Cause and Effect in a Quantum World

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 that Reichenbach's principle would seem to demand. From this perspective, Bell’s theorem is best understood as a challenge to providing a satisfactory causal explanation of the observed statistics (rather than as a challenge to maintaining locality and realism, as it is usually construed). A promising avenue to meet this challenge is to find an intrinsically quantum counterpart to Reichenbach’s principle. We here propose such a generalization and provide it with a rigorous justification that parallels the justification that can be given for the classical version. Specifically, we demonstrate that under the assumption that systems with no causal connection are represented by a product state and that quantum dynamics is fundamentally unitary, if a quantum system A is a complete common cause of quantum systems B and C, then the quantum channel from A to BC factorizes 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. Joint work with John-Mark A. Allen, Jonathan Barrett, Dominic C. Horsman, and Ciaran M. Lee.