{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:48:14Z","timestamp":1764859694560,"version":"3.41.2"},"reference-count":51,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","funder":[{"name":"Japan\u2019s MEXT Quantum Leap Flagship","award":["JPMXS0120319794"],"award-info":[{"award-number":["JPMXS0120319794"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2024,12]]},"abstract":"<jats:p> Complete positivity (CP) of a quantum dynamical map (QDM) is, in general, difficult to show when its master equation (ME) does not conform to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The GKSL ME describes Markovian dynamics, comprising a unitary component with time-independent Hermitian operators and a nonunitary component with time-independent Lindblad operators and positive time-independent damping rates. Recently, non-Markovian dynamics have received growing attention, and the various types of GKSL-like MEs with time-dependent operators are widely discussed; however, rigorous discussions on their CP conditions remain limited. This paper presents conditions for QDMs to be CP, whose MEs take the GKSL-like form with arbitrary time dependence. One case considered is where its ME takes the time-local integro-differential GKSL-like form, which includes CP-divisible cases. Another case considered is where the ME is time-non-local but can be approximated to be time-local in the weak-coupling regime. As a special case of the time-non-local case, the same discussion holds for the time-convoluted GKSL-like form, which should be compared to previous studies. <\/jats:p>","DOI":"10.1142\/s1230161224500173","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T01:43:48Z","timestamp":1735609428000},"source":"Crossref","is-referenced-by-count":1,"title":["CP Conditions for GKSL-Like Master Equations"],"prefix":"10.1142","volume":"31","author":[{"given":"Akane","family":"Watanabe","sequence":"first","affiliation":[{"name":"Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Makoto","family":"Unoki","sequence":"additional","affiliation":[{"name":"Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiromichi","family":"Nakazato","sequence":"additional","affiliation":[{"name":"Department of Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takayuki","family":"Suzuki","sequence":"additional","affiliation":[{"name":"National Institute of Information and Communications Technology, 4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"doi-asserted-by":"publisher","key":"S1230161224500173BIB001","DOI":"10.1088\/0305-4470\/12\/5\/007"},{"doi-asserted-by":"publisher","key":"S1230161224500173BIB002","DOI":"10.1007\/3-540-70861-8_1"},{"key":"S1230161224500173BIB003","first-page":"041024","volume":"10","author":"Alipour S.","year":"2020","journal-title":"Phys. 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