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:2406.17841 · Physical Review X

Probing Many-Body Bell Correlation Depth with Superconducting Qubits

Ke Wang, Weikang Li, Shibo Xu, Mengyao Hu, Jiachen Chen, Yaozu Wu, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Yu Qing Gao, Ziqi Tan, Zhengyi Cui, Aosai Zhang, Ning Wang, Yiren Zou, Tingting Li, Fanhao Shen, Jiarun Zhong, Zehang Bao, Zitian Zhu, Zixuan Song, Jinfeng Deng, Hang Dong, Xu Zhang, Pengfei Zhang, Wenjie Jiang, Zhide Lu, Zheng-Zhi Sun, Hekang Li, Qiujiang Guo, Zhen Wang, Patrick Emonts, Jordi Tura, Chao Song, H. Wang, Dong-Ling Deng

Published Apr 22, 2025• 6 citations
arXivHTMLPDF

Abstract

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.

DOI
10.1103/physrevx.15.021024

Related papers

Improved certification of Bell-operator correlations via optimization

Weikang Li, Mengyao Hu, Ke Wang +25 more

Bell nonlocality is an intrinsic feature of quantum mechanics, which can be detected via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here we present an optimization framework to detect Bell-operator correlations by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds compared to the original one, enabling a more robust certification of Bell-operator correlations. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical application, we experimentally exploit this method in an -like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, together with the combination of the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient certification techniques for Bell-operator correlations and enable broader experimental explorations.

arXiv:2407.12347•Physical Review A•Sep 15, 2026•0 citations

Experimental certification of multipartite Bell correlations using only few-body symmetric correlations

Jiacheng Sun, Mengyao Hu, Paweł Cieśliński +9 more

Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of $p_c\approx0.301$, compared with $p_c\approx0.048$ for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by $32$ and $8.9$ standard deviations, arising from postselected polarisation states with fidelities of $0.933(4)$ and $0.916(11)$ to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.

quant-pharXiv:2609.37442•Sep 30, 2026•0 citations

Tropical tensor networks and Bell inequalities

Hu, M.

Quantum computers promise computational capabilities beyond the reach of efficient classical methods, raising a central question: how can one rigorously certify nonclassical behavior in large-scale quantum devices under minimal assumptions? Bell nonlocality, the strongest and most device-independent form of quantum correlation, provides a natural framework to address this question. This thesis develops mathematical and experimental tools to detect and characterize Bell nonlocality in many-body quantum systems, with a focus on scalable Bell-inequality constructions, and the use of Bell operators as practical benchmarks for quantum processors. We first introduce a tropical tensor network framework that recasts the optimization of classical bounds for multipartite Bell inequalities as a tensor contraction in tropical algebra, enabling the characterization of broad inequality families and an extension to the thermodynamic limit. Building on this, we develop a systematic theory of translation-invariant Bell inequalities in one dimension. We then study two-dimensional spin models on the square lattice, quantifying how open, periodic, and topologically nontrivial boundary conditions modify the strength of certifiable Bell violations. On the experimental side, we demonstrate certified multipartite Bell-operator correlations on a programmable superconducting processor, including a 73-qubit honeycomb model, by mapping Bell inequalities onto many-body Hamiltonians. We further introduce a bidirectional optimization framework that co-designs Bell inequalities and Hamiltonians for a given device, yielding stronger and more noise-resilient certification.

•Jun 18, 2026•0 citations

Observing Bell Inequality Violation Beyond the Qubit Bound in a Spinor Bose--Einstein Condensate

Wenxin Xu, Junshuang Hu, Guillem Müller-Rigat +4 more

Correlations allowed by quantum mechanics can defy any classical explanation, with Bell nonlocality standing as their most profound and operationally powerful manifestation. While nonlocality has been demonstrated across a wide range of platforms, in many-body systems it has remained limited to ensembles of qubits, leaving the observation of higher-dimensional multipartite Bell correlations an open challenge. Here we report the observation of qutrit Bell correlations in a spin-1 $^{87}$Rb Bose-Einstein condensate via the violation of a Bell witness based on collective spin observables only. Exploiting spin-exchange collisions in an ensemble of $N \simeq 3.1 \times 10^{4}$ atoms, we generate spin-nematic squeezing of $-11.8(7)$ dB and observe a violation that surpasses the minimum bound achievable by a collection of $N$ qubits, providing direct evidence of genuine multipartite qutrit Bell correlations. Our results establish spinor Bose-Einstein condensates as a viable platform for investigating high-dimensional Bell correlations in the many-body regime, and demonstrate that coarse-grained collective measurements suffice to certify the dimensionality of quantum correlations at macroscopic scales.

quant-pharXiv:2608.24981•Aug 26, 2026•0 citations

Generalized Mermin Inequalities for Benchmarking Large-Scale GHZ States

Jianbin Cai, Junxiang Huang, Fynn Otto +15 more

Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors, but their application at large scales is hindered by the rapid decay of many-body correlators under noise and exponentially many terms in conventional Bell expressions. Here we address these scalability obstacles by introducing a finite-setting generalized Mermin family of state-tailored Bell inequalities with analytic certification bounds, in which the measurement-setting number $m$ provides an additional certification dimension complementary to the system size $n$. We show that, for the powers-of-two setting choices considered here, increasing $m$ leaves the ideal normalized multipartite quantum value unchanged while lowering the relevant classical bounds, thereby strengthening the Bell-violation ratios and yielding an improved noise-robustness scaling compared to the standard Mermin inequality. We test this construction experimentally on a programmable superconducting processor by preparing Greenberger-Horne-Zeilinger (GHZ) states of up to 80 qubits. Using randomized sampling for direct Bell-operator estimation, we observe Bell ratios that grow exponentially with system size, certify a nonlocality depth of 14, and show that increasing $m$ strengthens both the Bell ratio and depth certification. All results are obtained solely from measured correlators and analytical bounds, without readout correction, tomography, or model-based mitigation. Generalized Mermin inequalities therefore provide a sharper Bell benchmark for noisy large-scale GHZ states.

quant-pharXiv:2607.23574•Jul 28, 2026•0 citations

Experimental high-dimensional multi-qubit Bell non-locality on a superconducting quantum processor

Yousef Mafi, Ali G. Moghaddam, Teemu Ojanen

Combining recent advances in superconducting quantum hardware, we explore quantum correlations in a previously inaccessible regime by observing \emph{simultaneously} high-dimensional and many-body Bell non-locality. We report a high-confidence Bell violation in the correlations between two $d=64$-dimensional systems encoded in twelve qubits. For system sizes up to $d=32$, the strength of the observed nonlocal correlations exceeds the quantum upper bound for $d=2$ systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local. Our work illustrates how present-day quantum processors enable the exploration of fundamental predictions of quantum mechanics in previously inaccessible regimes and, in turn, how fundamental quantum effects can be used to benchmark their performance.

quant-pharXiv:2604.24740•Apr 28, 2026•0 citations
Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.
Bell nonlocality is an intrinsic feature of quantum mechanics, which can be detected via the violation of Bell inequalities. It is therefore a fundamental question to certify Bell nonlocality from experimental data. Here we present an optimization framework to detect Bell-operator correlations by exploring flexible mappings between Bell inequalities and Hamiltonians corresponding to the Bell operators. We show that several Hamiltonian models can be mapped to new inequalities with improved classical bounds compared to the original one, enabling a more robust certification of Bell-operator correlations. From the other direction, we investigate the mapping from fixed Bell inequalities to Hamiltonians, aiming to maximize quantum violations while considering experimental imperfections. As a practical application, we experimentally exploit this method in an -like honeycomb-lattice model utilizing over 70 superconducting qubits. The successful application of this technique, together with the combination of the two directions to form an optimization loop, may open new avenues for developing more practical and noise-resilient certification techniques for Bell-operator correlations and enable broader experimental explorations.
Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of pc≈0.301p_c\approx0.301pc​≈0.301, compared with pc≈0.048p_c\approx0.048pc​≈0.048 for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by 323232 and 8.98.98.9 standard deviations, arising from postselected polarisation states with fidelities of 0.933(4)0.933(4)0.933(4) and 0.916(11)0.916(11)0.916(11) to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.
Quantum computers promise computational capabilities beyond the reach of efficient classical methods, raising a central question: how can one rigorously certify nonclassical behavior in large-scale quantum devices under minimal assumptions? Bell nonlocality, the strongest and most device-independent form of quantum correlation, provides a natural framework to address this question. This thesis develops mathematical and experimental tools to detect and characterize Bell nonlocality in many-body quantum systems, with a focus on scalable Bell-inequality constructions, and the use of Bell operators as practical benchmarks for quantum processors. We first introduce a tropical tensor network framework that recasts the optimization of classical bounds for multipartite Bell inequalities as a tensor contraction in tropical algebra, enabling the characterization of broad inequality families and an extension to the thermodynamic limit. Building on this, we develop a systematic theory of translation-invariant Bell inequalities in one dimension. We then study two-dimensional spin models on the square lattice, quantifying how open, periodic, and topologically nontrivial boundary conditions modify the strength of certifiable Bell violations. On the experimental side, we demonstrate certified multipartite Bell-operator correlations on a programmable superconducting processor, including a 73-qubit honeycomb model, by mapping Bell inequalities onto many-body Hamiltonians. We further introduce a bidirectional optimization framework that co-designs Bell inequalities and Hamiltonians for a given device, yielding stronger and more noise-resilient certification.
Correlations allowed by quantum mechanics can defy any classical explanation, with Bell nonlocality standing as their most profound and operationally powerful manifestation. While nonlocality has been demonstrated across a wide range of platforms, in many-body systems it has remained limited to ensembles of qubits, leaving the observation of higher-dimensional multipartite Bell correlations an open challenge. Here we report the observation of qutrit Bell correlations in a spin-1 87^{87}87Rb Bose-Einstein condensate via the violation of a Bell witness based on collective spin observables only. Exploiting spin-exchange collisions in an ensemble of N≃3.1×104N \simeq 3.1 \times 10^{4}N≃3.1×104 atoms, we generate spin-nematic squeezing of −11.8(7)-11.8(7)−11.8(7) dB and observe a violation that surpasses the minimum bound achievable by a collection of NNN qubits, providing direct evidence of genuine multipartite qutrit Bell correlations. Our results establish spinor Bose-Einstein condensates as a viable platform for investigating high-dimensional Bell correlations in the many-body regime, and demonstrate that coarse-grained collective measurements suffice to certify the dimensionality of quantum correlations at macroscopic scales.
Multipartite Bell tests provide a correlation-only route to benchmarking quantum processors, but their application at large scales is hindered by the rapid decay of many-body correlators under noise and exponentially many terms in conventional Bell expressions. Here we address these scalability obstacles by introducing a finite-setting generalized Mermin family of state-tailored Bell inequalities with analytic certification bounds, in which the measurement-setting number mmm provides an additional certification dimension complementary to the system size nnn. We show that, for the powers-of-two setting choices considered here, increasing mmm leaves the ideal normalized multipartite quantum value unchanged while lowering the relevant classical bounds, thereby strengthening the Bell-violation ratios and yielding an improved noise-robustness scaling compared to the standard Mermin inequality. We test this construction experimentally on a programmable superconducting processor by preparing Greenberger-Horne-Zeilinger (GHZ) states of up to 80 qubits. Using randomized sampling for direct Bell-operator estimation, we observe Bell ratios that grow exponentially with system size, certify a nonlocality depth of 14, and show that increasing mmm strengthens both the Bell ratio and depth certification. All results are obtained solely from measured correlators and analytical bounds, without readout correction, tomography, or model-based mitigation. Generalized Mermin inequalities therefore provide a sharper Bell benchmark for noisy large-scale GHZ states.
Combining recent advances in superconducting quantum hardware, we explore quantum correlations in a previously inaccessible regime by observing \emph{simultaneously} high-dimensional and many-body Bell non-locality. We report a high-confidence Bell violation in the correlations between two d=64d=64d=64-dimensional systems encoded in twelve qubits. For system sizes up to d=32d=32d=32, the strength of the observed nonlocal correlations exceeds the quantum upper bound for d=2d=2d=2 systems, providing direct evidence of high-dimensional nonlocality. Furthermore, we demonstrate that the observed violation is genuinely collective: all qubits contribute to the nonlocal correlations, while most pairwise correlations across the bipartition remain Bell-local. Our work illustrates how present-day quantum processors enable the exploration of fundamental predictions of quantum mechanics in previously inaccessible regimes and, in turn, how fundamental quantum effects can be used to benchmark their performance.