{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T10:43:34Z","timestamp":1756896214608,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> In this note, we mainly study the necessary and sufficient conditions for the complete positivity of generalizations of depolarizing and transpose-depolarizing channels. Specifically, we define [Formula: see text] and [Formula: see text], where [Formula: see text] (the set of all bounded linear operators on the finite-dimensional Hilbert space [Formula: see text] is given and [Formula: see text] is the transpose of [Formula: see text] in a fixed orthonormal basis of [Formula: see text] First, we show that [Formula: see text] is completely positive if and only if [Formula: see text] is a positive map, which is equivalent to [Formula: see text] Moreover, [Formula: see text] is a completely positive map if and only if [Formula: see text] and [Formula: see text] At last, we also get that [Formula: see text] is a completely positive map if and only if [Formula: see text] with [Formula: see text] for all [Formula: see text] where [Formula: see text] are eigenvalues of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1230161221500062","type":"journal-article","created":{"date-parts":[[2021,12,21]],"date-time":"2021-12-21T02:47:10Z","timestamp":1640054830000},"source":"Crossref","is-referenced-by-count":2,"title":["Complete Positivity of Two Class of Maps Involving Depolarizing and Transpose-Depolarizing Channels"],"prefix":"10.1142","volume":"28","author":[{"given":"Xiuhong","family":"Sun","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an University of Science and Technology, Xi\u2019an 710054, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an, 710062, People\u2019s Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,12,21]]},"reference":[{"key":"S1230161221500062BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s11080-005-4482-3"},{"key":"S1230161221500062BIB002","first-page":"250","volume":"3","author":"Choi M. 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