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Quantum Reports

Verifying Quantum Network Nonlocality Based on the Extended Mermin Inequality

LI Xinyue, Yi Yang, Ming‐Xing Luo

Published May 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.3390/quantum8020041

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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.
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.
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.
Genuine multipartite nonlocality and nonlocality arising in networks composed of several independent sources have been separately investigated. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources allows for the certification of the non-classicality of all sources. In this paper, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high fidelity photonic quantum network by violating a single network Bell inequality.
Abstract The Greenberger–Horne–Zeilinger (GHZ) paradox shows that it is possible to create a multipartite state involving three or more particles in which the measurement outcomes of the particles are correlated in a way that cannot be explained by classical physics. We extend it to witness quantum networks. We first extend the GHZ paradox to simultaneously verify the GHZ state and Einstein–Podolsky–Rosen states on triangle networks. We then extend the GHZ paradox to witness the entanglement of chain networks consisting of multiple GHZ states. All the present results are robust against the noise.
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 and nonlocality arising in networks composed of several independent sources have been investigated separately. While some genuinely entangled states cannot be verified by violating a single Bell-type inequality, a quantum network consisting of different sources enables the certification of the nonclassicality of all sources. In this Letter, we propose the first method to verify both types of nonlocality simultaneously in a single experiment. We consider a quantum network comprising a bipartite source and a tripartite source. We demonstrate that there are quantum correlations that cannot be simulated if the tripartite source distributes biseparable systems while the bipartite source distributes even stronger-than-quantum systems. These correlations can be used to verify both the genuine multipartite nonlocality of generalized Greenberger-Horne-Zeilinger states and the full network nonlocality that is stronger than all the existing results. Experimentally, we observe both types of nonlocality in a high-fidelity photonic quantum network by violating a single network Bell inequality.