{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:48:58Z","timestamp":1760150938382,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T00:00:00Z","timestamp":1644192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971140"],"award-info":[{"award-number":["11971140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As already known by Rana\u2019s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [\u221212,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are \u221212. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is \u221212 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.<\/jats:p>","DOI":"10.3390\/e24020247","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T08:38:48Z","timestamp":1644223128000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Characterization of Maximally Entangled Two-Qubit States"],"prefix":"10.3390","volume":"24","author":[{"given":"Junjun","family":"Duan","sequence":"first","affiliation":[{"name":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6220-4218","authenticated-orcid":false,"given":"Lin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quan","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2412-8626","authenticated-orcid":false,"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"},{"name":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1103\/PhysRevLett.77.1413","article-title":"Separability criterion for density matrices","volume":"77","author":"Peres","year":"1996","journal-title":"Phys. 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