{"tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2023-03-01T00:00:00Z","abstract":[{"text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups.","lang":"eng"}],"page":"717-750","month":"03","publication_status":"published","ddc":["510"],"date_updated":"2023-08-14T11:39:28Z","volume":24,"oa_version":"Published Version","day":"01","file":[{"relation":"main_file","checksum":"8c7b185eba5ccd92ef55c120f654222c","file_size":554871,"content_type":"application/pdf","date_updated":"2023-08-14T11:38:28Z","access_level":"open_access","success":1,"file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","file_id":"14051","date_created":"2023-08-14T11:38:28Z","creator":"dernst"}],"publisher":"Springer Nature","intvolume":"        24","file_date_updated":"2023-08-14T11:38:28Z","scopus_import":"1","acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","date_created":"2022-09-11T22:01:57Z","year":"2023","citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>.","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","apa":"Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>."},"type":"journal_article","author":[{"first_name":"Melchior","last_name":"Wirth","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior"},{"first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang"}],"ec_funded":1,"department":[{"_id":"JaMa"}],"status":"public","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","isi":1,"article_type":"original","title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2105.08303"],"isi":["000837499800002"]},"publication":"Annales Henri Poincare","doi":"10.1007/s00023-022-01220-x","_id":"12087","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"]},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"oa":1}