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    Network nonlocality without entanglement of all sources

    Kaushiki Mukherjee1,* and Biswajit Paul2,†

    • 1Department of Mathematics, Government Girls' General Degree College, Ekbalpore, Kolkata 700023, India
    • 2Department of Mathematics, Balagarh Bijoy Krishna Mahavidyalaya, Hooghly, West Bengal 712501, India

    • *Contact author: kaushiki.wbes@gmail.com
    • †Contact author: biswajitbbkm01082019@gmail.com

    Phys. Rev. A 112, 032401 – Published 2 September, 2025

    DOI: https://doi.org/10.1103/hypy-f9bf

    Abstract

    Entanglement and nonlocality are two important nonclassical features of quantum correlations. Recently the study of quantum correlations in networks has undergone remarkable progress owing to technological development towards scalable quantum networks. However, compared to the standard Bell scenario, manifestation of the interplay between these two aspects has received less attention in network scenarios featuring independent sources. In this work we have analyzed the relation between entanglement content of the sources and detectable non-n-locality in two distinct network topologies (linear and star). We have studied the extremal violations of n-local inequalities (compatible with linear and star network) for any fixed amount of entanglement (in terms of concurrence) of the independent sources. It is observed that each of the sources must be entangled for detecting non-n-locality in a linear network. However, the same is not true for star n-local network. The present analysis reveals that entanglement of all the independent sources is not a necessity for generation of non-n-local correlations in star topology. Characterization of sources in terms of the minimum entanglement requirement for any fixed violation amount of the n-local inequalities is also provided. Interestingly, detection of non-n-locality is ensured in the network if product of concurrence of all the sources involved exceeds 12.

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