{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T05:04:57Z","timestamp":1780549497037,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T00:00:00Z","timestamp":1779926400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["24CX03003A and 26CX03002A"],"award-info":[{"award-number":["24CX03003A and 26CX03002A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR2023MA025 and ZR2025LLZ005"],"award-info":[{"award-number":["ZR2023MA025 and ZR2025LLZ005"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Nonlinear entanglement witnesses constructed from multiple linear entanglement witnesses and multiple copies of quantum states have recently been proposed as a powerful tool for entanglement detection. In this work, we show, via an explicit counterexample, that the fineness of linear witnesses generally fails to transfer to their tensor-product nonlinear counterparts. For the canonical family of nonlinear witnesses in the form of (\u03b1I\u2212L)\u2297(\u03b2I\u2212T), we rigorously prove that the optimal nonlinear witness is uniquely attained with weakly optimal parameters of \u03b1=\u03bbmax(L) and \u03b2=\u03bbmax(T). Meanwhile, we analytically demonstrate that the self-tensor products of two representative linear witnesses fail to detect any entangled state. The question of whether a nonlinear entanglement witness capable of detecting entanglement can be constructed by tensoring a linear witness with itself remains open.<\/jats:p>","DOI":"10.3390\/e28060608","type":"journal-article","created":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:17:31Z","timestamp":1780467451000},"page":"608","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Optimization and Self-Tensoring Construction of Nonlinear Entanglement Witnesses"],"prefix":"10.3390","volume":"28","author":[{"given":"Juan","family":"Yu","sequence":"first","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Li","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shu-Qian","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,28]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. 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