# A quantum causal discovery algorithm

## TL;DR

This paper introduces a quantum causal discovery algorithm that analyzes process matrices to determine causal order, Markovianity, and underlying mechanisms in quantum systems, advancing the field of quantum causal modeling.

## Contribution

It presents the first algorithm capable of discovering quantum causal models from process matrices, including causal order, Markovianity, and mechanisms.

## Key findings

- Identifies causal order in quantum processes.
- Detects Markovian vs non-Markovian processes.
- Reconstructs quantum causal mechanisms.

## Abstract

Finding a causal model for a set of classical variables is now a well-established task---but what about the quantum equivalent? Even the notion of a quantum causal model is controversial. Here, we present a causal discovery algorithm for quantum systems. The input to the algorithm is a process matrix describing correlations between quantum events. Its output consists of different levels of information about the underlying causal model. Our algorithm determines whether the process is causally ordered by grouping the events into causally-ordered non-signaling sets. It detects if all relevant common causes are included in the process, which we label Markovian, or alternatively if some causal relations are mediated through some external memory. For a Markovian process, it outputs a causal model, namely the causal relations and the corresponding mechanisms, represented as quantum states and channels. Our algorithm provides a first step towards more general methods for quantum causal discovery.