Conditional mutual information: A generalization of causal inference in quantum systems

TL;DR

This paper introduces a quantum causal index based on asymmetric quantum conditional mutual information to analyze causal relationships and influence propagation in quantum many-body systems, revealing finite-speed causal effects.

Contribution

It develops a quantum extension of causal inference using QCMI and demonstrates its application to spin chains, uncovering causal propagation dynamics.

Findings

Finite-speed causal influence propagation observed

Coherent oscillations in causal influence detected

QCMI effectively measures quantum causal relationships

Abstract

The concept of causality is fundamental to numerous scientific explanations; however, its extension to the quantum regime has yet to be rigorously explored. This letter introduces the development of a quantum causal index, a novel extension of the classical causal inference framework, tailored to learn the causal relationships inherent in quantum systems. Our study focuses on the asymmetric quantum conditional mutual information (QCMI), incorporating the von Neumann entropy, as a directional metric of causal influence in quantum many-body systems. We analyze spin chains using the QCMI, implementing a projective measurement on one site as the intervention and monitoring its effect on a distant site conditioned on intermediate spins. Additionally, we study the effective causal propagation velocity, which is the speed at which QCMI becomes significant at distant sites. These findings indicate the presence of finite-speed propagation of causal influence, along with the emergence of coherent oscillations.