{"id":"https://openalex.org/W3041416733","doi":"https://doi.org/10.1109/tit.2022.3142812","title":"A Tight Uniform Continuity Bound for the Arimoto-R\u00e9nyi Conditional Entropy and its Extension to Classical-Quantum States","display_name":"A Tight Uniform Continuity Bound for the Arimoto-R\u00e9nyi Conditional Entropy and its Extension to Classical-Quantum States","publication_year":2022,"publication_date":"2022-01-13","ids":{"openalex":"https://openalex.org/W3041416733","doi":"https://doi.org/10.1109/tit.2022.3142812","mag":"3041416733"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3142812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3142812","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":"https://arxiv.org/pdf/2007.05049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008100785","display_name":"Michael G. Jabbour","orcid":"https://orcid.org/0000-0003-1851-9540"},"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":true,"raw_author_name":"Michael G. Jabbour","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, U.K","Univ. of Cambridge"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108075277","display_name":"Nilanjana Datta","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":"Nilanjana Datta","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, U.K","Univ. of Cambridge"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge, U.K","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Univ. of Cambridge","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008100785"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.138,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50410656,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"68","issue":"4","first_page":"2169","last_page":"2181"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9987000226974487,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9987000226974487,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9868000149726868,"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/conditional-entropy","display_name":"Conditional entropy","score":0.7921544313430786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7310011982917786},{"id":"https://openalex.org/keywords/conditional-quantum-entropy","display_name":"Conditional quantum entropy","score":0.7030292749404907},{"id":"https://openalex.org/keywords/r\u00e9nyi-entropy","display_name":"R\u00e9nyi entropy","score":0.687687337398529},{"id":"https://openalex.org/keywords/min-entropy","display_name":"Min entropy","score":0.5920658111572266},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5669578909873962},{"id":"https://openalex.org/keywords/entropic-uncertainty","display_name":"Entropic uncertainty","score":0.5405125021934509},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.5358961820602417},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5086325407028198},{"id":"https://openalex.org/keywords/entropy-rate","display_name":"Entropy rate","score":0.46076393127441406},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4398413300514221},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.43711262941360474},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3670121431350708},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3610461354255676},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.3361237645149231},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20893847942352295},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.18240702152252197},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1719159185886383},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16195449233055115},{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.14926689863204956},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14839890599250793}],"concepts":[{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.7921544313430786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7310011982917786},{"id":"https://openalex.org/C16609844","wikidata":"https://www.wikidata.org/wiki/Q5159273","display_name":"Conditional quantum entropy","level":5,"score":0.7030292749404907},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.687687337398529},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.5920658111572266},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5669578909873962},{"id":"https://openalex.org/C37731324","wikidata":"https://www.wikidata.org/wiki/Q5380783","display_name":"Entropic uncertainty","level":4,"score":0.5405125021934509},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.5358961820602417},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5086325407028198},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.46076393127441406},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4398413300514221},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.43711262941360474},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3670121431350708},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3610461354255676},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.3361237645149231},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20893847942352295},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.18240702152252197},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1719159185886383},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16195449233055115},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.14926689863204956},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14839890599250793}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tit.2022.3142812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3142812","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:2007.05049","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.05049","pdf_url":"https://arxiv.org/pdf/2007.05049","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"},{"id":"mag:3041416733","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2007.05049.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-05022348v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05022348","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2022, 68 (4), pp.2169-2181. &#x27E8;10.1109/TIT.2022.3142812&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:pure.atira.dk:publications/4197a52c-ed62-4081-90d2-d0ff04624829","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/4197a52c-ed62-4081-90d2-d0ff04624829","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Jabbour , M G &amp; Datta , N 2022 , ' A Tight Uniform Continuity Bound for the Arimoto-R\u00e9nyi Conditional Entropy and its Extension to Classical-Quantum States ' , IEEE Transactions on Information Theory , vol. 68 , no. 4 , pp. 2169 - 2181 . https://doi.org/10.1109/TIT.2022.3142812","raw_type":"article"},{"id":"doi:10.48550/arxiv.2007.05049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2007.05049","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-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2007.05049","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2007.05049","pdf_url":"https://arxiv.org/pdf/2007.05049","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W135467536","https://openalex.org/W798717892","https://openalex.org/W1482224246","https://openalex.org/W1483547755","https://openalex.org/W1559699582","https://openalex.org/W1630138962","https://openalex.org/W1652585999","https://openalex.org/W1987805576","https://openalex.org/W1993376464","https://openalex.org/W1993611246","https://openalex.org/W1995875735","https://openalex.org/W2004980778","https://openalex.org/W2008375822","https://openalex.org/W2009379494","https://openalex.org/W2010138343","https://openalex.org/W2035245840","https://openalex.org/W2037772232","https://openalex.org/W2060588708","https://openalex.org/W2062843442","https://openalex.org/W2079429467","https://openalex.org/W2099111195","https://openalex.org/W2112267744","https://openalex.org/W2114921207","https://openalex.org/W2122882636","https://openalex.org/W2148587342","https://openalex.org/W2150154572","https://openalex.org/W2165203736","https://openalex.org/W2168365126","https://openalex.org/W2518435680","https://openalex.org/W2734727698","https://openalex.org/W2901568712","https://openalex.org/W2962719046","https://openalex.org/W2963157613","https://openalex.org/W2963451384","https://openalex.org/W2963845181","https://openalex.org/W2964157181","https://openalex.org/W2971860074","https://openalex.org/W2972008779","https://openalex.org/W2972631118","https://openalex.org/W3009567204","https://openalex.org/W3101663526","https://openalex.org/W3101827998","https://openalex.org/W3102490990","https://openalex.org/W3102855270","https://openalex.org/W3103345930","https://openalex.org/W3103409729","https://openalex.org/W3103413838","https://openalex.org/W3103953247","https://openalex.org/W3124160004","https://openalex.org/W3144969279","https://openalex.org/W4292058084","https://openalex.org/W6741150059","https://openalex.org/W6768250587","https://openalex.org/W6792728667"],"related_works":["https://openalex.org/W2071902828","https://openalex.org/W1559699582","https://openalex.org/W3098439769","https://openalex.org/W2022688366","https://openalex.org/W2734727698","https://openalex.org/W1983148686","https://openalex.org/W2189660299","https://openalex.org/W2043792910","https://openalex.org/W1562469111","https://openalex.org/W2621932747","https://openalex.org/W2483877878","https://openalex.org/W2139507220","https://openalex.org/W2116782009","https://openalex.org/W3104241674","https://openalex.org/W2338084826","https://openalex.org/W3102958844","https://openalex.org/W1500212248","https://openalex.org/W3099553964","https://openalex.org/W2404892103"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,70,163,181],"tight":[3,146,164],"uniform":[4,147,165],"continuity":[5,148,166],"bound":[6,149,167,204],"for":[7,22,150,168,184,205],"Arimoto\u2019s":[8],"version":[9],"of":[10,37,69,180,209],"the":[11,23,38,50,55,61,74,82,89,119,124,143,151,169,193,201,206,210,213],"conditional":[12,39,71,115,120,170,207],"<inline-formula":[13,25,40,126,171,185,215],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,26,41,127,172,186,216],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[15,27,42,128,173,187,217],"<tex-math":[16,28,43,129,174,188,218],"notation=\"LaTeX\">$\\alpha":[17,29,44,130,175,189,219],"$":[18,45,176,190],"</tex-math></inline-formula>":[19,33,46,133,177,191,222],"-R\u00e9nyi":[20,47,178],"entropy":[21,48,116,122,179,208],"range":[24,195],"\\in":[30],"[0,":[31],"1$":[32,132,221],").":[34],"This":[35,114,198],"definition":[36],"is":[49],"most":[51],"natural":[52],"one":[53],"among":[54],"multiple":[56],"forms":[57],"which":[58],"exist":[59],"in":[60,85,100,123,137,192,212],"literature,":[62],"since":[63],"it":[64,95],"satisfies":[65],"two":[66],"desirable":[67],"properties":[68],"entropy,":[72,79],"namely,":[73],"fact":[75],"that":[76,81],"conditioning":[77],"reduces":[78,117],"and":[80,111,135],"associated":[83],"reduction":[84],"uncertainty":[86],"cannot":[87],"exceed":[88],"information":[90,102,110],"gained":[91],"by":[92],"conditioning.":[93],"Furthermore,":[94],"has":[96],"found":[97],"interesting":[98],"applications":[99],"various":[101],"theoretic":[103],"tasks":[104],"such":[105],"as":[106,196],"guessing":[107],"with":[108],"side":[109],"sequential":[112],"decoding.":[113],"to":[118,141,161],"Shannon":[121],"limit":[125,214],"\\to":[131,220],",":[134],"this":[136],"turn":[138],"allows":[139],"us":[140],"recover":[142],"recently":[144],"obtained":[145],"latter":[152],"from":[153],"our":[154,159],"result.":[155],"Finally,":[156],"we":[157],"apply":[158],"result":[160],"obtain":[162],"classical-quantum":[182],"state,":[183],"same":[194],"above.":[197],"again":[199],"yields":[200],"corresponding":[202],"known":[203],"state":[211],".":[223]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}