Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple subfields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation of Reichenbach's principle and enabling causal inference with only observational data. However, it is still not clear how quantum causal inference can provide operational advantages in general cases. Here, we have devised a photonic setup and experimentally realized an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario, thus revealing a universal quantum advantage in causal inference over its classical counterpart. We further demonstrate the explainability and stability of our causal discovery method, which is widely sought in data processing algorithms. Employing a fully observational approach, our result paves the way for studying quantum causality in general settings.
Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple subfields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation of Reichenbach's principle and enabling causal inference with only observational data. However, it is still not clear how quantum causal inference can provide operational advantages in general cases. Here, we have devised a photonic setup and experimentally realized an algorithm capable of identifying any two-qubit statistical correlations generated by the two basic causal structures under an observational scenario, thus revealing a universal quantum advantage in causal inference over its classical counterpart. We further demonstrate the explainability and stability of our causal discovery method, which is widely sought in data processing algorithms. Employing a fully observational approach, our result paves the way for studying quantum causality in general settings.
Though the topic of causal inference is typically considered in the context of classical statistical models, recent years have seen great interest in extending causal inference techniques to quantum and generalized theories. Causal identification is a type of causal inference problem concerned with recovering from observational data and qualitative assumptions the causal mechanisms generating the data, and hence the effects of hypothetical interventions. A major obstacle to a theory of causal identification in the quantum setting is the question of what should play the role of "observational data," as any means of extracting data at a certain locus will almost certainly disturb the system. Hence, one might think a priori that quantum measurements are already too much like interventions, so that the problem of causal identification trivializes. This is not the case. Fixing a limited class of quantum instruments (namely the class of all projective measurements) to play the role of "observations," we note that as in the classical setting, there exist scenarios for which causal identification is not possible. We then present sufficient conditions for quantum causal identification, starting with a quantum analogue of the well-known "front-door criterion" and finishing with a broader class of scenarios for which the effect of a single intervention is identifiable. These results emerge from generalizing the process-theoretic account of classical causal inference due to Jacobs, Kissinger, and Zanasi beyond the setting of Markov categories, and thereby treating the classical and quantum problems uniformly.
The framework of causal models is ideally suited to formalizing certain conceptual problems in quantum the-ory, and conversely, a variety of tools developed by physicists studying the foundations of quantum theory have applications for causal inference. This talk reviews some of the connections between the two fields. In partic-ular, it is shown that certain correlations predicted by quantum theory and observed experimentally cannot be explained by any causal model while respecting the core principles of causal discovery algorithms. Nonetheless, it is argued that by understanding quantum theory as an innovation to the theory of Bayesian inference, one can introduce a quantum generalization of the notion of a causal model and salvage a causal explanation of these cor-relations without fine-tuning. Furthermore, experiments exhibiting certain quantum features, namely, coherence and entanglement, enable solutions to causal inference problems that are intractable classically. In particular, while passive observation of a pair of variables cannot determine the causal relation that holds between them according to classical physics, this is not the case in quantum physics. In other words, according to quantum theory, certain kinds of correlation do imply causation. The results of a quantum-optical experiment confirming these predictions will be presented. This talk is based on the work described in Refs. [1] and [2].
Identifying the causal structures between two statistically correlated events has been widely investigated in many fields of science. While some of the well-studied classical methods are carefully generalized to quantum version of causal inference for certain cases, an effective and efficient way to detect the more general quantum causal structures is still lacking. Here, we introduce a quantity named `Causal Determinant' to efficiently identify the quantum causal structures between two quantum systems and experimentally verify the validity of the method. According to the causal determinant, the quantum direct cause imposed by an arbitrary unitary operator can be perfectly discriminated with the quantum common cause, in which the two quantum systems share a joint quantum state. In addition, the causal determinant has the capability to discriminate between more general causal structures and predict the range of their parameters. The ability to detect more general quantum causal structures of our method can shed new light on the field of quantum causal inference.
We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.
It has long been recognized as a difficult problem to determine whether the observed statistical correlations between two classical variables arise from causality or from common causes. Recent research has shown that, in a quantum theoretical framework, the mechanisms of entanglement and quantum coherence provide advantages in tackling this problem. In some particular cases, quantum common causes and quantum causality can be effectively distinguished by using observations alone. However, these solutions do not apply to all cases. There still exist a large class of cases in which quantum common causes and quantum causality cannot be distinguished. In this paper, along the line of considering unitary transformation as causality in the quantum world, we formally show that quantum common causes and quantum causality are universally separable. Based on the analysis, we further provide a general method to discriminate the two.
An active area of research in the fields of machine learning and statistics is the development of causal discovery algorithms , the purpose of which is to infer the causal relations that hold among a set of variables from the correlations that these exhibit . We apply some of these algorithms to the correlations that arise for entangled quantum systems. We show that they cannot distinguish correlations that satisfy Bell inequalities from correlations that violate Bell inequalities, and consequently that they cannot do justice to the challenges of explaining certain quantum correlations causally. Nonetheless, by adapting the conceptual tools of causal inference, we can show that any attempt to provide a causal explanation of nonsignalling correlations that violate a Bell inequality must contradict a core principle of these algorithms, namely, that an observed statistical independence between variables should not be explained by fine-tuning of the causal parameters. In particular, we demonstrate the need for such fine-tuning for most of the causal mechanisms that have been proposed to underlie Bell correlations, including superluminal causal influences, superdeterminism (that is, a denial of freedom of choice of settings), and retrocausal influences which do not introduce causal cycles.