{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:26:07Z","timestamp":1763537167612,"version":"3.45.0"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"JSPS","award":["25K07036"],"award-info":[{"award-number":["25K07036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:p>In this paper we investigate quantum Hellinger type divergences which were studied by Bhatia-Gaubert-Jain (2019), Pitrik-Virosztek (2020), and Dinh-Lie-Osaka-Phan (2025). In particular, when [Formula: see text] is a convex function defined by the form [Formula: see text] ([Formula: see text]) and [Formula: see text] is an operator monotone function with [Formula: see text], we introduce the quantum quantitative measure [Formula: see text] for positive definite matrices [Formula: see text] and [Formula: see text], and show that [Formula: see text] is a quantum divergence in the sense of Bhatia-Gaubert-Jain and also show that it is jointly convex and satisfies the data processing property by a trace preserving positive unital map [Formula: see text], that is, [Formula: see text].<\/jats:p>","DOI":"10.1142\/s1230161225500131","type":"journal-article","created":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:21:11Z","timestamp":1763536871000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized Quantum Hellinger Divergences Generated by Monotone Functions"],"prefix":"10.1142","volume":"32","author":[{"given":"Hiroyuki","family":"Osaka","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, 525-8577 Japan"}]},{"given":"Hiroki","family":"Shudo","sequence":"additional","affiliation":[{"name":"Graduate school of science and engineering, Ritsumeikan University, Kusatsu, Shiga, 525-8577 Japan"}]}],"member":"219","published-online":{"date-parts":[[2025,11,15]]},"reference":[{"key":"S1230161225500131BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55978-8"},{"key":"S1230161225500131BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0653-8"},{"volume-title":"Positive definite matrices","year":"2007","author":"Bhatia R.","key":"S1230161225500131BIB003"},{"key":"S1230161225500131BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.exmath.2018.01.002"},{"key":"S1230161225500131BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-019-01156-0"},{"issue":"1","key":"S1230161225500131BIB006","first-page":"143","volume":"28","author":"Dinh T. H.","year":"2025","journal-title":"MIA"},{"key":"S1230161225500131BIB007","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0807965106"},{"key":"S1230161225500131BIB008","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1102518108"},{"key":"S1230161225500131BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.09.007"},{"key":"S1230161225500131BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-33-4199-9"},{"key":"S1230161225500131BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X17500234"},{"key":"S1230161225500131BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-04150-6"},{"issue":"1","key":"S1230161225500131BIB013","first-page":"66","volume":"94","author":"Hiai F.","year":"2022","journal-title":"Integral. Equa. Oper. Theory"},{"key":"S1230161225500131BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BF01371042"},{"key":"S1230161225500131BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2024.06.005"},{"key":"S1230161225500131BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-02104-6_5"},{"key":"S1230161225500131BIB017","first-page":"311","volume":"36","author":"Pedersen G. K.","year":"1972","journal-title":"Proc. Amer. Math. Soc."},{"key":"S1230161225500131BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s11005-020-01282-0"},{"key":"S1230161225500131BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/0034-4877(75)90061-0"},{"key":"S1230161225500131BIB020","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781316036587"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161225500131","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T07:21:15Z","timestamp":1763536875000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161225500131"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":20,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["10.1142\/S1230161225500131"],"URL":"https:\/\/doi.org\/10.1142\/s1230161225500131","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"type":"print","value":"1230-1612"},{"type":"electronic","value":"1793-7191"}],"subject":[],"published":{"date-parts":[[2025,9]]},"article-number":"2550013"}}