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

arXiv:1601.07555 · Physical Review Letters

Entropic Nonsignaling Correlations

Rafael Chaves, Costantino Budroni

Published Jun 13, 2016• 31 citations
arXivHTMLPDF

Abstract

We introduce the concept of entropic nonsignaling correlations, i.e., entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously. We characterize and show the relevance of these entropic correlations in a variety of different scenarios, ranging from typical Bell experiments to more refined descriptions such as bilocality and information causality. In particular, we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic Bell inequalities. Further, within the context of complex Bell networks, we show that entropic nonlocal correlations can be activated.

DOI
10.1103/physrevlett.116.240501

Related papers

The entropic approach to causal correlations

Nikolai Miklin, Alastair A. Abbott, Cyril Branciard +2 more

The existence of a global causal order between events places constraints on the correlations that parties may share. Such 'causal correlations' have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information—which is more naturally expressed in the entropic framework—that parties can communicate when operating in a definite causal order.

arXiv:1706.10270•New Journal of Physics•Sep 28, 2017•21 citations

Ruling out bipartite nonsignaling nonlocal models for tripartite correlations

Peter Bierhorst

Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so-obtained correlations, such as no-signaling, indeed hold, and show how to use the framework to derive Bell-inequality-type constraints on these correlations that can be robustly violated by tripartite quantum systems. In particular, we use this framework to rederive a version of one such constraint previously described in a paper of Chao and Reichardt, Test to separate quantum theory from non-signaling theories [arXiv:1706.02008 (2017)].

arXiv:2012.11132•Physical Review A•Jul 15, 2021•10 citations

Playing Nonlocal Games with Little to No Shared Randomness

Mingze Xu, Eric Chitambar

Bell nonlocality reveals correlations that cannot be explained by classical models and plays a central role in quantum information theory. In this work, we investigate classical models of Bell nonlocality under restrictions on shared randomness. For bipartite scenarios with bounded shared randomness, the set of classical correlations becomes nonconvex. We characterize the correlations achievable without shared randomness through the simultaneous evaluation of multiple linear Bell functionals. We then extend our analysis to quantum networks by relaxing the standard assumption of source independence. In this setting, the feasibility constraints derived for the bipartite case can be used to certify source dependence, and we further construct nonlinear inequalities that distinguish classical models with correlated sources from correlations achievable in standard quantum networks. As an application, we show that these nonlinear network inequalities give rise to an entropic Bell inequality for bipartite scenarios with limited shared randomness.

quant-pharXiv:2608.07833•Aug 11, 2026•0 citations

Causal hierarchy of multipartite Bell nonlocality

Rafael Chaves, Daniel Cavalcanti, Leandro Aolita

As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.

arXiv:1607.07666•Quantum•Aug 4, 2017•64 citations

Polynomial Bell Inequalities

Rafael Chaves

It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.

arXiv:1506.04325•Physical Review Letters•Jan 7, 2016•141 citations

Experimental activation of quantum nonlocality via a quantum network

Luis Villegas-Aguilar, Emanuele Polino, Sergei Slussarenko +7 more

Quantum nonlocality arising from entangled particles cannot be explained by any classical notion of local causality. In the standard Bell scenario with a source and two measurement stations, entangled states can lose their ability to exhibit nonlocality due to noisy conditions. Given the fundamental and technological significance of nonlocality and the fact that these noisy entangled states can naturally arise in practical situations, it is of utmost importance to unveil their nonlocality. Here, we demonstrate that nonlocal correlations can be generated from quantum states that cannot show nonlocality in bipartite Bell scenarios. We show how to robustly characterize these states and experimentally activate their nonlocality when embedded in a photonic network, by violating classical constraints in this quantum network. These results have implications in foundations of quantum nonlocality and direct applications to quantum technologies by significantly increasing the robustness of nonlocal correlations to noise.

Quantum Communications and Quantum Imaging•Oct 4, 2024•0 citations
We introduce the concept of entropic nonsignaling correlations, i.e., entropies arising from probabilistic theories that are compatible with the fact that we cannot transmit information instantaneously. We characterize and show the relevance of these entropic correlations in a variety of different scenarios, ranging from typical Bell experiments to more refined descriptions such as bilocality and information causality. In particular, we apply the framework to derive the first entropic inequality testing genuine tripartite nonlocality in quantum systems of arbitrary dimension and also prove the first known monogamy relation for entropic Bell inequalities. Further, within the context of complex Bell networks, we show that entropic nonlocal correlations can be activated.
The existence of a global causal order between events places constraints on the correlations that parties may share. Such 'causal correlations' have been the focus of recent attention, driven by the realization that some extensions of quantum mechanics may violate so-called causal inequalities. In this paper we study causal correlations from an entropic perspective, and we show how to use this framework to derive entropic causal inequalities. We consider two different ways to derive such inequalities. Firstly, we consider a method based on the causal Bayesian networks describing the causal relations between the parties. In contrast to the Bell-nonlocality scenario, where this method has previously been shown to be ineffective, we show that it leads to several interesting entropic causal inequalities. Secondly, we consider an alternative method based on counterfactual variables that has previously been used to derive entropic Bell inequalities. We compare the inequalities obtained via these two methods and discuss their violation by noncausal correlations. As an application of our approach, we derive bounds on the quantity of information—which is more naturally expressed in the entropic framework—that parties can communicate when operating in a definite causal order.
Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so-obtained correlations, such as no-signaling, indeed hold, and show how to use the framework to derive Bell-inequality-type constraints on these correlations that can be robustly violated by tripartite quantum systems. In particular, we use this framework to rederive a version of one such constraint previously described in a paper of Chao and Reichardt, Test to separate quantum theory from non-signaling theories [arXiv:1706.02008 (2017)].
Bell nonlocality reveals correlations that cannot be explained by classical models and plays a central role in quantum information theory. In this work, we investigate classical models of Bell nonlocality under restrictions on shared randomness. For bipartite scenarios with bounded shared randomness, the set of classical correlations becomes nonconvex. We characterize the correlations achievable without shared randomness through the simultaneous evaluation of multiple linear Bell functionals. We then extend our analysis to quantum networks by relaxing the standard assumption of source independence. In this setting, the feasibility constraints derived for the bipartite case can be used to certify source dependence, and we further construct nonlinear inequalities that distinguish classical models with correlated sources from correlations achievable in standard quantum networks. As an application, we show that these nonlinear network inequalities give rise to an entropic Bell inequality for bipartite scenarios with limited shared randomness.
As with entanglement, different forms of Bell nonlocality arise in the multipartite scenario. These can be defined in terms of relaxations of the causal assumptions in local hidden-variable theories. However, a characterisation of all the forms of multipartite nonlocality has until now been out of reach, mainly due to the complexity of generic multipartite causal models. Here, we employ the formalism of Bayesian networks to reveal connections among different causal structures that make a both practical and physically meaningful classification possible. Our framework holds for arbitrarily many parties. We apply it to study the tripartite scenario in detail, where we fully characterize all the nonlocality classes. Remarkably, we identify new highly nonlocal causal structures that cannot reproduce all quantum correlations. This shows, to our knowledge, the strongest form of quantum multipartite nonlocality known to date. Finally, as a by-product result, we derive a non-trivial Bell-type inequality with no quantum violation. Our findings constitute a significant step forward in the understanding of multipartite Bell nonlocality and open several venues for future research.
It is a recent realization that many of the concepts and tools of causal discovery in machine learning are highly relevant to problems in quantum information, in particular quantum nonlocality. The crucial ingredient in the connection between both fields is the mathematical theory of causality, allowing for the representation of arbitrary causal structures and providing a rigorous tool to reason about probabilistic causation. Indeed, Bell's theorem concerns a very particular kind of causal structure and Bell inequalities are a special case of linear constraints following from such models. It is thus natural to look for generalizations involving more complex Bell scenarios. The problem, however, relies on the fact that such generalized scenarios are characterized by polynomial Bell inequalities and no current method is available to derive them beyond very simple cases. In this work, we make a significant step in that direction, providing a new, general, and conceptually clear method for the derivation of polynomial Bell inequalities in a wide class of scenarios. We also show how our construction can be used to allow for relaxations of causal constraints and naturally gives rise to a notion of nonsignaling in generalized Bell networks.
Quantum nonlocality arising from entangled particles cannot be explained by any classical notion of local causality. In the standard Bell scenario with a source and two measurement stations, entangled states can lose their ability to exhibit nonlocality due to noisy conditions. Given the fundamental and technological significance of nonlocality and the fact that these noisy entangled states can naturally arise in practical situations, it is of utmost importance to unveil their nonlocality. Here, we demonstrate that nonlocal correlations can be generated from quantum states that cannot show nonlocality in bipartite Bell scenarios. We show how to robustly characterize these states and experimentally activate their nonlocality when embedded in a photonic network, by violating classical constraints in this quantum network. These results have implications in foundations of quantum nonlocality and direct applications to quantum technologies by significantly increasing the robustness of nonlocal correlations to noise.