Quantum common causes and quantum causal models

TL;DR

This paper extends Reichenbach's principle to quantum systems, proposing a quantum causal model framework that accounts for correlations in quantum experiments, especially Bell tests, under the assumption of unitary dynamics.

Contribution

It introduces a quantum analogue of Reichenbach's principle and develops a formalism for quantum causal models, addressing limitations of classical causal explanations in quantum contexts.

Findings

Quantum channels compatible with common causes must factorize under unitary dynamics.

The quantum Reichenbach's principle constrains quantum causal structures.

Examples demonstrate the application of the quantum causal model formalism.

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.