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Advanced Quantum Technologies

Witnessing Full Quantum Network Nonlocality by Employing Fewer Bell‐Like Inequalities

Shuyuan Yang, Kan He, Jinchuan Hou

Published Feb 1, 2026• 1 citation
Publisher

Abstract

ABSTRACT Full quantum network nonlocality (FQNN) is an innovative perspective which signifies that all sources within the network exhibit quantum characteristics. So far, FQNN has been certified by violating a single Bell‐like inequality, but only for star networks. No such test exists for general topologies. (Luo et al., Phys. Rev. A 110, 022617 (2024)) suggested iterating the FQNN criteria of star networks to cover general networks, since any general network can be decomposed into a collection of star subnetworks. However, this method requires a large number of inequalities for large networks. This paper aims to clarify how a smaller set of Bell‐like inequalities can be employed to detect FQNN in general networks. By exploiting the structural features of the network, we derive a new class of inequalities. Violations of these inequalities reveal the locations of several quantum sources, enabling the detection of overall FQNN with fewer tests. We demonstrate the advantage of our approach explicitly for two types of networks, ‐layer ‐forked tree‐shaped and Bethe lattice networks. We demonstrate an exponential reduction in the number of Bell‐like inequalities required to witness FQNNs on these two types of networks.

DOI
10.1002/qute.70224

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ABSTRACT Full quantum network nonlocality (FQNN) is an innovative perspective which signifies that all sources within the network exhibit quantum characteristics. So far, FQNN has been certified by violating a single Bell‐like inequality, but only for star networks. No such test exists for general topologies. (Luo et al., Phys. Rev. A 110, 022617 (2024)) suggested iterating the FQNN criteria of star networks to cover general networks, since any general network can be decomposed into a collection of star subnetworks. However, this method requires a large number of inequalities for large networks. This paper aims to clarify how a smaller set of Bell‐like inequalities can be employed to detect FQNN in general networks. By exploiting the structural features of the network, we derive a new class of inequalities. Violations of these inequalities reveal the locations of several quantum sources, enabling the detection of overall FQNN with fewer tests. We demonstrate the advantage of our approach explicitly for two types of networks, ‐layer ‐forked tree‐shaped and Bethe lattice networks. We demonstrate an exponential reduction in the number of Bell‐like inequalities required to witness FQNNs on these two types of networks.
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.
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.
Quantum networks play an important role in the fields of quantum information and quantum computation. One of the current problems for these networks concerns nonlocality. Characterizing and detecting nonlocality is relevant to the implementation of quantum networks and quantum repeaters, where Bell inequalities can be used to test if configurations are prepared correctly. This report contains an overview of an iterative method to find Bell inequalities for networks. Starting from a given network, this method constructs a new Bell inequality for a network containing one additional source and one additional party. We use this procedure to find new Bell inequalities for specific network structures and analyse how these can be used to detect nonlocality within a network. In the first part the Bell inequalities are considered from a more theoretical point of view. We focus on star-shaped networks and discuss violations predicted by quantum mechanics. We look for quantitative bounds describing a set of states that lead to violation, giving an indication of the required quality of the sources. Finally this method is applied to a setup similar to the one described by Bernien et al. We consider a network consisting of three parties and two sources. The effect of errors during preparation of an entangled pair of photons on the ability to detect nonlocality is evaluated. The same is done for the effect of measurement errors. Using numerical computations we show that violation of the Bell inequality can be improved by choosing different measurement angles.
The nonlocality arising in a multiparty network involving multiple independent sources radically differs from the standard multipartite Bell nonlocality involving a single source. The notion of the full network nonlocality (FNN) [A. Pozas-Kerstjens et al., Full network nonlocality, Phys. Rev. Lett. 128, 010403 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.010403] characterizes the quantum correlations that cannot be reproduced by a local-nonlocal model featuring one local source and the rest of nonlocal no-signaling sources. However, the demonstration of FNN was limited to bilocal and trilocal star-shaped network scenarios involving three or two dichotomic measurements for edge parties. In this Letter, we first demonstrate that a large class of prevailing network inequalities does not exhibit FNN. We then introduce an elegant set of arbitrary-party and unbounded-input network inequalities in star-shaped and linear-chain networks whose optimal quantum violation exhibits FNN, certifying that the nonlocality is genuinely distributed to the entire network. Contrasting to existing demonstrations of FNN that inevitably require fixed-input and four-output elegant joint measurements for the central party, our generalized inequalities are more experimentally friendly, requiring only two output measurements. Moreover, our derivation of optimal quantum violation is fully analytic and devoid of assuming the dimension of the quantum system, thereby showcasing its potential for device-independent self-testing.
Abstract Quantum networks with multiple sources always face performance challenges due to the vulnerability of quantum systems. Thus, it is highly desirable to have the capability to continuously monitor and determine the exact number of quantum sources versus classical sources present within the network. Hierarchical network nonlocality can reveal the relationship between network nonlocality and the number of quantum sources within the network, thus becoming a way to address the aforementioned issue. However, up to now, precise hierarchical network nonlocality inequalities have only been established for star networks, and cannot be obtained for other non-star structured networks [Phys. Rev. Lett. 128 010403 (2022) and Phys. Rev. A 110 022617 (2024)]. In this paper, we establish more refined criteria for hierarchical network nonlocality inequalities in arbitrary network structures. Violating such inequalities can reveal the exact number of quantum sources in the network. These results enhance the understanding of quantum source distribution in complex network topologies.
Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalization to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analyzing local and theory-independent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input-output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum elegant joint measurements.