must contain causal connections that could, in principle, allow for unobserved influences—such as faster-than-light signaling—and therefore require special, finely tuned choices of parameters to hide such influences from observation.
This finding provides a unified understanding of nonlocality and contextuality as violations of classical causality and could aid the development of novel quantum protocols that exploit these key resources.