{"id":"https://openalex.org/W1501376697","doi":"https://doi.org/10.1109/tit.2016.2545680","title":"Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map","display_name":"Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map","publication_year":2016,"publication_date":"2016-03-23","ids":{"openalex":"https://openalex.org/W1501376697","doi":"https://doi.org/10.1109/tit.2016.2545680","mag":"1501376697"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2545680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2545680","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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.00303","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000275259","display_name":"David Sutter","orcid":"https://orcid.org/0000-0001-9779-8888"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"David Sutter","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Zurich, Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Zurich, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040644995","display_name":"Marco Tomamichel","orcid":"https://orcid.org/0000-0001-5410-3329"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Marco Tomamichel","raw_affiliation_strings":["School of Physics, The University of Sydney, Sydney, NSW, Australia","[School of Physics, The University of Sydney, Sydney, NSW, Australia]"],"affiliations":[{"raw_affiliation_string":"School of Physics, The University of Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"[School of Physics, The University of Sydney, Sydney, NSW, Australia]","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008766821","display_name":"Aram W. Harrow","orcid":"https://orcid.org/0000-0003-3220-7682"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aram W. Harrow","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA","[Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA]"],"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"[Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5000275259"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":19.4393,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.99807679,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"62","issue":"5","first_page":"2907","last_page":"2913"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9972000122070312,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6320909857749939},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6249710321426392},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.42729124426841736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14602014422416687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1285175383090973},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07160952687263489}],"concepts":[{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6320909857749939},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6249710321426392},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.42729124426841736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14602014422416687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1285175383090973},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07160952687263489}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2016.2545680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2545680","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:oai:arXiv.org:1507.00303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00303","pdf_url":"https://arxiv.org/pdf/1507.00303","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.00303","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00303","pdf_url":"https://arxiv.org/pdf/1507.00303","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5799999833106995,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G5539695041","display_name":null,"funder_award_id":"W911NF-12-1-0486","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7489425848","display_name":null,"funder_award_id":"CCF-1452616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7929468754","display_name":null,"funder_award_id":"CCF-1111382","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8828173992","display_name":null,"funder_award_id":"258932","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W585133165","https://openalex.org/W639433093","https://openalex.org/W1481217622","https://openalex.org/W1482224246","https://openalex.org/W1577837803","https://openalex.org/W1661335496","https://openalex.org/W1686679909","https://openalex.org/W1914854949","https://openalex.org/W1947417802","https://openalex.org/W1948605327","https://openalex.org/W1963925013","https://openalex.org/W1968087916","https://openalex.org/W1984932894","https://openalex.org/W1985077192","https://openalex.org/W2027561650","https://openalex.org/W2056655757","https://openalex.org/W2059260201","https://openalex.org/W2069527447","https://openalex.org/W2076249063","https://openalex.org/W2079550971","https://openalex.org/W2105918132","https://openalex.org/W2105957088","https://openalex.org/W2118645726","https://openalex.org/W2122166994","https://openalex.org/W2124512402","https://openalex.org/W2134705177","https://openalex.org/W2144180948","https://openalex.org/W2154518298","https://openalex.org/W2188989666","https://openalex.org/W2189660299","https://openalex.org/W2229752136","https://openalex.org/W2963711068","https://openalex.org/W3098857864","https://openalex.org/W3099257677","https://openalex.org/W3100939261","https://openalex.org/W3101305655","https://openalex.org/W3101525167","https://openalex.org/W3101663526","https://openalex.org/W3103101214","https://openalex.org/W3103289615","https://openalex.org/W3105390789","https://openalex.org/W3105995555","https://openalex.org/W3144644885","https://openalex.org/W3194584304","https://openalex.org/W3213943817","https://openalex.org/W4211084734","https://openalex.org/W4230977805","https://openalex.org/W4285827723","https://openalex.org/W4310300362","https://openalex.org/W4385773637","https://openalex.org/W6639926825","https://openalex.org/W6678793272","https://openalex.org/W6687373073","https://openalex.org/W6689563411"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2077314575","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W2142036596"],"abstract_inverted_index":{"The":[0,89],"quantum":[1,16,49,105],"relative":[2,25,67,75],"entropy":[3,76],"between":[4,77],"two":[5],"states":[6,20],"satisfies":[7],"a":[8,39,82,93,112],"monotonicity":[9],"property":[10],"meaning":[11],"that":[12,30,42,63],"applying":[13],"the":[14,45,48,64,73,78,104,108,121,127,139,146],"same":[15],"channel":[17,50,106],"to":[18],"both":[19,52],"can":[21],"never":[22],"increase":[23],"their":[24],"entropy.":[26],"It":[27],"is":[28,33,38,69,92],"known":[29],"this":[31,55,59],"inequality":[32,60],"only":[34,136],"tight":[35],"when":[36],"there":[37],"recovery":[40,90,99],"map":[41,91],"exactly":[43],"reverses":[44,103],"effects":[46],"of":[47,66,96,142],"on":[51,107,120,138],"states.":[53],"In":[54],"paper,":[56],"we":[57,115],"strengthen":[58],"by":[61,72,130],"showing":[62],"difference":[65],"entropies":[68],"bounded":[70],"below":[71],"measured":[74],"first":[79],"state":[80,84],"and":[81,101,132,145],"recovered":[83],"from":[85],"its":[86],"processed":[87],"version.":[88],"convex":[94],"combination":[95],"rotated":[97],"Petz":[98],"maps":[100,144],"perfectly":[102],"second":[109],"state.":[110],"As":[111],"special":[113],"case,":[114],"reproduce":[116],"recent":[117],"lower":[118],"bounds":[119],"conditional":[122],"mutual":[123],"information,":[124],"such":[125],"as":[126],"one":[128],"proved":[129],"Fawzi":[131],"Renner.":[133],"Our":[134],"proof":[135],"relies":[137],"elementary":[140],"properties":[141],"pinching":[143],"operator":[147],"logarithm.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}