Quantum speedup in testing causal relationships

Abstract

The study of physical processes often requires testing alternative hypotheses on the causal dependencies among a set of variables. When only a finite amount of data is available, the problem is to infer the correct hypothesis with the smallest probability of error. In this talk I will provide a general framework, which can be used to formulate causal hypotheses in a theory-independent way. In this framework, one can fix a set of hypothesis and determine how well they can be tested in different theories. As an example, I will consider the task of identifying the effect of a given variable. I will show that a quantum setup can identify the effect with exponentially smaller probability of error than the best setup for the classical version of the problem. The origin of the speedup is the availability of quantum strategies that run multiple tests in a superposition.