Quantum advantage in testing causal structures

The ability to identify cause-effect relations is a fundamental primitive in a large variety of areas, including machine learning, genetics, and finance. A canonical approach is to formulate alternative hypotheses on the cause-effect relations characterizing a given phenomenon, and testing them against another through statistical trials.

Recently, simple examples showed that quantum mechanics can outperform classical mechanics for such a causal hypothesis testing scenario. However, the advantages only hold for very specific instances in which the experimenter can probe the systems in a strongly restricted way. When arbitrary interventions are allowed, the advantages vanish. In this work we show for the first time that quantum strategies can greatly speed up the identification even in the fully interventionist scheme.

More precisely, we show that quantum mechanics can yield an exponentially smaller probability of error for causal hypothesis testing, compared to the best possible classical strategies. The same working principle leads to advantages in the detection of a causal link between two variables, and in the identification of the cause of a given variable.