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Quantum Common Causes and Quantum Causal Models

John-Mark A. Allen, Jonathan Barrett, Dominic C. Horsman, Ciarán M. Lee, and Robert W. Spekkens
Phys. Rev. X 7, 031021 – Published 31 July 2017
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Abstract

Reichenbach’s principle asserts that if two observed variables are found to be correlated, then there should be a causal explanation of these correlations. Furthermore, if the explanation is in terms of a common cause, then the conditional probability distribution over the variables given the complete common cause should factorize. The principle is generalized by the formalism of causal models, in which the causal relationships among variables constrain the form of their joint probability distribution. In the quantum case, however, the observed correlations in Bell experiments cannot be explained in the manner Reichenbach’s principle would seem to demand. Motivated by this, we introduce a quantum counterpart to the principle. We demonstrate that under the assumption that quantum dynamics is fundamentally unitary, if a quantum channel with input A and outputs B and C is compatible with A being a complete common cause of B and C, then it must factorize in a particular way. Finally, we show how to generalize our quantum version of Reichenbach’s principle to a formalism for quantum causal models and provide examples of how the formalism works.

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  • Received 5 April 2017

DOI:https://doi.org/10.1103/PhysRevX.7.031021

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)

Quantum Information, Science & Technology

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Causality in the Quantum World

Published 31 July 2017

A new model extends the definition of causality to quantum-mechanical systems.

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Authors & Affiliations

John-Mark A. Allen1, Jonathan Barrett1, Dominic C. Horsman2, Ciarán M. Lee3, and Robert W. Spekkens4

  • 1Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom
  • 2Department of Physics, University of Durham, South Road, Durham DH1 3LE, United Kingdom
  • 3Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • 4Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

Popular Summary

Causal reasoning is the basis for explaining the world around us. For instance, if sales of ice cream are high on the same days of the year that many people get sunburned, a likely explanation is that the sun was shining on these days and that the hot sun induced both sunburns and the desire to eat ice cream. Indeed, the scientific method itself is a statement about causality: If physical variables are found to be correlated, then there ought to be a causal explanation for this fact (i.e., Reichenbach’s principle). Despite the central role of causal explanation in science, Bell’s theorem—which has now been experimentally verified to extremely high accuracy—shows that certain quantum correlations have no natural causal explanation. Here, we generalize causal reasoning to the quantum world and provide a natural causal explanation of quantum correlations and phenomena.

We theoretically develop a quantum version of Reichenbach’s principle—which reduces to the classical version in the appropriate limit—using the assumption that quantum dynamics is fundamentally unitary. Our work sheds light on the nature of causality in the quantum realm and also has practical applications: As large-scale quantum communication networks—a primer for a quantum internet—are fast becoming possible with today’s technology, having a unified way to discuss and develop new cryptographic and information processing protocols is critical.

We expect that our findings will motivate future efforts to understand the link between quantum theory and general relativity.

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Vol. 7, Iss. 3 — July - September 2017

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