{"id":"https://openalex.org/W4390691320","doi":"https://doi.org/10.1109/tit.2024.3351963","title":"Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification","display_name":"Optimal Second-Order Rates for Quantum Soft Covering and Privacy Amplification","publication_year":2024,"publication_date":"2024-01-10","ids":{"openalex":"https://openalex.org/W4390691320","doi":"https://doi.org/10.1109/tit.2024.3351963"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3351963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3351963","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084108418","display_name":"Yuchen Shen","orcid":"https://orcid.org/0000-0002-1181-5198"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Chen Shen","raw_affiliation_strings":["Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan","Department of Electrical Engineering National Taiwan University, Taipei, Taiwan (R.O.C.)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"Department of Electrical Engineering National Taiwan University, Taipei, Taiwan (R.O.C.)","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070262067","display_name":"Li Gao","orcid":"https://orcid.org/0000-0002-9220-0119"},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li Gao","raw_affiliation_strings":["Department of Mathematics, University of Houston, Houston, TX, USA"],"raw_orcid":"https://orcid.org/0000-0002-9220-0119","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Houston, Houston, TX, USA","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048882236","display_name":"Hao\u2013Chung Cheng","orcid":"https://orcid.org/0000-0003-4499-4679"},"institutions":[{"id":"https://openalex.org/I154864474","display_name":"National Taiwan University of Science and Technology","ror":"https://ror.org/00q09pe49","country_code":"TW","type":"education","lineage":["https://openalex.org/I154864474"]},{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]},{"id":"https://openalex.org/I4210108919","display_name":"Foxconn (Taiwan)","ror":"https://ror.org/01v3aym70","country_code":"TW","type":"company","lineage":["https://openalex.org/I4210108919"]},{"id":"https://openalex.org/I4210119858","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210119858"]},{"id":"https://openalex.org/I4403386790","display_name":"National Center for Theoretical Sciences, Physics Division","ror":"https://ror.org/02mh1d616","country_code":null,"type":"facility","lineage":["https://openalex.org/I4210119858","https://openalex.org/I4403386790"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hao-Chung Cheng","raw_affiliation_strings":["Department of Electrical Engineering, Graduate Institute of Communication Engineering, the Department of Mathematics, the Institute of Applied Mathematical Sciences, and the Center for Quantum Science and Engineering, National Taiwan University, Taipei, Taiwan","Department of Electrical Engineering, the Graduate Institute of Communication Engineering, the Department of Mathematics, and the Institute of Applied Mathematical Sciences, and the Center for Quantum Science and Engineering, National Taiwan University, Taipei, Taiwan (R.O.C.)","Hon Hai (Foxconn) Quantum Computing Center, New Taipei City, Taiwan (R.O.C.)","Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan (R.O.C.)"],"raw_orcid":"https://orcid.org/0000-0003-4499-4679","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Graduate Institute of Communication Engineering, the Department of Mathematics, the Institute of Applied Mathematical Sciences, and the Center for Quantum Science and Engineering, National Taiwan University, Taipei, Taiwan","institution_ids":["https://openalex.org/I154864474"]},{"raw_affiliation_string":"Department of Electrical Engineering, the Graduate Institute of Communication Engineering, the Department of Mathematics, and the Institute of Applied Mathematical Sciences, and the Center for Quantum Science and Engineering, National Taiwan University, Taipei, Taiwan (R.O.C.)","institution_ids":["https://openalex.org/I16733864"]},{"raw_affiliation_string":"Hon Hai (Foxconn) Quantum Computing Center, New Taipei City, Taiwan (R.O.C.)","institution_ids":["https://openalex.org/I4210108919"]},{"raw_affiliation_string":"Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan (R.O.C.)","institution_ids":["https://openalex.org/I4210119858","https://openalex.org/I4403386790"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7053,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90483545,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"70","issue":"7","first_page":"5077","last_page":"5091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994000196456909,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994000196456909,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9986000061035156,"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":0.9962000250816345,"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/trace-distance","display_name":"Trace distance","score":0.6469535231590271},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.5886064767837524},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5321824550628662},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.5205153822898865},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.478362500667572},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.4384472966194153},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.43678486347198486},{"id":"https://openalex.org/keywords/mutual-information","display_name":"Mutual information","score":0.4353538155555725},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4327126741409302},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.4125974178314209},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40053364634513855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3502444922924042},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24781107902526855},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.1373458206653595},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1280106008052826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10414150357246399}],"concepts":[{"id":"https://openalex.org/C105063144","wikidata":"https://www.wikidata.org/wiki/Q7831154","display_name":"Trace distance","level":4,"score":0.6469535231590271},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.5886064767837524},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5321824550628662},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.5205153822898865},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.478362500667572},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4384472966194153},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.43678486347198486},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.4353538155555725},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4327126741409302},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.4125974178314209},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40053364634513855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3502444922924042},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24781107902526855},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.1373458206653595},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1280106008052826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10414150357246399}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2024.3351963","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3351963","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.75}],"awards":[{"id":"https://openalex.org/G1418129637","display_name":null,"funder_award_id":"112-2636-E-002-009","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G1577247482","display_name":null,"funder_award_id":"NTU-113L891605","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"},{"id":"https://openalex.org/G2379267560","display_name":null,"funder_award_id":"112-2119-M-001-006","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G3001454219","display_name":null,"funder_award_id":"NTU-113L900702","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"},{"id":"https://openalex.org/G322332536","display_name":null,"funder_award_id":"112-2124-M-002-003","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G738129518","display_name":null,"funder_award_id":"NTU-112V1904-4","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"},{"id":"https://openalex.org/G7737297726","display_name":null,"funder_award_id":"111-2813-C-002-099-E","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G7855059434","display_name":null,"funder_award_id":"112-2119-M-007-006","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G8459602367","display_name":null,"funder_award_id":"NTU-112L900702","funder_id":"https://openalex.org/F4320321408","funder_display_name":"Ministry of Education"}],"funders":[{"id":"https://openalex.org/F4320321408","display_name":"Ministry of Education","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":101,"referenced_works":["https://openalex.org/W906791365","https://openalex.org/W1481217622","https://openalex.org/W1499934958","https://openalex.org/W1588709600","https://openalex.org/W1604817450","https://openalex.org/W1776233866","https://openalex.org/W1794253150","https://openalex.org/W1955330666","https://openalex.org/W1955655900","https://openalex.org/W1963589622","https://openalex.org/W1963925013","https://openalex.org/W1968087916","https://openalex.org/W1987336330","https://openalex.org/W1989338245","https://openalex.org/W1990187371","https://openalex.org/W1995875735","https://openalex.org/W1996053641","https://openalex.org/W2001619599","https://openalex.org/W2007661134","https://openalex.org/W2007737215","https://openalex.org/W2013695092","https://openalex.org/W2027642452","https://openalex.org/W2035972614","https://openalex.org/W2091240287","https://openalex.org/W2092119860","https://openalex.org/W2103674915","https://openalex.org/W2104340231","https://openalex.org/W2106864314","https://openalex.org/W2112065886","https://openalex.org/W2114473497","https://openalex.org/W2114805880","https://openalex.org/W2115328106","https://openalex.org/W2119541381","https://openalex.org/W2122166994","https://openalex.org/W2134348739","https://openalex.org/W2139236075","https://openalex.org/W2141432745","https://openalex.org/W2144180948","https://openalex.org/W2154564336","https://openalex.org/W2162635854","https://openalex.org/W2163484647","https://openalex.org/W2164253138","https://openalex.org/W2166302514","https://openalex.org/W2166827316","https://openalex.org/W2167830490","https://openalex.org/W2168792807","https://openalex.org/W2180630352","https://openalex.org/W2242421097","https://openalex.org/W2263335765","https://openalex.org/W2292970846","https://openalex.org/W2293665602","https://openalex.org/W2548783102","https://openalex.org/W2609234978","https://openalex.org/W2750244421","https://openalex.org/W2791848241","https://openalex.org/W2804172638","https://openalex.org/W2883360900","https://openalex.org/W2900230570","https://openalex.org/W2950067144","https://openalex.org/W2952297488","https://openalex.org/W2963818496","https://openalex.org/W2964059052","https://openalex.org/W2969644469","https://openalex.org/W2990961515","https://openalex.org/W3098108619","https://openalex.org/W3098995074","https://openalex.org/W3099232516","https://openalex.org/W3099410101","https://openalex.org/W3099883761","https://openalex.org/W3100210526","https://openalex.org/W3100438626","https://openalex.org/W3100955123","https://openalex.org/W3101381962","https://openalex.org/W3101663526","https://openalex.org/W3101953664","https://openalex.org/W3102288805","https://openalex.org/W3102602776","https://openalex.org/W3102660043","https://openalex.org/W3103744872","https://openalex.org/W3104064455","https://openalex.org/W3104789413","https://openalex.org/W3128157579","https://openalex.org/W3135566506","https://openalex.org/W3160869769","https://openalex.org/W3214095954","https://openalex.org/W4206039841","https://openalex.org/W4213004663","https://openalex.org/W4221163362","https://openalex.org/W4226136255","https://openalex.org/W4226362612","https://openalex.org/W4285134240","https://openalex.org/W4297688295","https://openalex.org/W4297944615","https://openalex.org/W4301258660","https://openalex.org/W4312889713","https://openalex.org/W6636836932","https://openalex.org/W6638173902","https://openalex.org/W6767558323","https://openalex.org/W6784576191","https://openalex.org/W6811176204","https://openalex.org/W6811451432"],"related_works":["https://openalex.org/W2975604236","https://openalex.org/W3022655582","https://openalex.org/W2954849343","https://openalex.org/W3134129340","https://openalex.org/W2816784085","https://openalex.org/W1479897377","https://openalex.org/W2161963661","https://openalex.org/W3005577593","https://openalex.org/W2903293040","https://openalex.org/W4289144918"],"abstract_inverted_index":{"We":[0,65,132],"study":[1],"quantum":[2,9,19,30,43,140,146],"soft":[3],"covering":[4],"and":[5,27,39,60,113,144],"privacy":[6],"amplification":[7],"against":[8,42],"side":[10],"information.":[11],"The":[12,32],"former":[13],"task":[14,34],"aims":[15,35],"to":[16,36,52,123,155],"approximate":[17],"a":[18,24,29],"state":[20,59],"by":[21,79,102,138],"sampling":[22],"from":[23],"prior":[25],"distribution":[26],"querying":[28],"channel.":[31],"latter":[33],"extract":[37],"uniform":[38],"independent":[40,112],"randomness":[41,95],"adversaries.":[44],"For":[45],"both":[46],"tasks,":[47,118],"we":[48],"use":[49],"trace":[50,168,181],"distance":[51,182],"measure":[53],"the":[54,57,61,68,80,92,103,117,128,139,145,156,162,167],"closeness":[55],"between":[56],"processed":[58],"ideal":[62],"target":[63],"state.":[64],"show":[66],"that":[67],"minimal":[69],"amount":[70],"of":[71,116,127,180],"samples":[72],"for":[73,96],"achieving":[74],"an":[75,97],"\u03b5-covering":[76],"is":[77,100,177],"given":[78,137],"(1":[81,105],"\u2212":[82,106],"\u03b5)-hypothesis":[83,107],"testing":[84,108],"information":[85,142,148],"(with":[86],"additional":[87],"logarithmic":[88],"additive":[89],"terms),":[90],"while":[91],"maximal":[93],"extractable":[94],"\u03b5-secret":[98],"extractor":[99],"characterized":[101],"conditional":[104,147],"entropy.":[109],"When":[110],"performing":[111],"identical":[114],"repetitions":[115],"our":[119,152],"one-shot":[120],"characterizations":[121],"lead":[122],"tight":[124],"asymptotic":[125,164],"expansions":[126],"above-mentioned":[129],"operational":[130],"quantities.":[131],"establish":[133],"their":[134],"second-order":[135],"rates":[136,165],"mutual":[141],"variance":[143],"variance,":[149],"respectively.":[150],"Moreover,":[151],"results":[153],"extend":[154],"moderate":[157],"deviation":[158],"regime,":[159],"which":[160],"are":[161],"optimal":[163],"when":[166],"distances":[169],"vanish":[170],"at":[171],"sub-exponential":[172],"speed.":[173],"Our":[174],"proof":[175],"technique":[176],"direct":[178],"analysis":[179],"without":[183],"smoothing.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}