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

Laser Physics Letters

Detection of nonlocality for high-dimensional quantum states via dimensional reduction

Minglei Wan, Li Xu, Jing Wang, Ming Li

Published Sep 1, 2026• 0 citations
Publisher

Abstract

Abstract This paper investigates the problem of nonlocality detection for high-dimensional quantum states. To overcome the complexity of measurement settings and Bell-operator optimization in high-dimensional systems, we propose a nonlocality detection framework based on dimensional reduction and chained Bell inequalities. By employing local projection operators, arbitrary high-dimensional bipartite quantum states are mapped onto effective two-qubit subsystems. We prove that if any projected subsystem violates a chained Bell inequality, then the original high-dimensional quantum state must be nonlocal. Furthermore, the framework is generalized to multipartite quantum systems. By projecting multipartite high-dimensional states onto effective multiqubit states and applying Svetlichny inequalities, sufficient criteria for detecting genuine multipartite nonlocality are established. Our approach significantly reduces the complexity of nonlocality detection in high-dimensional systems and provides a scalable theoretical framework for studying nonlocal correlations in complex quantum systems.

DOI
10.1088/1612-202x/ae9ea3

Related papers

Wigner-approach-enabled detection of multipartite nonlocality using all different bipartitions

Sumit Nandi, Debashis Saha, Dipankar Home +1 more

Distinct from Bell's approach, Wigner derived a form of local realist (LR) inequality which is quantum-mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such a generalized Wigner inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present paper, this limitation has been overcome by formulating a further generalization of Wigner's approach through the derivation of a set of LR inequalities with respect to all different bipartitions of a $N$-partite system. Quantum-mechanical violations of all individual LR inequalities belonging to such a set would rigorously certify multipartite nonlocality by also providing a finer characterization of the nature of multipartite nonlocality in the following sense. The quantum-mechanical violation of any given inequality of our complete set of LR inequalities would enable identification of the corresponding bipartition which exhibits nonlocality. This is in contrast to other multipartite LR inequalities such as the Svetlichny inequality or its generalization that cannot be used to detect whether there is any particular bipartition which is nonlocally correlated. The efficacy of the scheme developed in this paper is illustrated for the tripartite and quadripartite states.

arXiv:2202.11475•Physical Review A•Dec 2, 2022•5 citations

Observing High-Dimensional Nonlocality using Multi-Outcome Spectral Measurements

Jonathan Leach, Kiki Dekkers, Laura Serino +5 more

Abstract Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements, since the emulation of these with separate dichotomic projections opens a binarisation loophole that local hidden variable theories can exploit. Here we show that the joint spectral intensity of a two-photon entangled state contains access to the necessary multi-outcome measurements to overcome this obstacle and certify nonlocality for high-dimensional states. This result is contrary to the belief that the joint spectral intensity is a phase-insensitive quantity and does not have sufficient information to certify entanglement or nonlocality. Using this approach, we violate the CGLMP Bell inequality up to dimension d = 8, all with negligible p-values, and for the first time close the binarisation loophole in high-dimensional Bell experiments. Guaranteeing nonlocal correlations using frequency-only measurements removes the technological hurdle of measurements in the temporal domain, thus greatly simplifying any practical implementation of future high-dimensional quantum information protocols.

•Aug 19, 2025•0 citations

Single Bell inequality to detect genuine nonlocality in three-qubit pure genuinely entangled states

Ignacy Stachura, Owidiusz Makuta, Remigiusz Augusiak

Abstract It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in Curchod et al (2019 New J. Phys. 21 023016) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver finer Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.

arXiv:2406.14078•New Journal of Physics•Sep 1, 2024•2 citations

Characterizing nonlocal correlations through various n -locality inequalities in a quantum network

Sneha Munshi, A. K. Pan

The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. Despite the initial independence of resources, the multiple observers in the network can suitably choose measurements on their local subsystems and generate a form of quantum nonlocality across the network. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin et al. [Phys. Rev. A 96, 020304 (2017)] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Furthermore, we propose a set of $n$-locality inequalities in a star-network configuration where each of the $n$ parties performs an arbitrary number of dichotomic measurements and demonstrates the above correspondence between the quantum violations of the $n$-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of $n$-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.

arXiv:2112.15451•Physical Review A•Mar 30, 2022•23 citations

Unbounded sequential multipartite nonlocality via violation of Mermin inequality

Bang-Zhu Shen, Mao-Sheng Li

Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in $n$-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.

arXiv:2406.11466•Jun 17, 2024•0 citations

The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy

Gerard Anglès Munné, Paweł Cieśliński, Jan Wójcik +1 more

Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict monogamy: a violation of one inequality precludes violations of other inequalities on the overlapping subsystems. In the multipartite setting, however, Bell nonlocality becomes inherently polygamous. This was previously shown for subsystems obtained by removing a single particle from an $N$-partite system. Here, we generalize this result to arbitrary $(N-k)$-partite subsystems. We demonstrate that a single $N$-qubit state can violate all $\binom{N}{k}$ relevant Bell inequalities simultaneously. We further construct an $N$-qubit Bell inequality, obtained by symmetrizing the $(N-k)$-qubit ones, that is maximally violated by states exhibiting this generalized polygamy. We compare these violations with those achievable by GHZ states and show that polygamy offers an advantage in multipartite scenarios, providing new insights into scalable certification of non-classicality in quantum devices. Our analysis relies on symmetry properties of the MABK inequalities. Finally, we show that this behavior can occur across multiple subsystem sizes, a phenomenon we call hyper-polygamy. These structures reveal the remarkable abundance of nonlocality present in multipartite quantum states and offer perspectives for their applications in quantum technologies.

quant-pharXiv:2512.09034•Advanced Quantum Technologies•Dec 11, 2025•0 citations
Abstract This paper investigates the problem of nonlocality detection for high-dimensional quantum states. To overcome the complexity of measurement settings and Bell-operator optimization in high-dimensional systems, we propose a nonlocality detection framework based on dimensional reduction and chained Bell inequalities. By employing local projection operators, arbitrary high-dimensional bipartite quantum states are mapped onto effective two-qubit subsystems. We prove that if any projected subsystem violates a chained Bell inequality, then the original high-dimensional quantum state must be nonlocal. Furthermore, the framework is generalized to multipartite quantum systems. By projecting multipartite high-dimensional states onto effective multiqubit states and applying Svetlichny inequalities, sufficient criteria for detecting genuine multipartite nonlocality are established. Our approach significantly reduces the complexity of nonlocality detection in high-dimensional systems and provides a scalable theoretical framework for studying nonlocal correlations in complex quantum systems.
Distinct from Bell's approach, Wigner derived a form of local realist (LR) inequality which is quantum-mechanically violated for a bipartite maximally entangled state. Subsequently, this approach was generalized to obtain a multipartite LR inequality. However, the violation of such a generalized Wigner inequality does not guarantee nonlocality between all possible different bipartitions of the multipartite system. In the present paper, this limitation has been overcome by formulating a further generalization of Wigner's approach through the derivation of a set of LR inequalities with respect to all different bipartitions of a NNN-partite system. Quantum-mechanical violations of all individual LR inequalities belonging to such a set would rigorously certify multipartite nonlocality by also providing a finer characterization of the nature of multipartite nonlocality in the following sense. The quantum-mechanical violation of any given inequality of our complete set of LR inequalities would enable identification of the corresponding bipartition which exhibits nonlocality. This is in contrast to other multipartite LR inequalities such as the Svetlichny inequality or its generalization that cannot be used to detect whether there is any particular bipartition which is nonlocally correlated. The efficacy of the scheme developed in this paper is illustrated for the tripartite and quadripartite states.
Abstract Violation of Bell inequalities is an essential requirement for many quantum information and communication protocols. In high-dimensional systems, Bell inequality tests face the challenge of implementing genuinely multi-outcome measurements, since the emulation of these with separate dichotomic projections opens a binarisation loophole that local hidden variable theories can exploit. Here we show that the joint spectral intensity of a two-photon entangled state contains access to the necessary multi-outcome measurements to overcome this obstacle and certify nonlocality for high-dimensional states. This result is contrary to the belief that the joint spectral intensity is a phase-insensitive quantity and does not have sufficient information to certify entanglement or nonlocality. Using this approach, we violate the CGLMP Bell inequality up to dimension d = 8, all with negligible p-values, and for the first time close the binarisation loophole in high-dimensional Bell experiments. Guaranteeing nonlocal correlations using frequency-only measurements removes the technological hurdle of measurements in the temporal domain, thus greatly simplifying any practical implementation of future high-dimensional quantum information protocols.
Abstract It remains an open question whether every pure multipartite state that is genuinely entangled is also genuinely nonlocal. Recently, a new general construction of Bell inequalities allowing the detection of genuine multipartite nonlocality (GMNL) in quantum states was proposed in Curchod et al (2019 New J. Phys. 21 023016) with the aim of addressing the above problem. Here we show how, in a simple manner, one can improve this construction to deliver finer Bell inequalities for detection of GMNL. Remarkably, we then prove one of the improved Bell inequalities to be powerful enough to detect GMNL in every three-qubit genuinely entangled state. We also generalize some of these inequalities to detect not only GMNL but also nonlocality depth in multipartite states and we present a possible way of generalizing them to the case of more outcomes.
The multipartite quantum networks feature multiple independent sources, in contrast to the conventional multipartite Bell experiment involving a single source. Despite the initial independence of resources, the multiple observers in the network can suitably choose measurements on their local subsystems and generate a form of quantum nonlocality across the network. So far, network nonlocality has been explored when each source produces a two-qubit entangled state. In this work we demonstrate the network nonlocality when each party performs a black-box measurement, and the dimension of the system remains unspecified. In an interesting work, by considering each source produces two-qubit entangled states in the conventional bilocal scenario, Gisin et al. [Phys. Rev. A 96, 020304 (2017)] demonstrated a correspondence between the violations of bipartite Clauser-Horne-Shimony-Halt inequality and the bilocality inequality. We introduce a variant of the sum-of-squares approach to reproduce their results without assuming the dimension of the system. We then generalize the argument for network nonlocality in star-network topology. Furthermore, we propose a set of nnn-locality inequalities in a star-network configuration where each of the nnn parties performs an arbitrary number of dichotomic measurements and demonstrates the above correspondence between the quantum violations of the nnn-locality inequalities and the chained Bell inequalities. A similar correspondence is demonstrated based on a recently formulated family of nnn-locality inequalities whose optimal quantum violation cannot be obtained when each source emits a two-qubit entangled state and requires multiple copies of two-qubit entangled states. Throughout this paper, each party in the network performs black-box measurements, and the dimension of the system remains unspecified.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.
Non-classical quantum correlations underpin both the foundations of quantum mechanics and modern quantum technologies. Among them, Bell nonlocality is a central example. For bipartite Bell inequalities, nonlocal correlations obey strict monogamy: a violation of one inequality precludes violations of other inequalities on the overlapping subsystems. In the multipartite setting, however, Bell nonlocality becomes inherently polygamous. This was previously shown for subsystems obtained by removing a single particle from an NNN-partite system. Here, we generalize this result to arbitrary (N−k)(N-k)(N−k)-partite subsystems. We demonstrate that a single NNN-qubit state can violate all (Nk)\binom{N}{k}(kN​) relevant Bell inequalities simultaneously. We further construct an NNN-qubit Bell inequality, obtained by symmetrizing the (N−k)(N-k)(N−k)-qubit ones, that is maximally violated by states exhibiting this generalized polygamy. We compare these violations with those achievable by GHZ states and show that polygamy offers an advantage in multipartite scenarios, providing new insights into scalable certification of non-classicality in quantum devices. Our analysis relies on symmetry properties of the MABK inequalities. Finally, we show that this behavior can occur across multiple subsystem sizes, a phenomenon we call hyper-polygamy. These structures reveal the remarkable abundance of nonlocality present in multipartite quantum states and offer perspectives for their applications in quantum technologies.