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arXiv:2501.08079

Quantum-informed learning of genuine network nonlocality beyond idealized resources

Anantha Krishnan Sunilkumar, Anil Shaji, Debashis Saha

Published Jan 14, 2025• 0 citations
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Abstract

We address the characterization of genuine network nonlocal correlations, which remain highly challenging due to the non-convex nature of local correlations even in the distinct triangle scenario with three sources and three observers implementing one four-outcome measurement. We introduce a scalable causally inferred Bayesian learning framework called the Layered Local Hidden Variable Neural Network (Layered LHV-Net) to learn the local statistics in network Bell tests. Using this framework, we identify a new class of measurement settings that exhibit the most robust nonlocality compared to previously known measurements. Remarkably, our study shows that the nonlocality measure becomes non-zero only when the visibility of the shared Bell state exceeds 0.94, surpassing previously reported noise robustness thresholds. Further, we examine correlations where shared states originate from dissimilar sources, finding that nonlocality is observed only if all the involved states are sufficiently entangled. Finally, we analyze a scenario in which the sources are allowed to share classical randomness. We find that nonlocal correlations persist even when the sources share up to 3 units of randomness, whereas a local model reproducing the quantum correlations only becomes possible when 4 units of shared randomness are available. Apart from the results, the work succeeds in showing that quantum-informed machine learning approaches as foundational frameworks can greatly benefit the field of quantum information.

DOI
10.48550/arxiv.2501.08079

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We address the characterization of genuine network nonlocal correlations, which remain highly challenging due to the non-convex nature of local correlations even in the distinct triangle scenario with three sources and three observers implementing one four-outcome measurement. We introduce a scalable causally inferred Bayesian learning framework called the Layered Local Hidden Variable Neural Network (Layered LHV-Net) to learn the local statistics in network Bell tests. Using this framework, we identify a new class of measurement settings that exhibit the most robust nonlocality compared to previously known measurements. Remarkably, our study shows that the nonlocality measure becomes non-zero only when the visibility of the shared Bell state exceeds 0.94, surpassing previously reported noise robustness thresholds. Further, we examine correlations where shared states originate from dissimilar sources, finding that nonlocality is observed only if all the involved states are sufficiently entangled. Finally, we analyze a scenario in which the sources are allowed to share classical randomness. We find that nonlocal correlations persist even when the sources share up to 3 units of randomness, whereas a local model reproducing the quantum correlations only becomes possible when 4 units of shared randomness are available. Apart from the results, the work succeeds in showing that quantum-informed machine learning approaches as foundational frameworks can greatly benefit the field of quantum information.
Measurement correlations in quantum systems can exhibit nonlocal behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, it is in general not known which states are local and which ones are not. In particular, it remains an outstanding challenge to explicitly construct local hidden-variable (LHV) models for arbitrary multipartite entangled states. To address this, we use gradient-descent algorithms from machine learning to find LHV models that reproduce the statistics of arbitrary measurements for quantum many-body states. In contrast to previous approaches, our method employs a general ansatz, enabling it to discover LHV models for all local states. Therefore, it for example provides actual estimates for the critical noise levels at which two-qubit Werner states and three-qubit Greenberger-Horne-Zeilinger and W states become local. Furthermore, we find evidence suggesting that two-spin subsystems in the ground states of translationally invariant Hamiltonians are genuinely local, while bigger subsystems are in general not. Our method now offers a quantitative tool for determining the regimes of nonlocality in any given physical context, such as nonequilibrium, decoherence, or disorder.
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The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.
In recent years, the study of Bell nonlocality has been generalized to quantum networks, where multiple independent sources distribute physical systems to distant parties who perform local measurements. In this context, a central open question is to identify the minimal network configuration in which quantum resources produce Bell nonlocal correlations. Here we address this question and show that quantum nonlocality is possible in the triangle network where the parties have no input choices and produce only binary-valued outcomes. To do so, we start by identifying a family of target distributions and proving their nonlocality. Next, we construct an explicit quantum model that reproduces the target distributions to machine precision. For this, we develop an efficient method for parameterizing quantum distributions in networks, inspired by the formalism of higher-order quantum operations. When considering the number of observed variables and their cardinality, this constitutes the smallest scenario possible that supports quantum nonlocality in networks. Moreover, by analyzing the explicit quantum model, we obtain new insights into how nonlocal distributions can be generated in quantum networks.
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.
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.