{"id":"https://openalex.org/W2065212772","doi":"https://doi.org/10.1142/s1230161208000110","title":"Unital Positive Maps and Quantum States","display_name":"Unital Positive Maps and Quantum States","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2065212772","doi":"https://doi.org/10.1142/s1230161208000110","mag":"2065212772"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161208000110","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161208000110","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022860121","display_name":"M. Asorey","orcid":"https://orcid.org/0000-0003-3669-6241"},"institutions":[{"id":"https://openalex.org/I255234318","display_name":"Universidad de Zaragoza","ror":"https://ror.org/012a91z28","country_code":"ES","type":"education","lineage":["https://openalex.org/I255234318"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"M. Asorey","raw_affiliation_strings":["Departamento de F\u00edsica Te\u00f3rica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica Te\u00f3rica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain","institution_ids":["https://openalex.org/I255234318"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056187445","display_name":"Andrzej Kossakowski","orcid":null},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"A. Kossakowski","raw_affiliation_strings":["Institute of Physics, Nicolaus Copernicus University, 87\u2013100 Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Nicolaus Copernicus University, 87\u2013100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I3019271933","https://openalex.org/I4210086947"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069373327","display_name":"G. Marmo","orcid":"https://orcid.org/0000-0003-2662-2193"},"institutions":[{"id":"https://openalex.org/I4210108560","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Napoli","ror":"https://ror.org/015kcdd40","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210108560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Marmo","raw_affiliation_strings":["Dipartimento di Scienze Fisiche, Universit\u00e1 Federico II di Napoli and INFN, Sezione di Napoli, Complesso Univ. di Monte Sant' Angelo, Via Cintia, 80125 Napoli, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze Fisiche, Universit\u00e1 Federico II di Napoli and INFN, Sezione di Napoli, Complesso Univ. di Monte Sant' Angelo, Via Cintia, 80125 Napoli, Italy","institution_ids":["https://openalex.org/I4210108560"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048345745","display_name":"E. C. G. Sudarshan","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. C. G. Sudarshan","raw_affiliation_strings":["Department of Physics, University of Texas at Austin, Austin, Texas 78712-1081, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, University of Texas at Austin, Austin, Texas 78712-1081, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5022860121"],"corresponding_institution_ids":["https://openalex.org/I255234318"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.08414196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"15","issue":"02","first_page":"123","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unital","display_name":"Unital","score":0.8907575607299805},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6444104313850403},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.615066409111023},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.5705958604812622},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4869728982448578},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.471897691488266},{"id":"https://openalex.org/keywords/relation","display_name":"Relation (database)","score":0.44987526535987854},{"id":"https://openalex.org/keywords/witness","display_name":"Witness","score":0.44152557849884033},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.4385715126991272},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34279581904411316},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.24989855289459229},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.20876291394233704},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20171338319778442},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1317218542098999},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1300923228263855},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0963645875453949},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.06527984142303467}],"concepts":[{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.8907575607299805},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6444104313850403},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.615066409111023},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.5705958604812622},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4869728982448578},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.471897691488266},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.44987526535987854},{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.44152557849884033},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.4385715126991272},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34279581904411316},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.24989855289459229},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.20876291394233704},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20171338319778442},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1317218542098999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1300923228263855},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0963645875453949},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06527984142303467},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1230161208000110","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161208000110","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.6982","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.6982","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0808.0427v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W114144072","https://openalex.org/W1484246869","https://openalex.org/W1602420091","https://openalex.org/W1606975474","https://openalex.org/W1968384714","https://openalex.org/W1970556775","https://openalex.org/W1988421997","https://openalex.org/W1992488636","https://openalex.org/W1992929677","https://openalex.org/W1993277889","https://openalex.org/W1997082258","https://openalex.org/W2000407553","https://openalex.org/W2007396583","https://openalex.org/W2009525268","https://openalex.org/W2013991693","https://openalex.org/W2015775929","https://openalex.org/W2016866105","https://openalex.org/W2019441029","https://openalex.org/W2027787642","https://openalex.org/W2033249635","https://openalex.org/W2035682720","https://openalex.org/W2048648826","https://openalex.org/W2053784052","https://openalex.org/W2062292260","https://openalex.org/W2074286205","https://openalex.org/W2074676574","https://openalex.org/W2083886939","https://openalex.org/W2089408664","https://openalex.org/W2090421743","https://openalex.org/W2114851694","https://openalex.org/W2116102644","https://openalex.org/W2121992052","https://openalex.org/W2314893122","https://openalex.org/W2331274486","https://openalex.org/W2950357124","https://openalex.org/W3100314707","https://openalex.org/W3186886419","https://openalex.org/W4297590171"],"related_works":["https://openalex.org/W4315777779","https://openalex.org/W2949852445","https://openalex.org/W2052819035","https://openalex.org/W2056239989","https://openalex.org/W2065212772","https://openalex.org/W4298357107","https://openalex.org/W2292173295","https://openalex.org/W3100900846","https://openalex.org/W4311251692","https://openalex.org/W3106440870"],"abstract_inverted_index":{"We":[0,35],"analyze":[1],"the":[2,5,26,37],"structure":[3],"of":[4,7,39],"subset":[6,27],"states":[8],"generated":[9,28],"by":[10,29],"unital":[11],"completely":[12],"positive":[13,40],"quantum":[14,46],"maps.":[15],"A":[16],"witness":[17],"certifying":[18],"that":[19],"a":[20,30],"state":[21],"does":[22],"not":[23],"belong":[24],"to":[25,45],"given":[31],"map":[32],"is":[33],"constructed.":[34],"analyse":[36],"representations":[38],"maps":[41],"and":[42],"their":[43],"relation":[44],"Perron-Frobenius":[47],"theory.":[48]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}