{"id":"https://openalex.org/W2513705652","doi":"https://doi.org/10.1109/tit.2016.2639521","title":"Pretty Good Measures in Quantum Information Theory","display_name":"Pretty Good Measures in Quantum Information Theory","publication_year":2016,"publication_date":"2016-12-14","ids":{"openalex":"https://openalex.org/W2513705652","doi":"https://doi.org/10.1109/tit.2016.2639521","mag":"2513705652"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2639521","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2639521","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/1608.08229","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040810573","display_name":"Raban Iten","orcid":"https://orcid.org/0000-0001-5332-5093"},"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":false,"raw_author_name":"Raban Iten","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067801862","display_name":"Joseph M. Renes","orcid":"https://orcid.org/0000-0003-2302-8025"},"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":false,"raw_author_name":"Joseph M. Renes","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","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":false,"raw_author_name":"David Sutter","raw_affiliation_strings":["Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland"],"raw_orcid":"https://orcid.org/0000-0001-9779-8888","affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":1.1488,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.78776355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"63","issue":"2","first_page":"1270","last_page":"1279"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991999864578247,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9923999905586243,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.6283891201019287},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5793467164039612},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.5764378905296326},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5375091433525085},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5018494129180908},{"id":"https://openalex.org/keywords/singlet-state","display_name":"Singlet state","score":0.45836740732192993},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.45669254660606384},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.4514138996601105},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.41284823417663574},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40898197889328003},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3916236162185669},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35540515184402466},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2738453149795532},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25068631768226624},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10325098037719727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6283891201019287},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5793467164039612},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.5764378905296326},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5375091433525085},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5018494129180908},{"id":"https://openalex.org/C33062035","wikidata":"https://www.wikidata.org/wiki/Q3296863","display_name":"Singlet state","level":3,"score":0.45836740732192993},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.45669254660606384},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.4514138996601105},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.41284823417663574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40898197889328003},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3916236162185669},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35540515184402466},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2738453149795532},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25068631768226624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10325098037719727},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C181500209","wikidata":"https://www.wikidata.org/wiki/Q215328","display_name":"Excited state","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"score":0.0},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2016.2639521","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2639521","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:1608.08229","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.08229","pdf_url":"https://arxiv.org/pdf/1608.08229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1608.08229","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.08229","pdf_url":"https://arxiv.org/pdf/1608.08229","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},"sustainable_development_goals":[],"awards":[],"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/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2513705652.pdf","grobid_xml":"https://content.openalex.org/works/W2513705652.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W1539221996","https://openalex.org/W1621050367","https://openalex.org/W1640062563","https://openalex.org/W1836320178","https://openalex.org/W1885293871","https://openalex.org/W1922128166","https://openalex.org/W1970957908","https://openalex.org/W1976865215","https://openalex.org/W1979692012","https://openalex.org/W1983051686","https://openalex.org/W1990977790","https://openalex.org/W1995989441","https://openalex.org/W2002420498","https://openalex.org/W2004980778","https://openalex.org/W2017580271","https://openalex.org/W2031967104","https://openalex.org/W2033934891","https://openalex.org/W2035792087","https://openalex.org/W2037670238","https://openalex.org/W2047937345","https://openalex.org/W2055611553","https://openalex.org/W2058041395","https://openalex.org/W2063443840","https://openalex.org/W2087844534","https://openalex.org/W2094966623","https://openalex.org/W2101060409","https://openalex.org/W2105211531","https://openalex.org/W2106654982","https://openalex.org/W2107387696","https://openalex.org/W2122166994","https://openalex.org/W2144277460","https://openalex.org/W2153235257","https://openalex.org/W2163484647","https://openalex.org/W2164253138","https://openalex.org/W2164818780","https://openalex.org/W2164957410","https://openalex.org/W2167346196","https://openalex.org/W2168792807","https://openalex.org/W2180630352","https://openalex.org/W2242640103","https://openalex.org/W2949368822","https://openalex.org/W2950182478","https://openalex.org/W2950789679","https://openalex.org/W3098315206","https://openalex.org/W3098857864","https://openalex.org/W3100132343","https://openalex.org/W3100174796","https://openalex.org/W3100438626","https://openalex.org/W3100638609","https://openalex.org/W3101431262","https://openalex.org/W3101663526","https://openalex.org/W3102672936","https://openalex.org/W3103695971","https://openalex.org/W3103744872","https://openalex.org/W3103812487","https://openalex.org/W4251166215","https://openalex.org/W4255333822","https://openalex.org/W4285719527","https://openalex.org/W4298298355","https://openalex.org/W6632391084","https://openalex.org/W6637017589","https://openalex.org/W6690539871","https://openalex.org/W6785983528"],"related_works":["https://openalex.org/W3208095355","https://openalex.org/W2177370417","https://openalex.org/W2052507016","https://openalex.org/W2180461068","https://openalex.org/W2051816080","https://openalex.org/W178140751","https://openalex.org/W1191014223","https://openalex.org/W1137063513","https://openalex.org/W4310813911","https://openalex.org/W3182726073"],"abstract_inverted_index":{"Quantum":[0],"generalizations":[1,24],"of":[2,13,22,61,124],"R\u00e9nyi's":[3],"entropies":[4],"are":[5,75],"a":[6,11,48,54,82,116],"useful":[7],"tool":[8],"to":[9,27,88],"describe":[10],"variety":[12],"operational":[14],"tasks":[15],"in":[16],"quantum":[17,33,39],"information":[18],"processing.":[19],"Two":[20],"families":[21,60],"such":[23],"turn":[25],"out":[26],"be":[28],"particularly":[29],"useful:":[30],"the":[31,37,89,93,97,106,125],"Petz":[32],"R\u00e9nyi":[34,40],"divergence":[35,41],"D\u0305\u03b1and":[36],"minimal":[38],"D\u0303\u03b1.":[42],"In":[43],"this":[44],"paper,":[45],"we":[46],"prove":[47],"reverse":[49],"Araki-Lieb-Thirring":[50],"inequality":[51],"that":[52],"implies":[53,92],"new":[55,117],"relation":[56,87],"between":[57,96],"these":[58],"two":[59],"divergences,":[62],"namely,":[63],"\u03b1D\u0305\u03b1(Q\u2225\u03c3)":[64],"\u2264":[65],"D\u0303\u03b1(Q\u2225\u03c3)":[66],"for":[67,122],"\u03b1":[68],"\u2208[0,1]":[69],"and":[70,73,99,108,119,129],"where":[71],"Q":[72],"\u03c3":[74],"density":[76],"operators.":[77],"This":[78],"bound":[79],"suggests":[80],"defining":[81],"\u201dpretty":[83],"good":[84,101,110,127],"fidelity,\u201d":[85],"whose":[86],"usual":[90],"fidelity":[91],"known":[94],"relations":[95],"optimal":[98,107],"pretty":[100,109,126],"measurement":[102,128],"as":[103,105],"well":[104],"singlet":[111,130],"fraction.":[112,131],"We":[113],"also":[114],"find":[115],"necessary":[118],"sufficient":[120],"condition":[121],"optimality":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
