{"id":"https://openalex.org/W4407425875","doi":"https://doi.org/10.1109/tit.2025.3649040","title":"Uhlmann\u2019s Theorem for Measured Divergences","display_name":"Uhlmann\u2019s Theorem for Measured Divergences","publication_year":2025,"publication_date":"2025-12-29","ids":{"openalex":"https://openalex.org/W4407425875","doi":"https://doi.org/10.1109/tit.2025.3649040"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2025.3649040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649040","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kun Fang","orcid":"https://orcid.org/0000-0002-9232-6846"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kun Fang","raw_affiliation_strings":["School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, Guangdong, China"],"raw_orcid":"https://orcid.org/0000-0002-9232-6846","affiliations":[{"raw_affiliation_string":"School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen, Guangdong, China","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017261970","display_name":"Hamza Fawzi","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hamza Fawzi","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K"],"raw_orcid":"https://orcid.org/0000-0001-6026-4102","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023562540","display_name":"Omar Fawzi","orcid":"https://orcid.org/0000-0001-8491-0359"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Omar Fawzi","raw_affiliation_strings":["Inria, ENS de Lyon, UCBL, LIP, Lyon Cedex 07, France"],"raw_orcid":"https://orcid.org/0000-0001-8491-0359","affiliations":[{"raw_affiliation_string":"Inria, ENS de Lyon, UCBL, LIP, Lyon Cedex 07, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I100532134"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210116924"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00920723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"3","first_page":"1751","last_page":"1760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14351","display_name":"Statistical and Computational Modeling","score":0.8871999979019165,"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/T14351","display_name":"Statistical and Computational Modeling","score":0.8871999979019165,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.8192999958992004,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48155477643013},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.440077006816864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43824300169944763},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3679999113082886},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3402389883995056},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33569425344467163},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0604405403137207}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48155477643013},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.440077006816864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43824300169944763},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3679999113082886},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3402389883995056},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33569425344467163},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0604405403137207},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2025.3649040","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2025.3649040","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.48550/arxiv.2502.07745","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:arXiv.org:2502.07745","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.07745","pdf_url":"https://arxiv.org/pdf/2502.07745","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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-05638763v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05638763","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":"IEEE Transactions on Information Theory, 2026, 72 (3), pp.1751-1760. &#x27E8;10.1109/TIT.2025.3649040&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.2502.07745","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2502.07745","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2502.07745","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1583853050","display_name":null,"funder_award_id":"12404569","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2330084786","display_name":null,"funder_award_id":"851716","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5388051471","display_name":null,"funder_award_id":"851716","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"},{"id":"https://openalex.org/G5508686167","display_name":null,"funder_award_id":"92470113","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5917528678","display_name":null,"funder_award_id":"101017733","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6612625481","display_name":null,"funder_award_id":"France 2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G705399293","display_name":null,"funder_award_id":"ANR-22-PETQ-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7362582964","display_name":null,"funder_award_id":"JCYJ20241202124023031","funder_id":"https://openalex.org/F4320329791","funder_display_name":"Shenzhen Fundamental Research Program"},{"id":"https://openalex.org/G8786121556","display_name":null,"funder_award_id":"EP/X032051/1","funder_id":"https://openalex.org/F4320314731","funder_display_name":"UK Research and Innovation"}],"funders":[{"id":"https://openalex.org/F4320314707","display_name":"Government of the United Kingdom","ror":"https://ror.org/05wnh3t63"},{"id":"https://openalex.org/F4320314731","display_name":"UK Research and Innovation","ror":"https://ror.org/001aqnf71"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329791","display_name":"Shenzhen Fundamental Research Program","ror":null},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W152055444","https://openalex.org/W4406168614","https://openalex.org/W2471548350","https://openalex.org/W2042036132","https://openalex.org/W1968087916","https://openalex.org/W1621050367","https://openalex.org/W4403349361","https://openalex.org/W7128315943","https://openalex.org/W4417223359","https://openalex.org/W2013567929","https://openalex.org/W4412605493","https://openalex.org/W2189660299","https://openalex.org/W2338342209","https://openalex.org/W4244969988","https://openalex.org/W4250589301","https://openalex.org/W4249667877","https://openalex.org/W2144180948","https://openalex.org/W2949342341","https://openalex.org/W1985077192","https://openalex.org/W2804172638","https://openalex.org/W4387665617","https://openalex.org/W2160706065","https://openalex.org/W2122166994","https://openalex.org/W2168792807","https://openalex.org/W1745229717","https://openalex.org/W4250131430","https://openalex.org/W4386525918","https://openalex.org/W2979219632","https://openalex.org/W4291278293","https://openalex.org/W4289655238","https://openalex.org/W2959461928","https://openalex.org/W3012290080"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Uhlmann\u2019s":[0,76,99],"theorem":[1,77,100],"is":[2],"a":[3,79],"cornerstone":[4],"of":[5,31,82],"quantum":[6,13,68,116,143],"information":[7,69],"theory,":[8],"stating":[9],"that":[10,36],"for":[11,92,101,131],"any":[12,19],"state":[14,20],"\u03c1<italic":[15,40,53],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16,22,29,33,41,45,54,58,85,139],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">AB</i>":[17,30,42,46],"and":[18,43,56,65,122,145],"\u03c3<italic":[21,28,32,44,57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>,":[23],"there":[24],"exists":[25],"an":[26],"extension":[27],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>":[34,55],"such":[35],"the":[37,48,88,102,106,120],"fidelity":[38,49,103],"between":[39,50],"equals":[47],"their":[51,147],"marginals":[52],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>.":[59],"This":[60],"property":[61,129],"underpins":[62],"many":[63],"results":[64],"applications":[66],"in":[67],"science.":[70],"In":[71],"this":[72,128,134],"work,":[73],"we":[74],"generalize":[75],"to":[78,105],"broad":[80],"class":[81],"measured":[83,89,137],"<italic":[84,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f</i>-divergences,":[86],"including":[87,119],"\u03b1-R\u00e9nyi":[90],"divergences":[91,144],"all":[93],"\u03b1":[94,109],"\u2265":[95],"0.":[96],"The":[97],"well-known":[98],"corresponds":[104],"special":[107],"case":[108],"=":[110],"1/2.":[111],"Since":[112],"most":[113],"commonly":[114],"used":[115],"R\u00e9nyi":[117,124],"divergences,":[118,125],"Petz":[121],"sandwiched":[123],"cannot":[126],"satisfy":[127],"(except":[130],"degenerate":[132],"cases),":[133],"fundamentally":[135],"distinguishes":[136],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f</i>-divergences":[140],"from":[141],"other":[142],"highlights":[146],"unique":[148],"mathematical":[149],"structure.":[150]},"counts_by_year":[],"updated_date":"2026-06-08T08:47:23.578185","created_date":"2025-02-13T00:00:00"}
