{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:24:42Z","timestamp":1764174282826,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2016,9,21]],"date-time":"2016-09-21T00:00:00Z","timestamp":1474416000000},"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":["11401007","11301124","11371114","11301077"],"award-info":[{"award-number":["11401007","11301124","11371114","11301077"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We derive exactly the differential entropy of the joint distribution of eigenvalues of Wishart matrices. Based on this result, we calculate the differential entropy of the joint distribution of eigenvalues of random mixed quantum states, which is induced by taking the partial trace over the environment of Haar-distributed bipartite pure states. Then, we investigate the differential entropy of the joint distribution of diagonal entries of random mixed quantum states. Finally, we investigate the relative entropy between these two kinds of distributions.<\/jats:p>","DOI":"10.3390\/e18090342","type":"journal-article","created":{"date-parts":[[2016,9,21]],"date-time":"2016-09-21T10:11:26Z","timestamp":1474452686000},"page":"342","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices"],"prefix":"10.3390","volume":"18","author":[{"given":"Laizhen","family":"Luo","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China"},{"name":"School of Applied Science, Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiamei","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Anhui University of Technology, Ma\u2019Anshan 243032, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shifang","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,9,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/s10955-006-9058-2","article-title":"Differential entropy and dynamics of uncertainty","volume":"123","author":"Garbaczewski","year":"2006","journal-title":"J. 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