Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Observational-interventional Bell inequalities

Davide Poderini, Ranieri Nery, George Moreno, Santiago Zamora, Pedro Lauand, Rafael Chaves

Published Oct 21, 2024• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.110.042213

Related papers

Observational-Interventional Bell Inequalities

Davide Poderini, Ranieri Nery, George Moreno +3 more

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.

arXiv:2404.05015•Apr 7, 2024•0 citations

Causal Data Fusion with Quantum Confounders

Pedro Lauand, Bereket Ngussie Bekele, Elie Wolfe

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.

arXiv:2405.19278•May 29, 2024•0 citations

Experimental test of quantum causal influences

Iris Agresti, Davide Poderini, Beatrice Polacchi +8 more

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.

arXiv:2108.08926•Science Advances•Feb 25, 2022•22 citations

Latent splitting as a causal probe

Santiago Zamora, Pedro Lauand, Isadora Veeren +2 more

Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such interventions, however, become uninformative when all observable variables are space-like separated. To address this limitation, we introduce the latent splitting procedure, a generalization of interventions to quantum networks in which controlled manipulations are applied to latent quantum systems. We show that latent splitting enables the detection of nonclassicality by combining observational and interventional data even when conventional interventions fail. Focusing on the triangle network, we derive new analytical witnesses that robustly certify nonclassicality, including nonlinear inequalities for minimal binary-variable scenarios and extensions of the nonclassical region of previously proposed experiments.

quant-pharXiv:2601.06265•Physical Review A•Jan 13, 2026•0 citations

Quantum violations in the Instrumental scenario and their relations to the Bell scenario

Thomas van Himbeeck, Brask Bohr, Jonatan, Stefano Pironio +3 more

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.

•Jan 1, 2018•33 citations

Bell's Inequality, Causal Bounds, and Quantum Bayesian Computation: A Unified Framework

Nick Polson, Vadim Sokolov, Daniel Zantedeschi

Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through non-commutativity, reaching the Tsirelson bound $2\sqrt{2}$ for CHSH. We show that this polytope structure is not specific to quantum foundations: it appears identically in the causal inference literature, where the instrumental inequality, the Balke--Pearl linear programming bounds, and the Tian--Pearl probabilities of causation all arise as facets of the same marginal compatibility polytope. Fine's theorem -- that CHSH inequalities hold if and only if a joint distribution exists -- is precisely the pivot: the instrumental variable model in causal inference is structurally equivalent to the Bell local hidden-variable model, with the instrument playing the role of the measurement setting and the latent confounder playing the role of the hidden variable $λ$. We develop this correspondence in detail, extending it to algorithmic (Kolmogorov complexity) and entropic formulations of Bell inequalities, the NPA semidefinite programming hierarchy, and the MIP$^*$=RE undecidability result. We further show that the Born-rule / Bayes-rule duality underlying quantum Bayesian computation exploits the same non-commutativity that enables Bell violation, providing polynomial speedups for posterior inference. The framework yields a concrete dictionary between quantum information theory, causal econometrics, and Bayesian computation, and suggests new directions including NPA-based quantum causal inference algorithms and quantum architectures for function approximation.

quant-pharXiv:2603.28973•Apr 1, 2026•0 citations
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.
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.
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.
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.
Generalizations of Bell's framework to causal networks have yielded new foundational insights and applications, including the use of interventions to enhance the detection of nonclassicality in scenarios with communication. Such interventions, however, become uninformative when all observable variables are space-like separated. To address this limitation, we introduce the latent splitting procedure, a generalization of interventions to quantum networks in which controlled manipulations are applied to latent quantum systems. We show that latent splitting enables the detection of nonclassicality by combining observational and interventional data even when conventional interventions fail. Focusing on the triangle network, we derive new analytical witnesses that robustly certify nonclassicality, including nonlinear inequalities for minimal binary-variable scenarios and extensions of the nonclassical region of previously proposed experiments.
The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. Here, we go in the opposite direction and identify the simplest causal structure which exhibits a separation between classical, quantum, and post-quantum correlations. It arises in the so-called Instrumental scenario, known from classical causal models. We derive inequalities for this scenario and show that they are closely related to well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt inequality, which enables us to easily identify their classical, quantum, and post-quantum bounds as well as strategies violating the first two. The relations that we uncover imply that the quantum or post-quantum advantages witnessed by the violation of our Instrumental inequalities are not fundamentally different from those witnessed by the violations of standard inequalities in the usual Bell scenario. However, non-classical tests in the Instrumental scenario require fewer input choices than their Bell scenario counterpart, which may have potential implications for device-independent protocols.
Bell inequalities characterize the boundary of the local-realist correlation polytope -- the set of joint probability distributions achievable by classical hidden-variable models. Quantum mechanics exceeds this boundary through non-commutativity, reaching the Tsirelson bound 222\sqrt{2}22​ for CHSH. We show that this polytope structure is not specific to quantum foundations: it appears identically in the causal inference literature, where the instrumental inequality, the Balke--Pearl linear programming bounds, and the Tian--Pearl probabilities of causation all arise as facets of the same marginal compatibility polytope. Fine's theorem -- that CHSH inequalities hold if and only if a joint distribution exists -- is precisely the pivot: the instrumental variable model in causal inference is structurally equivalent to the Bell local hidden-variable model, with the instrument playing the role of the measurement setting and the latent confounder playing the role of the hidden variable λλλ. We develop this correspondence in detail, extending it to algorithmic (Kolmogorov complexity) and entropic formulations of Bell inequalities, the NPA semidefinite programming hierarchy, and the MIP∗^*∗=RE undecidability result. We further show that the Born-rule / Bayes-rule duality underlying quantum Bayesian computation exploits the same non-commutativity that enables Bell violation, providing polynomial speedups for posterior inference. The framework yields a concrete dictionary between quantum information theory, causal econometrics, and Bayesian computation, and suggests new directions including NPA-based quantum causal inference algorithms and quantum architectures for function approximation.