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

Physica Scripta

Verifying quantum network nonlocality based on the extended Svetlichny inequality

LI Xinyue, Yan-Han Yang, Li-Ming Zhao, 罗明星

Published May 21, 2026• 0 citations
Publisher

Abstract

Abstract This work presents an extension of the Svetlichny inequality to star-topology quantum networks, enabling the verification of network nonlocality in distributed architectures. The proposed framework uses joint measurements at a central node to certify the entanglement properties between peripheral nodes after their local measurement collapse. We further generalize this methodology to composite quantum networks, constructed from multiple EPR pairs and featuring hybrid star-chain structures, thereby demonstrating its applicability to complex entanglement configurations.

DOI
10.1088/1402-4896/ae719b

Related papers

Verifying Quantum Network Nonlocality Based on the Extended Mermin Inequality

LI Xinyue, Yi Yang, Ming‐Xing Luo

This work proposes an extended Mermin inequality based on a hybrid classical model that involves only one classical source, with the remaining sources being post-quantum. In a chain-structured quantum network consisting of hybrid Einstein–Podolsky–Rosen (EPR) pairs and Greenberger–Horne–Zeilinger (GHZ) states, joint measurements are performed at the central node, while local measurements are conducted at the peripheral nodes. This setup shows that the obtained quantum correlations can violate the proposed inequality with fewer measurement settings, thereby verifying network nonlocality. Furthermore, we extend this method to chain networks of arbitrary length n and show that the proposed inequality remains effective in verifying network nonlocality.

Quantum Reports•May 1, 2026•0 citations

Verifying full quantum network nonlocality in arbitrary configurations by nonlinear Bell-like inequalities

Shuyuan Yang, Jinchuan Hou, Kan He +1 more

Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.

quant-pharXiv:2608.10972•Aug 12, 2026•0 citations

Certifying genuine multipartite nonlocality without inequality in quantum networks

Qing Fa Zhou, Xin-Yu Xu, Shu-Ming Hu +5 more

Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.

Physical Review A•May 22, 2023•3 citations

Device-independent verification of controlled non-local CNOT quantum gate

LI YiNing, GONG NengFei, TIAN YueHan +1 more

Controlled non-local quantum gate operations reveal the cooperative and supervisory relationships of the controller and the non-local gate operators in a quantum networks, which is an essential feature for building multi-party quantum computing networks, and their security relies on quantum entanglement resources. To understand the behavior of vendors who substitute quantum entanglement resources with classical-quantum hybrid resources, this paper proposes a device-independent verification scheme for controlled non-local CNOT quantum gates. Moreover, it formulates a Svetlichny-type inequality to conduct an effective verification of the utilization of entanglement resources in nonlocal gate operations, particularly in instances where the Svetlichny inequality is not applicable. Our scheme offers a theoretical foundation for constructing secure distributed quantum computing networks in the future.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Feb 24, 2025•0 citations

Network nonlocality with tripartite entangled sources

Sudip Chakrabarty, Amit Kundu

Quantum networks are built from independent sources, and their nonlocality has mostly been studied with sources that emit bipartite entangled states. A source of three entangled qubits is richer, since its nonlocality can be tested by the Mermin or the more demanding Svetlichny inequality. We ask how network nonlocality relates to these two single-source notions and find that the answer depends on the wiring. When two central nodes without inputs share every source, Bell-state measurements turn every Svetlichny violation into a network violation, and even all entangled generalised Greenberger-Horne-Zeilinger states violate the network inequality. When a single central node is shared, the relation reverses, and a network violation requires a Mermin violation of the source. With more sources, the maximal violation depends on whether their number is even or odd, and we give tight bounds for both cases. These results show that the way multipartite sources are wired decides which kind of nonlocality a network inherits.

quant-pharXiv:2610.35838•Oct 27, 2026•0 citations

Verifying hierarchical network nonlocality in general quantum networks

Shuyuan Yang, Jinchuan Hou, Kan He

Abstract Recently, a class of innovative notions on quantum network nonlocality (QNN), called full quantum network nonlocality (FQNN), have been proposed in Phys. Rev. Lett. 128 010403 (2022). As the generalization of full network nonlocality (FNN), l-level quantum network nonlocality (l-QNN) was defined in arxiv. 2306.15717 quant-ph (2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.

Chinese Physics B•Apr 12, 2024•4 citations
Abstract This work presents an extension of the Svetlichny inequality to star-topology quantum networks, enabling the verification of network nonlocality in distributed architectures. The proposed framework uses joint measurements at a central node to certify the entanglement properties between peripheral nodes after their local measurement collapse. We further generalize this methodology to composite quantum networks, constructed from multiple EPR pairs and featuring hybrid star-chain structures, thereby demonstrating its applicability to complex entanglement configurations.
This work proposes an extended Mermin inequality based on a hybrid classical model that involves only one classical source, with the remaining sources being post-quantum. In a chain-structured quantum network consisting of hybrid Einstein–Podolsky–Rosen (EPR) pairs and Greenberger–Horne–Zeilinger (GHZ) states, joint measurements are performed at the central node, while local measurements are conducted at the peripheral nodes. This setup shows that the obtained quantum correlations can violate the proposed inequality with fewer measurement settings, thereby verifying network nonlocality. Furthermore, we extend this method to chain networks of arbitrary length n and show that the proposed inequality remains effective in verifying network nonlocality.
Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
Controlled non-local quantum gate operations reveal the cooperative and supervisory relationships of the controller and the non-local gate operators in a quantum networks, which is an essential feature for building multi-party quantum computing networks, and their security relies on quantum entanglement resources. To understand the behavior of vendors who substitute quantum entanglement resources with classical-quantum hybrid resources, this paper proposes a device-independent verification scheme for controlled non-local CNOT quantum gates. Moreover, it formulates a Svetlichny-type inequality to conduct an effective verification of the utilization of entanglement resources in nonlocal gate operations, particularly in instances where the Svetlichny inequality is not applicable. Our scheme offers a theoretical foundation for constructing secure distributed quantum computing networks in the future.
Quantum networks are built from independent sources, and their nonlocality has mostly been studied with sources that emit bipartite entangled states. A source of three entangled qubits is richer, since its nonlocality can be tested by the Mermin or the more demanding Svetlichny inequality. We ask how network nonlocality relates to these two single-source notions and find that the answer depends on the wiring. When two central nodes without inputs share every source, Bell-state measurements turn every Svetlichny violation into a network violation, and even all entangled generalised Greenberger-Horne-Zeilinger states violate the network inequality. When a single central node is shared, the relation reverses, and a network violation requires a Mermin violation of the source. With more sources, the maximal violation depends on whether their number is even or odd, and we give tight bounds for both cases. These results show that the way multipartite sources are wired decides which kind of nonlocality a network inherits.
Abstract Recently, a class of innovative notions on quantum network nonlocality (QNN), called full quantum network nonlocality (FQNN), have been proposed in Phys. Rev. Lett. 128 010403 (2022). As the generalization of full network nonlocality (FNN), l-level quantum network nonlocality (l-QNN) was defined in arxiv. 2306.15717 quant-ph (2024). FQNN is a NN that can be generated only from a network with all sources being non-classical. This is beyond the existing standard network nonlocality, which may be generated from a network with only a non-classical source. One of the challenging tasks is to establish corresponding Bell-like inequalities to demonstrate the FQNN or l-QNN. Up to now, the inequality criteria for FQNN and l-QNN have only been established for star and chain networks. In this paper, we devote ourselves to establishing Bell-like inequalities for networks with more complex structures. Note that star and chain networks are special kinds of tree-shaped networks. We first establish the Bell-like inequalities for verifying l-QNN in k-forked tree-shaped networks. Such results generalize the existing inequalities for star and chain networks. Furthermore, we find the Bell-like inequality criteria for l-QNN for general acyclic and cyclic networks. Finally, we discuss the demonstration of l-QNN in the well-known butterfly networks.