A quantum advantage for inferring causal structure

Abstract

The problem of inferring causal relations from observed correlations is relevant to a wide variety of scientific disciplines. Yet given the 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. Only a randomized trial can settle the issue. Here we consider the problem of causal inference for quantum variables. We show that the analogue of a randomized trial, causal tomography, yields a complete solution. We also show that, in contrast to the classical case, one can sometimes infer the causal structure from observations alone. We implement a quantum-optical experiment wherein we control the causal relation between two optical modes, and two measurement schemes-with and without randomization-that extract this relation from the observed correlations. Our results show that entanglement and quantum coherence provide an advantage for causal inference.T he slogan 'correlation does not imply causation' is meant to capture the fact that any joint probability distribution over two variables can be explained not only by a causal influence of one variable on the other, but also by a common cause acting on both 1 . We here investigate whether a similar ambiguity holds for quantum systems, and we show that, surprisingly, it does not.Finding causal explanations of observed correlations is a fundamental problem in science, with applications ranging from medicine and genetics to economics 2,3 . As a practical illustration, consider a drug trial. Naively, a correlation between the variables treatment and recovery may suggest a causal influence of the former on the latter. But suppose men are more likely than women to seek treatment, and also more likely to recover spontaneously, regardless of treatment. In this case, gender is a common cause, inducing correlations between treatment and recovery even if there is no cause-effect relation between them.Unless one can make strong assumptions about the nature of the causal mechanisms 4 , the only way to distinguish between the two possibilities is to replace observation of the early variable with an intervention on it. For instance, pharmaceutical companies do not leave the choice of treatment to the subjects of their trials, but carefully randomize the assignment of drug or placebo. This ensures that the administered treatment is statistically independent of any potential common causes with recovery. Consequently, any correlations with recovery that persist herald a directed causal influence. The question of whether there were in fact common causes can be answered by tracking whether recovery correlates with the subjects' intent to treat. Thus, the ability to intervene allows a complete solution of the causal inference problem: it reveals both which variables are causes of which others and, via the strength of the correlations, the precise mathematical form of the causal dependencies.In this article, we consider the quantum version of this causal inference probl...

Geometric representation of two-qubit entanglement witnesses

“…[33] shows that E for such an operator is a circular disc with centre c = 0 and radius 1. Any W ∈ EW 4 must lie in the xz plane, and so optimal witnesses within EW 4 are represented by the xz unit disc itself.…”

Causality in the Quantum World

“…For instance, finding quantum-classical separations in the correlations achievable in novel causal scenarios might lead to new device-independent protocols [11], such as randomness extraction and secure key distribution. Quantum causal models may also provide novel schemes for simulating many-body systems in condensed matter physics [12] and novel means for inferring the underlying causal structure from quantum correlations [13,14].…”

Explaining quantum correlations through evolution of causal models

“…The fundamental implications of quantum theory shed new light on this debate. It is thought these implications may lead to new insights into the foundations of quantum theory, and possibly even quantum theories of gravity [1][2][3][4][5][6][7][8][9][10].These realizations have their roots in the EinsteinPodolski-Rosen thought experiment [11] and the fundamental theorems of Bell [12] and of Kochen and Specker [13]. A cornerstone of modern physics, Bell's theorem, rigorously excludes classical concepts of causality.…”

“…The fundamental implications of quantum theory shed new light on this debate. It is thought these implications may lead to new insights into the foundations of quantum theory, and possibly even quantum theories of gravity [1][2][3][4][5][6][7][8][9][10].…”