{"id":"https://openalex.org/W2045376036","doi":"https://doi.org/10.1109/cdc.2013.6760928","title":"Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations","display_name":"Contraction and stability analysis of steady-states for open quantum systems described by Lindblad differential equations","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2045376036","doi":"https://doi.org/10.1109/cdc.2013.6760928","mag":"2045376036"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6760928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1302.6899","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065752316","display_name":"Pierre Rouchon","orcid":"https://orcid.org/0000-0001-6160-5634"},"institutions":[{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Rouchon","raw_affiliation_strings":["Centre Automatique et Syst\u00e8mes, Mines ParisTech, Paris cedex, France","Centre Autom. et Syst., Math. et Syst., Mines ParisTech, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines ParisTech, Paris cedex, France","institution_ids":["https://openalex.org/I70768539"]},{"raw_affiliation_string":"Centre Autom. et Syst., Math. et Syst., Mines ParisTech, Paris, France","institution_ids":["https://openalex.org/I70768539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016288250","display_name":"Alain Sarlette","orcid":"https://orcid.org/0000-0001-5909-437X"},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Alain Sarlette","raw_affiliation_strings":["SYSTeMS research group at Ghent University, Zwijnaarde, Belgium","SYSTeMS Research Group, Ghent University, Zwijnaarde, Belgium#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SYSTeMS research group at Ghent University, Zwijnaarde, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"SYSTeMS Research Group, Ghent University, Zwijnaarde, Belgium#TAB#","institution_ids":["https://openalex.org/I32597200"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"34","issue":null,"first_page":"6568","last_page":"6573"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.551257848739624},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5474104285240173},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4656928777694702},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.44541600346565247},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41063857078552246},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36498773097991943},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3471285104751587},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3306649327278137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2961958348751068},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.23150748014450073}],"concepts":[{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.551257848739624},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5474104285240173},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4656928777694702},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.44541600346565247},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41063857078552246},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36498773097991943},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3471285104751587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3306649327278137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2961958348751068},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23150748014450073},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2013.6760928","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6760928","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1302.6899","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1302.6899","pdf_url":"https://arxiv.org/pdf/1302.6899","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00971495v1","is_oa":false,"landing_page_url":"https://minesparis-psl.hal.science/hal-00971495","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Dec 2013, Firenze, Italy. pp.6568 - 6573, ⟨10.1109/CDC.2013.6760928⟩","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1302.6899","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1302.6899","pdf_url":"https://arxiv.org/pdf/1302.6899","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4596822079","display_name":null,"funder_award_id":"ANR-2011-BS01-017-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7905394774","display_name":null,"funder_award_id":"2011-BS01-017-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2045376036.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W234706490","https://openalex.org/W251857204","https://openalex.org/W1578322733","https://openalex.org/W1616849956","https://openalex.org/W1631356911","https://openalex.org/W1643301482","https://openalex.org/W1993580202","https://openalex.org/W2000842907","https://openalex.org/W2011170321","https://openalex.org/W2015683881","https://openalex.org/W2025744050","https://openalex.org/W2036024084","https://openalex.org/W2053798711","https://openalex.org/W2063937117","https://openalex.org/W2065730083","https://openalex.org/W2070212877","https://openalex.org/W2084864304","https://openalex.org/W2091996493","https://openalex.org/W2092285095","https://openalex.org/W2125303188","https://openalex.org/W2134889984","https://openalex.org/W2189531290","https://openalex.org/W2505136320","https://openalex.org/W2764347725","https://openalex.org/W3099557771","https://openalex.org/W3104759269","https://openalex.org/W3105696575","https://openalex.org/W4285719527","https://openalex.org/W4299321766","https://openalex.org/W6609104113","https://openalex.org/W6785725915"],"related_works":["https://openalex.org/W3025685350","https://openalex.org/W1524573362","https://openalex.org/W1972689493","https://openalex.org/W2356401532","https://openalex.org/W1968841476","https://openalex.org/W2393800486","https://openalex.org/W2315528930","https://openalex.org/W4293997864","https://openalex.org/W2079804735","https://openalex.org/W2411175714"],"abstract_inverted_index":{"For":[0],"discrete-time":[1],"quantum":[2,94],"systems,":[3,39],"governed":[4,40],"by":[5,41,59,71,80,98],"Kraus":[6],"maps,":[7],"the":[8,15,22,60,65,78,110,114,134],"work":[9],"of":[10,17,33,54,113],"D.":[11],"Petz":[12],"has":[13,119],"characterized":[14],"set":[16,32,56],"universal":[18],"contraction":[19],"metrics.":[20],"In":[21,101],"present":[23],"paper,":[24],"we":[25,103],"use":[26],"this":[27,55],"characterization":[28],"to":[29,91,133,140],"derive":[30],"a":[31,47,73,82,87,93,120,130],"quadratic":[34,66],"Lyapunov":[35,67,84],"functions":[36],"for":[37,63,86],"continuous-time":[38],"Lindblad":[42,88,107],"differential":[43],"equations,":[44],"that":[45,105,141],"have":[46],"steady-state":[48],"with":[49],"full":[50],"rank.":[51],"An":[52],"extremity":[53],"is":[57,69],"given":[58],"Bures":[61],"metric,":[62],"which":[64,118,124],"function":[68,85],"obtained":[70],"inverting":[72],"Sylvester":[74],"equation.":[75],"We":[76],"illustrate":[77],"method":[79],"providing":[81],"strict":[83],"equation":[89,108],"designed":[90],"stabilize":[92],"electrodynamic":[95],"\u201ccat\u201d":[96],"state":[97],"reservoir":[99],"engineering.":[100],"fact":[102],"prove":[104],"any":[106],"on":[109],"Hilbert":[111],"space":[112],"(truncated)":[115],"harmonic":[116],"oscillator,":[117],"full-rank":[121],"equilibrium":[122],"and":[123],"has,":[125],"among":[126],"its":[127],"decoherence":[128],"channels,":[129],"channel":[131],"corresponding":[132],"photon":[135],"loss":[136],"operator,":[137],"globally":[138],"converges":[139],"equilibrium.":[142]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}