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

arXiv: https://arxiv.org/abs/2104.13227 · HTML: https://mlsanity.com/paper/2104.13227/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 24 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Inferring latent structures via information inequalities](https://mlsanity.com/paper/1407.2256/) (2014)
- [Language Modeling with Reduced Densities](https://mlsanity.com/paper/2007.03834/) (2020)
- [Inferring causal structure: a quantum advantage](https://mlsanity.com/paper/1406.5036/) (2014)
- [Quantifying causal influences in the presence of a quantum common cause](https://mlsanity.com/paper/2007.01221/) (2020)
- [Accounting for hidden common causes when inferring cause and effect from observational data](https://mlsanity.com/paper/1801.00727/) (2018)

## Abstract (arXiv)

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.