{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:27:45Z","timestamp":1753882065605,"version":"3.41.2"},"reference-count":53,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p> We generalize a recent result stating that all analytic quantum dynamics can be represented exactly as the reduction of unitary dynamics generated by a time- dependent Hamiltonian. More precisely, we prove that the partial trace over analytic paths of unitaries can approximate any Lipschitz-continuous quantum dynamics arbitrarily well. Equivalently, all such dynamics can be approximated by analytic Kraus operators. We conclude by discussing potential improvements and generalizations of these results, their limitations, and the general challenges one has to overcome when trying to relate dynamics to quantities on the system\u2013environment level. <\/jats:p>","DOI":"10.1142\/s1230161224500045","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T07:14:27Z","timestamp":1712560467000},"source":"Crossref","is-referenced-by-count":2,"title":["Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics"],"prefix":"10.1142","volume":"31","author":[{"given":"Frederik","family":"vom Ende","sequence":"first","affiliation":[{"name":"Dahlem Center for Complex Quantum Systems, Freie Universit\u00e4t Berlin, Arnimallee 14, 14195 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,4,5]]},"reference":[{"key":"S1230161224500045BIB001","volume-title":"Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables","author":"Abramowitz M.","year":"1972","edition":"10"},{"key":"S1230161224500045BIB002","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.052103"},{"key":"S1230161224500045BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/09500340701352581"},{"key":"S1230161224500045BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.107.337"},{"key":"S1230161224500045BIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.70.012106"},{"volume-title":"The Theory of Open Quantum Systems","year":"2002","author":"Breuer H.-P.","key":"S1230161224500045BIB006"},{"key":"S1230161224500045BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/033"},{"key":"S1230161224500045BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-022-01211-y"},{"key":"S1230161224500045BIB009","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-019-39140-2"},{"key":"S1230161224500045BIB010","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.104.070406"},{"key":"S1230161224500045BIB011","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.94.020103"},{"key":"S1230161224500045BIB012","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.4.040304"},{"key":"S1230161224500045BIB013","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.032328"},{"key":"S1230161224500045BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/BF00532512"},{"volume-title":"Quantum Theory of Open Systems","year":"1976","author":"Davies E.","key":"S1230161224500045BIB015"},{"key":"S1230161224500045BIB016","volume-title":"Foundations of Modern Analysis","volume":"1","author":"Dieudonn\u00e9 J.","year":"1969"},{"key":"S1230161224500045BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/S0034-4877(09)90022-2"},{"key":"S1230161224500045BIB018","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.032111"},{"key":"S1230161224500045BIB019","first-page":"466","volume":"89","author":"Dole\u017eal V.","year":"1964","journal-title":"Cas. Pestovani Mat."},{"key":"S1230161224500045BIB020","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107340701"},{"key":"S1230161224500045BIB021","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.55.2290"},{"volume-title":"Counterexamples in Analysis","year":"2003","author":"Gelbaum B.","key":"S1230161224500045BIB022"},{"key":"S1230161224500045BIB023","doi-asserted-by":"publisher","DOI":"10.1063\/1.522979"},{"key":"S1230161224500045BIB024","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.89.042120"},{"volume-title":"Functional Analysis and Semigroups","year":"1957","author":"Hille E.","key":"S1230161224500045BIB025"},{"key":"S1230161224500045BIB026","doi-asserted-by":"publisher","DOI":"10.1515\/9783110273403"},{"volume-title":"Matrix Analysis","year":"1987","author":"Horn R.","key":"S1230161224500045BIB027"},{"volume-title":"Perturbation Theory for Linear Operators","year":"1980","author":"Kato T.","key":"S1230161224500045BIB028"},{"volume-title":"Quantum Control in Infinite Dimensions and Banach-Lie Algebras: Pure Point Spectrum","year":"2018","author":"Keyl M.","key":"S1230161224500045BIB029"},{"key":"S1230161224500045BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161209000190"},{"key":"S1230161224500045BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2008.07.023"},{"key":"S1230161224500045BIB032","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.917696"},{"volume-title":"Topology of Metric Spaces","year":"2005","author":"Kumaresan S.","key":"S1230161224500045BIB033"},{"key":"S1230161224500045BIB034","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608499"},{"key":"S1230161224500045BIB035","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15564-2"},{"key":"S1230161224500045BIB036","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198514855.001.0001"},{"key":"S1230161224500045BIB037","doi-asserted-by":"publisher","DOI":"10.22331\/q-2021-01-28-391"},{"key":"S1230161224500045BIB038","doi-asserted-by":"publisher","DOI":"10.1063\/1.2218675"},{"key":"S1230161224500045BIB039","doi-asserted-by":"publisher","DOI":"10.22331\/q-2018-07-11-76"},{"key":"S1230161224500045BIB040","volume-title":"Real and Complex Analysis","author":"Rudin W.","year":"1986","edition":"3"},{"key":"S1230161224500045BIB041","volume-title":"Functional Analysis","author":"Rudin W.","year":"1991","edition":"2"},{"key":"S1230161224500045BIB042","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.18.2379"},{"key":"S1230161224500045BIB043","doi-asserted-by":"publisher","DOI":"10.1088\/0953-4075\/44\/15\/154013"},{"volume-title":"Quantum-Embeddable Stochastic Matrices","year":"2023","author":"Shahbeigi F.","key":"S1230161224500045BIB044"},{"key":"S1230161224500045BIB045","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0577-7"},{"key":"S1230161224500045BIB046","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.030402"},{"key":"S1230161224500045BIB047","first-page":"1319","volume":"23","author":"vom Ende F.","year":"2023","journal-title":"Quantum Inf. Comput."},{"key":"S1230161224500045BIB048","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161223500038"},{"key":"S1230161224500045BIB049","doi-asserted-by":"publisher","DOI":"10.1063\/1.5095868"},{"key":"S1230161224500045BIB050","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161223500051"},{"key":"S1230161224500045BIB051","doi-asserted-by":"publisher","DOI":"10.1063\/1.4907384"},{"key":"S1230161224500045BIB052","doi-asserted-by":"publisher","DOI":"10.1017\/9781316848142"},{"key":"S1230161224500045BIB053","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-008-0411-y"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161224500045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T07:14:47Z","timestamp":1712560487000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1230161224500045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3]]},"references-count":53,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["10.1142\/S1230161224500045"],"URL":"https:\/\/doi.org\/10.1142\/s1230161224500045","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"type":"print","value":"1230-1612"},{"type":"electronic","value":"1793-7191"}],"subject":[],"published":{"date-parts":[[2024,3]]},"article-number":"2450004"}}