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...

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.

Collective phenomena are studied in a range of contexts—from controlling locust plagues to efficiently evacuating stadiums—but the central question remains: how can a large number of independent individuals form a seemingly perfectly coordinated whole? Previous attempts to answer this question have reduced the individuals to featureless particles, assumed particular interactions between them and studied the resulting collective dynamics. While this approach has provided useful insights, it cannot guarantee that the assumed individual-level behaviour is accurate, and, moreover, does not address its origin—that is, the question of why individuals would respond in one way or another. We propose a new approach to studying collective behaviour, based on the concept of learning agents : individuals endowed with explicitly modelled sensory capabilities, an internal mechanism for deciding how to respond to the sensory input and rules for modifying these responses based on past experience. This detailed modelling of individuals favours a more natural choice of parameters than in typical swarm models, which minimises the risk of spurious dependences or overfitting. Most notably, learning agents need not be programmed with particular responses, but can instead develop these autonomously, allowing for models with fewer implicit assumptions. We illustrate these points with the example of marching locusts, showing how learning agents can account for the phenomenon of density-dependent alignment. Our results suggest that learning agent-based models are a powerful tool for studying a broader class of problems involving collective behaviour and animal agency in general.

Wireless communication derives its power from the simultaneous emission of signals in multiple directions. However, in the context of quantum communication, this phenomenon must be reconciled carefully with the no-cloning principle. In this context, we here study how wireless communication of quantum information can be realized via relativistic fields. To this end, we extend existing frameworks to allow for a non-perturbative description of, e.g., quantum state transfer. We consider, in particular, the case of 1+1 spacetime dimensions, which already allows a number of interesting scenarios, pointing to, for example, new methods for tasks similar to quantum secret sharing. arXiv:1708.04249v2 [quant-ph]