Inferring causal structure: a quantum advantage

These authors contributed equally to this work. The real surprise, however, is that even if one only has the ability to passively observe the early system, the quantum correlations hold signatures of the causal structure--in other words, certain types of correlation do imply causation. In a recent paper, Fitzsimons, Jones and Vedral [3] defined a function of the observed correlations which acts as a witness of direct causal influence, by ruling out a purely common-cause explanation. We here present the larger framework that places this result on an equal footing with an analogous result for common-cause relations. The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unless one can implement a randomized intervention. We here consider the problem of causal inference for quantum variables. We introduce causal tomography, which unifies and generalizes conventional quantum tomography schemes to provide a complete solution to the causal inference problem using a quantum analogue of a randomized trial. We furthermore show that, in contrast to the classical case, observed quantum correlations alone can sometimes provide a solution. We implement a quantum-optical experiment that allows us to control the causal relation between two optical modes, and two measurement schemes--one with and one without randomization-- that extract this relation from the observed correlations.