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 and outputs and is compatible with being a complete common cause of and , 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.
4 More- 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)
Viewpoint
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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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.