Unbounded-input explicit Bell inequalities for general quantum networks

• URL: http://arxiv.org/abs/2509.04767v1
• Date: Fri, 05 Sep 2025 02:54:58 GMT
• Title: Unbounded-input explicit Bell inequalities for general quantum networks
• Authors: Yao Xiao, Fenzhuo Guo, Haifeng Dong, Fei Gao,
• Abstract summary: Quantum nonlocality in networks underpins large-scale quantum communication and poses fundamental challenges for its characterization.<n>We construct a family of explicit nonlinear Bell inequalities to verify the nonlocality across the general multi-input quantum networks.<n>We demonstrate that these inequalities can, in a device-independent manner, distinguish between network topologies of equal size that differ in the number of leaf nodes.
• Score: 11.96589786407141
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum nonlocality in networks featuring multiple independent sources underpins large-scale quantum communication and poses fundamental challenges for its characterization. In this work, we construct a family of explicit nonlinear Bell inequalities to verify the nonlocality across the general multi-input quantum networks. The construction of these inequalities relies on the number of leaf nodes, a network parameter that can be identified by a linear-time algorithm. Our approach establishes a structural connection between bipartite full-correlation Bell inequalities and network Bell inequalities, enabling the analytical derivation of optimal quantum violations and the conditions under which they occur. We further quantify the upper bound on maximal violations achievable by arbitrary two-qubit mixed states in such networks, under separable measurements, and evaluate the noise robustness of the proposed inequalities via the visibilities of Werner states. Finally, we demonstrate that these inequalities can, in a device-independent manner, distinguish between network topologies of equal size that differ in the number of leaf nodes.

Related papers

• Local models and Bell inequalities for the minimal triangle network [84.67234803583032]
  Nonlocal correlations enable surprising phenomena in quantum information and quantum foundations.<n>We study one of the simplest scenarios, namely that of distributions invariant under permutations of parties in the minimal triangle network.<n>We provide new insights on the existence of a classical-quantum gap in the triangle network with binary outcomes.
  arXiv  Detail & Related papers  (2025-03-20T19:11:06Z)
• Asymptotic robustness of entanglement in noisy quantum networks and graph connectivity [46.44827993583994]
  We show that when the links are noisy two drastically different behaviors can occur regarding the global entanglement properties of the network. While in certain configurations the network displays genuine multipartite entanglement (GME) for any system size provided the noise level is below a certain threshold, in others GME is washed out if the system size is big enough for any fixed non-zero level of noise.
  arXiv  Detail & Related papers  (2024-11-19T15:01:50Z)
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs [0.0]
  Bell experiment in the network gives rise to a form of quantum nonlocality which is conceptually different from traditional multipartite Bell nonlocality. We introduce an elegant sum-of-squares approach that enables the optimization in quantum theory without specifying the dimension of the quantum system.
  arXiv  Detail & Related papers  (2023-11-08T11:51:04Z)
• Hierarchical certification of nonclassical network correlations [50.32788626697182]
  We derive linear and nonlinear Bell-like inequalities for networks, whose violation certifies the absence of a minimum number of classical sources in them. We insert this assumption, which leads to results more amenable to certification in experiments.
  arXiv  Detail & Related papers  (2023-06-27T18:00:01Z)
• Persistency of non-n-local correlations in noisy linear networks [0.0]
  Linear n-local networks are compatible with quantum repeaters based entanglement distribution protocols. Error in entanglement generation, communication over noisy quantum channels and imperfections in measurements result in decay of quantumness across such networks.
  arXiv  Detail & Related papers  (2022-08-14T14:47:07Z)
• Bell inequalities for nonlocality depth [0.0]
  When three or more particles are considered, quantum correlations can be stronger than correlations generated by so-called hybrid local hidden variable models. We provide an exhaustive classification of Bell inequalities to characterize various hybrid scenarios in four- and five-particle systems.
  arXiv  Detail & Related papers  (2022-05-09T13:03:03Z)
• Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
  We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
  arXiv  Detail & Related papers  (2022-03-30T18:00:00Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Full network nonlocality [68.8204255655161]
  We introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. We show that the most well-known network Bell test does not witness full network nonlocality. More generally, we point out that established methods for analysing local and theory-independent correlations in networks can be combined in order to deduce sufficient conditions for full network nonlocality.
  arXiv  Detail & Related papers  (2021-05-19T18:00:02Z)
• Exploring Bell nonlocality of quantum networks with stabilizing and logical operators [0.0]
  Knowing the stabilizing and logical operators indeed provides a new way of exploring Bell non-locality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. The tilted nonlinear Bell inequalities tailored for specific non-maximal entangled stabilizer states are also explored.
  arXiv  Detail & Related papers  (2021-05-09T05:13:41Z)
• Maximal qubit violation of n-local inequalities in quantum network [0.0]
  Source independent quantum networks are considered as a natural generalization to the Bell scenario. We consider the complexities in the quantum networks with an arbitrary number of parties distributed in chain-shaped and star-shaped networks.
  arXiv  Detail & Related papers  (2020-11-06T18:45:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.