{"id":"https://openalex.org/W3210042290","doi":null,"title":"Exponent in Smoothing the Max-Relative Entropy and Its Application to Quantum Privacy Amplification.","display_name":"Exponent in Smoothing the Max-Relative Entropy and Its Application to Quantum Privacy Amplification.","publication_year":2021,"publication_date":"2021-11-01","ids":{"openalex":"https://openalex.org/W3210042290","mag":"3210042290"},"language":"en","primary_location":{"id":"mag:3210042290","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2111.01075","pdf_url":null,"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,"listed_in":[],"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},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2111.01075","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100343552","display_name":"Ke Li","orcid":"https://orcid.org/0000-0002-3944-8449","observed_orcids":["https://orcid.org/0000-0002-3944-8449","https://orcid.org/0000-0003-0190-0003"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ke Li","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3944-8449","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102845640","display_name":"Yongsheng Yao","orcid":"https://orcid.org/0000-0001-5368-3245","observed_orcids":["https://orcid.org/0000-0001-5368-3245"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongsheng Yao","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-5368-3245","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":1.0,"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":1.0,"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":9.999999747378752e-05,"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":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-side-information","display_name":"quantum side information","score":0.9169999957084656},{"id":"https://openalex.org/keywords/randomness-extraction","display_name":"randomness extraction","score":0.8069999814033508},{"id":"https://openalex.org/keywords/quantum-key-distribution","display_name":"quantum key distribution","score":0.4490000009536743},{"id":"https://openalex.org/keywords/error-exponent","display_name":"reliability function","score":0.5339999794960022},{"id":"https://openalex.org/keywords/channel-coding","display_name":"channel coding","score":0.5920000076293945}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7779840230941772},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.719512403011322},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6087603569030762},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.553059995174408},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5422435998916626},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5390979051589966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5297844409942627},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.4993906021118164},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.47955867648124695},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4399903118610382},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.42788970470428467},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.419174462556839},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35312819480895996},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25133925676345825},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.24231207370758057},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.2004098892211914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18251684308052063},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.09565195441246033},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:3210042290","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2111.01075","pdf_url":null,"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,"listed_in":[],"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}],"best_oa_location":{"id":"mag:3210042290","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2111.01075","pdf_url":null,"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,"listed_in":[],"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},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W1598556089","https://openalex.org/W1604817450","https://openalex.org/W1621050367","https://openalex.org/W1646511125","https://openalex.org/W1745229717","https://openalex.org/W1776233866","https://openalex.org/W1968087916","https://openalex.org/W1968720171","https://openalex.org/W1989338245","https://openalex.org/W1990187371","https://openalex.org/W1993944611","https://openalex.org/W1996053641","https://openalex.org/W2002420498","https://openalex.org/W2005530146","https://openalex.org/W2011008529","https://openalex.org/W2013567929","https://openalex.org/W2013695092","https://openalex.org/W2023885784","https://openalex.org/W2027642452","https://openalex.org/W2033879010","https://openalex.org/W2034307424","https://openalex.org/W2035972614","https://openalex.org/W2043792910","https://openalex.org/W2050847409","https://openalex.org/W2052207834","https://openalex.org/W2066873261","https://openalex.org/W2091240287","https://openalex.org/W2099111195","https://openalex.org/W2105211531","https://openalex.org/W2122166994","https://openalex.org/W2132840498","https://openalex.org/W2144277460","https://openalex.org/W2148587342","https://openalex.org/W2150154572","https://openalex.org/W2154300278","https://openalex.org/W2157041209","https://openalex.org/W2159023941","https://openalex.org/W2159628417","https://openalex.org/W2167346196","https://openalex.org/W2168792807","https://openalex.org/W2180630352","https://openalex.org/W2403732950","https://openalex.org/W2758224462","https://openalex.org/W2791848241","https://openalex.org/W3100230369","https://openalex.org/W3100438626","https://openalex.org/W3103101214","https://openalex.org/W3104064455","https://openalex.org/W3104490977","https://openalex.org/W3105289656","https://openalex.org/W3160869769"],"related_works":["https://openalex.org/W4312889713","https://openalex.org/W4289655181","https://openalex.org/W7134057016","https://openalex.org/W2029358194","https://openalex.org/W4226362612","https://openalex.org/W3160869769","https://openalex.org/W4221163362","https://openalex.org/W1968720171","https://openalex.org/W42921363","https://openalex.org/W7203669113"],"abstract_inverted_index":{"The":[0],"max-relative":[1,38],"entropy":[2],"together":[3],"with":[4],"its":[5],"smoothed":[6],"version":[7],"is":[8,100,139],"a":[9,102,145],"basic":[10],"tool":[11],"in":[12,35,127,141,154],"quantum":[13,33,52],"information":[14],"theory.":[15],"In":[16],"this":[17,43],"paper,":[18],"we":[19,56,112,121],"derive":[20],"the":[21,25,28,32,37,46,62,65,68,82,90,95,107,115,128,132,136,151],"exact":[22,116],"exponent":[23,63,153],"for":[24,61,106],"decay":[26],"of":[27,31,48,64,67,97,109,150],"small":[29],"modification":[30],"state":[34],"smoothing":[36],"entropy.":[39,77],"We":[40],"then":[41],"apply":[42],"result":[44],"to":[45,148],"problem":[47],"privacy":[49],"amplification":[50],"against":[51],"side":[53],"information,":[54],"and":[55,89,124],"obtain":[57],"an":[58],"upper":[59,79,133],"bound":[60,80,85,134,138],"decreasing":[66],"insecurity,":[69],"measured":[70],"using":[71],"either":[72],"purified":[73],"distance":[74],"or":[75],"relative":[76],"Our":[78],"complements":[81],"earlier":[83],"lower":[84,137],"established":[86],"by":[87],"Hayashi,":[88],"two":[91],"bounds":[92],"match":[93],"when":[94],"rate":[96],"randomness":[98],"extraction":[99],"above":[101],"critical":[103],"value.":[104],"Thus,":[105],"case":[108],"high":[110],"rate,":[111],"have":[113],"determined":[114],"security":[117],"exponent.":[118],"Following":[119],"this,":[120],"give":[122],"examples":[123],"show":[125],"that":[126,149],"low-rate":[129],"case,":[130],"neither":[131],"nor":[135],"tight":[140],"general.":[142],"This":[143],"exhibits":[144],"picture":[146],"similar":[147],"error":[152],"channel":[155],"coding.":[156]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2021-11-08T00:00:00"}
