From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization of Bell's theorem to quantum networks has led to several breakthrough results and novel applications. Here, we consider the problem of causal data fusion, where we piece together multiple datasets collected under heterogeneous conditions. In particular, we show quantum experiments can generate observational and interventional data with a non-classical signature when pieced together that cannot be reproduced classically. We prove this quantum non-classicality emerges from the fusion of the datasets and is present in a plethora of scenarios, even where standard Bell non-classicality is impossible. Furthermore, we show that non-classicality genuine to the fusion of multiple data tables is achievable with quantum resources. Our work shows incorporating interventions -- a central tool in causal inference -- can be a powerful tool to detect non-classicality beyond the violation of a standard Bell inequality. In a companion article "Quantum Non-classicality from Causal Data Fusion", we extend our investigation considering all latent exogenous causal structures with 3 observable variables.
From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization of Bell's theorem to quantum networks has led to several breakthrough results and novel applications. Here, we consider the problem of causal data fusion, where we piece together multiple datasets collected under heterogeneous conditions. In particular, we show quantum experiments can generate observational and interventional data with a non-classical signature when pieced together that cannot be reproduced classically. We prove this quantum non-classicality emerges from the fusion of the datasets and is present in a plethora of scenarios, even where standard Bell non-classicality is impossible. Furthermore, we show that non-classicality genuine to the fusion of multiple data tables is achievable with quantum resources. Our work shows incorporating interventions -- a central tool in causal inference -- can be a powerful tool to detect non-classicality beyond the violation of a standard Bell inequality. In a companion article "Quantum Non-classicality from Causal Data Fusion", we extend our investigation considering all latent exogenous causal structures with 3 observable variables.
Bell's theorem can be understood as establishing the incompatibility of quantum correlations with any classical causal explanation. Causal inference, however, relies not only on passive observations but also on interventions. Here we ask when the observational and interventional data collected on a given causal structure can all be reproduced by a single classical causal model, which is a particular instance of the data fusion problem in causal inference [Bareinboim and Pearl, PNAS 113, 7345 (2016)]. We show that quantum systems give rise to a new form of nonclassicality in this setting, namely: when the data tables associated with each (non)intervention paradigm admit classical explanations, but no single classical model explains the different intervention paradigms when considered jointly. We call this nonclassicality in the synthesis of the data fusion. We assess the prevalence of such fusion by partitioning all marginalized causal structures over three observed variables into exactly two categories: those which can and those which cannot exhibit such nonclassicality. For all those that can, we present explicit quantum violations of the associated causal inequalities.
Since Bell's theorem, it is known that local realism fails to explain quantum phenomena. Bell inequality violations manifestly show the incompatibility of quantum theory with classical notions of cause and effect. As recently found, however, the instrumental scenario-a pivotal tool in causal inference-allows for nonclassicality signatures going beyond this paradigm. If we are not limited to observational data and can intervene in our setup, then we can witness quantum violations of classical bounds on the causal influence among the involved variables even when no Bell-like violation is possible. That is, through interventions, the quantum behavior of a system that would seem classical can be demonstrated. Using a photonic setup-faithfully implementing the instrumental causal structure and switching between observation and intervention run by run-we experimentally witness such a nonclassicality. We also test quantum bounds for the causal influence, showing that they provide a reliable tool for quantum causal modeling.
Bell's theorem is often considered the most stringent notion of nonclassicality. The generalization of Bell's theorem to causal networks offers interesting new perspectives on the phenomenon of quantum nonclassicality and prompts us with a fundamental inquiry: what is the simplest scenario leading to the incompatibility between quantum correlations and the classical theory of causality? Here, we demonstrate that quantum nonclassicality is possible in an entanglement swapping network consisting of only three dichotomic variables, without the need for the locality assumption or external measurement choices. We also show that interventions, a central tool in the field of causal inference, significantly improve the noise robustness of this new kind of nonclassical behavior, making it feasible for experimental tests with current technology.
Generalizations of Bell's theorem, particularly within quantum networks, are now being analyzed through the causal inference lens. However, the exploration of interventions, a central concept in causality theory, remains significantly unexplored. In this work we give an initial step in this direction, by analyzing the instrumental scenario and proposing novel hybrid Bell inequalities integrating observational and interventional data. Focusing on binary outcomes with any number of inputs, we obtain the complete characterization of the observational-interventional polytope, equivalent to a Hardy-like Bell inequality albeit describing a distinct quantum experiment. To illustrate its applications, we show a significant enhancement regarding threshold detection efficiencies for quantum violations also showing the use of these hybrid approach in quantum steering scenarios.
Generalizations of Bell's theorem, particularly within quantum networks, are now being analyzed through the lens of causal inference. However, the exploration of interventions, a central concept in causality theory, remains significantly unexplored. In this work, we take an initial step in this direction, by analyzing the instrumental scenario and proposing hybrid Bell inequalities integrating observational and interventional data. Focusing on binary outcomes with any number of inputs, we obtain the complete characterization of the observational-interventional polytope, equivalent to a Hardy-like Bell inequality, albeit describing a distinct quantum experiment. To illustrate its applications, we show a significant enhancement regarding threshold detection efficiencies for quantum violations also showing the use of this hybrid approach in quantum steering scenarios.
Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question, we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even postquantum nature of a common cause. In particular, by considering the simplest instrumental scenario-for which violation of Bell inequalities is not possible-we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus, answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.