Quantum d-separation and quantum belief propagation

TL;DR

This paper introduces quantum analogs of d-separation and belief propagation, aiming to extend Judea Pearl's classical causal inference framework into the quantum domain, potentially enabling quantum causal models.

Contribution

It proposes the first formal definitions of quantum d-separation and quantum belief propagation, bridging classical causal inference and quantum information theory.

Findings

Quantum d-separation generalizes classical d-separation principles.

Quantum belief propagation extends classical BP to quantum networks.

Potential to translate Pearl's causal Bayesian networks into quantum systems.

Abstract

The goal of this paper is to generalize classical d-separation and classical Belief Propagation (BP) to the quantum realm. Classical d-separation is an essential ingredient of most of Judea Pearl's work. It is crucial to all 3 rungs of what Pearl calls the 3 rungs of Causation. So having a quantum version of d-separation and BP probably implies that most of Pearl's Bayesian networks work, including his theory of causality, can be translated in a straightforward manner to the quantum realm.