{"id":"https://openalex.org/W2519202260","doi":"https://doi.org/10.1109/tit.2018.2854766","title":"Energy-Constrained Private and Quantum Capacities of Quantum Channels","display_name":"Energy-Constrained Private and Quantum Capacities of Quantum Channels","publication_year":2018,"publication_date":"2018-12-01","ids":{"openalex":"https://openalex.org/W2519202260","doi":"https://doi.org/10.1109/tit.2018.2854766","mag":"2519202260"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2854766","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2854766","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/1609.01997","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037632925","display_name":"Mark M. Wilde","orcid":"https://orcid.org/0000-0002-3916-4462"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mark M. Wilde","raw_affiliation_strings":["Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3916-4462","affiliations":[{"raw_affiliation_string":"Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074920553","display_name":"Haoyu Qi","orcid":"https://orcid.org/0000-0002-0636-7925"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Haoyu Qi","raw_affiliation_strings":["Department of Physics and Astronomy, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, LA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, Hearne Institute for Theoretical Physics, Louisiana State University, Baton Rouge, LA, USA","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3928,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.95396856,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"64","issue":"12","first_page":"7802","last_page":"7827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9993000030517578,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.5883681774139404},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"Quantum capacity","score":0.5703359842300415},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5279898643493652},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5176066160202026},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.510263204574585},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4690055549144745},{"id":"https://openalex.org/keywords/amplitude-damping-channel","display_name":"Amplitude damping channel","score":0.4557560980319977},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.4538726210594177},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.44241228699684143},{"id":"https://openalex.org/keywords/observable","display_name":"Observable","score":0.4415963590145111},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.429287314414978},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42636895179748535},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.41363513469696045},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3922586441040039},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38167861104011536},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.315674364566803},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24441269040107727},{"id":"https://openalex.org/keywords/quantum-network","display_name":"Quantum network","score":0.21082597970962524}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5883681774139404},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.5703359842300415},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5279898643493652},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5176066160202026},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.510263204574585},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4690055549144745},{"id":"https://openalex.org/C206040425","wikidata":"https://www.wikidata.org/wiki/Q4748511","display_name":"Amplitude damping channel","level":5,"score":0.4557560980319977},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.4538726210594177},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.44241228699684143},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4415963590145111},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.429287314414978},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42636895179748535},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.41363513469696045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3922586441040039},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38167861104011536},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.315674364566803},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24441269040107727},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.21082597970962524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2018.2854766","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2854766","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:1609.01997","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.01997","pdf_url":"https://arxiv.org/pdf/1609.01997","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":"pmh:oai:digitalcommons.lsu.edu:physics_astronomy_pubs-6705","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/physics_astronomy_pubs/5625","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:physics_astronomy_pubs-6705","is_oa":false,"landing_page_url":"https://repository.lsu.edu/physics_astronomy_pubs/5625","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1609.01997","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.01997","pdf_url":"https://arxiv.org/pdf/1609.01997","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":"Affordable and clean energy","score":0.8299999833106995,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1574629514","display_name":null,"funder_award_id":"CCF-1350397","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"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":120,"referenced_works":["https://openalex.org/W602904462","https://openalex.org/W906791365","https://openalex.org/W1480262205","https://openalex.org/W1491656027","https://openalex.org/W1494099594","https://openalex.org/W1522874822","https://openalex.org/W1549607042","https://openalex.org/W1559699582","https://openalex.org/W1621050367","https://openalex.org/W1728437521","https://openalex.org/W1785526227","https://openalex.org/W1870862908","https://openalex.org/W1887941508","https://openalex.org/W1899018334","https://openalex.org/W1963552431","https://openalex.org/W1971279958","https://openalex.org/W1971585707","https://openalex.org/W1977545330","https://openalex.org/W1978930518","https://openalex.org/W1983148686","https://openalex.org/W1990977980","https://openalex.org/W1992717794","https://openalex.org/W1993574974","https://openalex.org/W1993611246","https://openalex.org/W1995532371","https://openalex.org/W1998193140","https://openalex.org/W1998573231","https://openalex.org/W2003227025","https://openalex.org/W2015132296","https://openalex.org/W2016251501","https://openalex.org/W2017102239","https://openalex.org/W2024823087","https://openalex.org/W2027561650","https://openalex.org/W2027642452","https://openalex.org/W2034274945","https://openalex.org/W2035792087","https://openalex.org/W2036911202","https://openalex.org/W2037747187","https://openalex.org/W2040133029","https://openalex.org/W2040211109","https://openalex.org/W2043769961","https://openalex.org/W2043920035","https://openalex.org/W2044528981","https://openalex.org/W2056721621","https://openalex.org/W2057574680","https://openalex.org/W2059823455","https://openalex.org/W2061684843","https://openalex.org/W2066079856","https://openalex.org/W2072867330","https://openalex.org/W2074384947","https://openalex.org/W2089507606","https://openalex.org/W2089602236","https://openalex.org/W2091310682","https://openalex.org/W2093694754","https://openalex.org/W2108415401","https://openalex.org/W2116679455","https://openalex.org/W2118945164","https://openalex.org/W2121213780","https://openalex.org/W2123142728","https://openalex.org/W2128386771","https://openalex.org/W2129110882","https://openalex.org/W2132333350","https://openalex.org/W2139236075","https://openalex.org/W2141185014","https://openalex.org/W2141412822","https://openalex.org/W2142734877","https://openalex.org/W2147311608","https://openalex.org/W2153967767","https://openalex.org/W2158969655","https://openalex.org/W2162644822","https://openalex.org/W2164047376","https://openalex.org/W2167346196","https://openalex.org/W2265116054","https://openalex.org/W2273682834","https://openalex.org/W2287954541","https://openalex.org/W2289204408","https://openalex.org/W2301860273","https://openalex.org/W2333041090","https://openalex.org/W2341140804","https://openalex.org/W2401830326","https://openalex.org/W2467435161","https://openalex.org/W2515797450","https://openalex.org/W2546207189","https://openalex.org/W2557405109","https://openalex.org/W2588842163","https://openalex.org/W2588979507","https://openalex.org/W2594901681","https://openalex.org/W2741983064","https://openalex.org/W2785148687","https://openalex.org/W2804172638","https://openalex.org/W2963154570","https://openalex.org/W2963806987","https://openalex.org/W2966190690","https://openalex.org/W2983536868","https://openalex.org/W3098019513","https://openalex.org/W3098989707","https://openalex.org/W3099252196","https://openalex.org/W3100095540","https://openalex.org/W3101546802","https://openalex.org/W3101698424","https://openalex.org/W3101790948","https://openalex.org/W3102125882","https://openalex.org/W3102602776","https://openalex.org/W3102756624","https://openalex.org/W3103786315","https://openalex.org/W3104200005","https://openalex.org/W3104656332","https://openalex.org/W3104746849","https://openalex.org/W3104876448","https://openalex.org/W3106117517","https://openalex.org/W3106384386","https://openalex.org/W3106514171","https://openalex.org/W3124160004","https://openalex.org/W3213943817","https://openalex.org/W4229909698","https://openalex.org/W4243174996","https://openalex.org/W4243381896","https://openalex.org/W4300840296","https://openalex.org/W6628727055","https://openalex.org/W6693138899"],"related_works":["https://openalex.org/W2030160643","https://openalex.org/W3208208393","https://openalex.org/W2132333350","https://openalex.org/W2963686166","https://openalex.org/W3101698424","https://openalex.org/W1977821353","https://openalex.org/W2292970846","https://openalex.org/W2264989289","https://openalex.org/W1989739346","https://openalex.org/W3100282202"],"abstract_inverted_index":{"This":[0],"paper":[1],"establishes":[2],"a":[3,27,41,113,124],"general":[4],"theory":[5],"of":[6,12,111,146,192,200,203],"energy-constrained":[7,20,80,139],"quantum":[8,13,24,156],"and":[9,45,93,120,159],"private":[10,38],"capacities":[11,68],"channels.":[14],"We":[15,54,74,149],"begin":[16],"by":[17],"defining":[18],"various":[19],"communication":[21,25,39],"tasks,":[22,102],"including":[23],"with":[26,33,40,49],"uniform":[28,42],"energy":[29,36,43,52,105],"constraint,":[30,37,44],"entanglement":[31],"transmission":[32,48],"an":[34,50,95],"average":[35,51],"secret":[46],"key":[47],"constraint.":[53],"develop":[55],"several":[56,161],"code":[57],"conversions,":[58],"which":[59],"allow":[60],"us":[61],"to":[62,70,85,144,154,179],"conclude":[63],"non-trivial":[64],"relations":[65],"between":[66],"the":[67,71,78,86,89,99,104,108,121,137,147,166,188,198],"corresponding":[69],"above":[72],"tasks.":[73],"then":[75],"show":[76],"how":[77],"regularized,":[79],"coherent":[81,140],"information":[82,141],"is":[83,94,142],"equal":[84,143],"capacity":[87],"for":[88,98,117],"first":[90],"two":[91,101],"tasks":[92],"achievable":[96],"rate":[97],"latter":[100],"whenever":[103],"observable":[106],"satisfies":[107,123],"Gibbs":[109],"condition":[110],"having":[112],"well-defined":[114],"thermal":[115],"state":[116],"all":[118,145],"temperatures":[119],"channel":[122],"finite":[125],"output-entropy":[126],"condition.":[127],"For":[128],"degradable":[129,155],"channels":[130,158],"satisfying":[131],"these":[132,193],"conditions,":[133],"we":[134,171],"find":[135],"that":[136],"single-letter":[138],"capacities.":[148],"finally":[150],"apply":[151],"our":[152],"results":[153,162,174,194],"Gaussian":[157],"recover":[160],"already":[163],"established":[164],"in":[165,175,187],"literature":[167,189],"(in":[168],"some":[169,184],"cases,":[170],"prove":[172],"new":[173],"this":[176],"domain).":[177],"Contrary":[178],"what":[180],"may":[181],"appear":[182],"from":[183],"statements":[185],"made":[186],"recently,":[190],"proofs":[191],"do":[195],"not":[196],"require":[197],"solution":[199],"any":[201],"kind":[202],"minimum":[204],"output":[205],"entropy":[206,209],"conjecture":[207],"or":[208],"photon-number":[210],"inequality.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-11-23T00:00:00"}