{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,18]],"date-time":"2026-07-18T16:57:18Z","timestamp":1784393838944,"version":"3.55.0"},"reference-count":43,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T00:00:00Z","timestamp":1652400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12171290"],"award-info":[{"award-number":["12171290"]}]},{"name":"National Natural Science Foundation of China","award":["12071336"],"award-info":[{"award-number":["12071336"]}]},{"name":"National Natural Science Foundation of China","award":["20200011"],"award-info":[{"award-number":["20200011"]}]},{"name":"Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province","award":["12171290"],"award-info":[{"award-number":["12171290"]}]},{"name":"Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province","award":["12071336"],"award-info":[{"award-number":["12071336"]}]},{"name":"Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province","award":["20200011"],"award-info":[{"award-number":["20200011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the last decade, much attention has been focused on examining the nonlocality of various quantum networks, which are fundamental for long-distance quantum communications. In this paper, we consider the nonlocality of any forked tree-shaped network, where each node, respectively, shares arbitrary number of bipartite sources with other nodes in the next \u201clayer\u201d. The Bell-type inequalities for such quantum networks are obtained, which are, respectively, satisfied by all (tn\u22121)-local correlations and all local correlations, where tn denotes the total number of nodes in the network. The maximal quantum violations of these inequalities and the robustness to noise in these networks are also discussed. Our network can be seen as a generalization of some known quantum networks.<\/jats:p>","DOI":"10.3390\/e24050691","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T09:27:56Z","timestamp":1652520476000},"page":"691","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Quantum Nonlocality in Any Forked Tree-Shaped Network"],"prefix":"10.3390","volume":"24","author":[{"given":"Lihua","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematical Science, Shanxi University, Taiyuan 030006, China"},{"name":"School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofei","family":"Qi","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Shanxi University, Taiyuan 030006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6534-9228","authenticated-orcid":false,"given":"Jinchuan","family":"Hou","sequence":"additional","affiliation":[{"name":"College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1103\/PhysRev.47.777","article-title":"Can quantum-mechanical description of physical reality be considered complete?","volume":"47","author":"Einstein","year":"1935","journal-title":"Phys. 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