Quantum causal inference in the presence of hidden common causes: An entropic approach

TL;DR

This paper introduces an entropic framework for quantum causal inference that effectively identifies hidden common causes in quantum systems, outperforming classical methods and unifying classical and quantum causal analysis.

Contribution

It develops a scalable entropic approach for inferring causality in quantum systems with latent confounders, bridging classical and quantum causal inference.

Findings

Validated the approach on entangled qubits with noisy channels

Identified latent confounders in quantum systems

Outperformed classical causal inference methods

Abstract

Quantum causality is an emerging field of study which has the potential to greatly advance our understanding of quantum systems. In this paper, we put forth a theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. For this purpose, we leverage the tradeoff between the entropy of hidden cause and the conditional mutual information of observed variables to develop a scalable algorithmic approach for inferring causality in the presence of latent confounders (common causes) in quantum systems. As an application, we consider a system of three entangled qubits and transmit the second and third qubits over separate noisy quantum channels. In this model, we validate that the first qubit is a latent confounder and the common cause of the second and third qubits. In contrast, when two entangled qubits are prepared and one of them is sent over a noisy channel, there is no common confounder. We also demonstrate that the proposed approach outperforms the results of classical causal inference for the Tubingen database when the variables are classical by exploiting quantum dependence between variables through density matrices rather than joint probability distributions. Thus, the proposed approach unifies classical and quantum causal inference in a principled way.