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The aforementioned monotones can be utilized to identify states that are non-reachable from an initial state by the time evolution and include all constraints imposed by conserved quantities, providing a generalization of Noether's theorem for this class of dynamics. As a special case, the generator itself can be considered a symmetry, resulting in non-trivial constraints over the time evolution, even if all conserved quantities trivialize. The construction utilizes tools from quantum information-geometry, mainly the theory of monotone Riemannian metrics. We analyze the prototypical cases of dephasing and Davies generators.<\/jats:p>","DOI":"10.22331\/q-2020-04-30-261","type":"journal-article","created":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T13:11:50Z","timestamp":1588252310000},"page":"261","source":"Crossref","is-referenced-by-count":8,"title":["Symmetries and monotones in Markovian quantum dynamics"],"prefix":"10.22331","volume":"4","author":[{"given":"Georgios","family":"Styliaris","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Zanardi","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2020,4,30]]},"reference":[{"key":"0","unstructured":"Lev D. 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