{"id":"https://openalex.org/W2094676669","doi":"https://doi.org/10.1109/tit.2012.2218792","title":"Polar Codes for Classical-Quantum Channels","display_name":"Polar Codes for Classical-Quantum Channels","publication_year":2012,"publication_date":"2012-09-14","ids":{"openalex":"https://openalex.org/W2094676669","doi":"https://doi.org/10.1109/tit.2012.2218792","mag":"2094676669"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2218792","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2218792","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/1109.2591","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/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Mark M. Wilde","raw_affiliation_strings":["School of Computer Science, McGill University, Montreal, QC, Canada","[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, McGill University, Montreal, QC, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"[Sch. of Comput. Sci., McGill Univ., Montreal, QC, Canada]","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049404285","display_name":"Saikat Guha","orcid":"https://orcid.org/0000-0002-2581-4380"},"institutions":[{"id":"https://openalex.org/I1306686416","display_name":"RTX (United States)","ror":"https://ror.org/0354t7b78","country_code":"US","type":"company","lineage":["https://openalex.org/I1306686416"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Saikat Guha","raw_affiliation_strings":["Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, MA, USA","Quantum Inf. Process. Group, Raytheon BBN Technol., Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, MA, USA","institution_ids":["https://openalex.org/I1306686416"]},{"raw_affiliation_string":"Quantum Inf. Process. Group, Raytheon BBN Technol., Cambridge, MA, USA","institution_ids":["https://openalex.org/I1306686416"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037632925"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":15.2743,"has_fulltext":false,"cited_by_count":120,"citation_normalized_percentile":{"value":0.99222751,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"59","issue":"2","first_page":"1175","last_page":"1187"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9994999766349792,"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/T12029","display_name":"DNA and Biological Computing","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/classical-capacity","display_name":"Classical capacity","score":0.5293888449668884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.502117395401001},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"Quantum capacity","score":0.49787235260009766},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.4841664433479309},{"id":"https://openalex.org/keywords/polar-code","display_name":"Polar code","score":0.48076388239860535},{"id":"https://openalex.org/keywords/channel-capacity","display_name":"Channel capacity","score":0.47961413860321045},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.46964165568351746},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.46959272027015686},{"id":"https://openalex.org/keywords/puncturing","display_name":"Puncturing","score":0.4466910660266876},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.40065088868141174},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3937002718448639},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37127619981765747},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3542519807815552},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34940874576568604},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.30050578713417053},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.2312820851802826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2066328227519989},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18327376246452332},{"id":"https://openalex.org/keywords/quantum-network","display_name":"Quantum network","score":0.17229267954826355},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09903672337532043}],"concepts":[{"id":"https://openalex.org/C168090291","wikidata":"https://www.wikidata.org/wiki/Q5128319","display_name":"Classical capacity","level":5,"score":0.5293888449668884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.502117395401001},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.49787235260009766},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.4841664433479309},{"id":"https://openalex.org/C2778396592","wikidata":"https://www.wikidata.org/wiki/Q7209069","display_name":"Polar code","level":3,"score":0.48076388239860535},{"id":"https://openalex.org/C97744766","wikidata":"https://www.wikidata.org/wiki/Q870845","display_name":"Channel capacity","level":3,"score":0.47961413860321045},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.46964165568351746},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46959272027015686},{"id":"https://openalex.org/C2778808095","wikidata":"https://www.wikidata.org/wiki/Q3899825","display_name":"Puncturing","level":2,"score":0.4466910660266876},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.40065088868141174},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3937002718448639},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37127619981765747},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3542519807815552},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34940874576568604},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.30050578713417053},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.2312820851802826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2066328227519989},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18327376246452332},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.17229267954826355},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09903672337532043}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2012.2218792","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2218792","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:1109.2591","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.2591","pdf_url":"https://arxiv.org/pdf/1109.2591","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:digitalcommons.lsu.edu:physics_astronomy_pubs-6803","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/physics_astronomy_pubs/5723","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:CiteSeerX.psu:10.1.1.765.4357","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.4357","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1109.2591.pdf","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:physics_astronomy_pubs-6803","is_oa":false,"landing_page_url":"https://repository.lsu.edu/physics_astronomy_pubs/5723","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:1109.2591","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.2591","pdf_url":"https://arxiv.org/pdf/1109.2591","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320312572","display_name":"Minist\u00e8re du D\u00e9veloppement \u00c9conomique, de l\u2019Innovation et de l\u2019Exportation","ror":null},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332434","display_name":"ExxonMobil Research and Engineering Company","ror":"https://ror.org/01xcepn55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W285471286","https://openalex.org/W639433093","https://openalex.org/W1522029393","https://openalex.org/W1536930200","https://openalex.org/W1568529095","https://openalex.org/W1621050367","https://openalex.org/W1629914808","https://openalex.org/W1631356911","https://openalex.org/W1785526227","https://openalex.org/W1793914521","https://openalex.org/W1882122127","https://openalex.org/W1968522320","https://openalex.org/W1974241974","https://openalex.org/W1988155384","https://openalex.org/W1995875735","https://openalex.org/W2001619599","https://openalex.org/W2009191939","https://openalex.org/W2013695092","https://openalex.org/W2051869207","https://openalex.org/W2055534149","https://openalex.org/W2063568508","https://openalex.org/W2071087711","https://openalex.org/W2074384947","https://openalex.org/W2075176455","https://openalex.org/W2079748983","https://openalex.org/W2096894382","https://openalex.org/W2097527197","https://openalex.org/W2099111195","https://openalex.org/W2100479399","https://openalex.org/W2105918132","https://openalex.org/W2114473497","https://openalex.org/W2118905418","https://openalex.org/W2122312868","https://openalex.org/W2139784773","https://openalex.org/W2141107613","https://openalex.org/W2141412822","https://openalex.org/W2145712176","https://openalex.org/W2150498905","https://openalex.org/W2151036026","https://openalex.org/W2154193570","https://openalex.org/W2154564336","https://openalex.org/W2158137498","https://openalex.org/W2164368671","https://openalex.org/W2166827316","https://openalex.org/W2167346196","https://openalex.org/W2167830490","https://openalex.org/W2295517275","https://openalex.org/W2561321245","https://openalex.org/W2764347725","https://openalex.org/W2952322103","https://openalex.org/W2952954835","https://openalex.org/W2993383518","https://openalex.org/W3037524284","https://openalex.org/W3098032907","https://openalex.org/W3099330432","https://openalex.org/W3099516920","https://openalex.org/W3100243009","https://openalex.org/W3102928882","https://openalex.org/W3106210707","https://openalex.org/W3123299285","https://openalex.org/W3148774511","https://openalex.org/W4206028667","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3102664240","https://openalex.org/W2040161280","https://openalex.org/W3098640227","https://openalex.org/W2236399401","https://openalex.org/W2030160643","https://openalex.org/W2594901681","https://openalex.org/W2141412822","https://openalex.org/W2077996616","https://openalex.org/W2963792517","https://openalex.org/W1622368049"],"abstract_inverted_index":{"Holevo,":[0],"Schumacher,":[1],"and":[2,27,102,160,200,213],"Westmoreland's":[3],"coding":[4],"theorem":[5],"guarantees":[6],"the":[7,15,33,72,80,110,119,129,134,137,153,157,164,183,190,214,235,238,252,255,262,265],"existence":[8,34],"of":[9,17,35,46,53,82,97,109,136,171,237,264,283],"codes":[10,47,65,70,208],"that":[11,66,189,243,254,278],"are":[12,67,113,122,174],"capacity-achieving":[13],"for":[14,48,79,115,125,149,195,280],"task":[16],"sending":[18],"classical":[19,25,83,198],"data":[20,116,126,150],"over":[21],"a":[22,95,107,146,244,281,287],"channel":[23,73,140,191],"with":[24,128,197,261],"inputs":[26,199],"quantum":[28,184,201,245,288],"outputs.":[29,202],"Although":[30],"they":[31],"demonstrated":[32],"such":[36],"codes,":[37],"their":[38],"proof":[39],"does":[40],"not":[41],"provide":[42],"an":[43,88],"explicit":[44],"construction":[45],"this":[49,54,59,172,211,268],"task.":[50],"The":[51,69,139,167],"aim":[52],"paper":[55,173],"is":[56,87,217,234],"to":[57,133,145,187,286],"fill":[58],"gap":[60],"by":[61,77,99],"constructing":[62],"near-explicit":[63],"\u201cpolar\u201d":[64],"capacity-achieving.":[68],"exploit":[71,272],"polarization":[74,86,141,192],"phenomenon":[75],"observed":[76],"Arikan":[78],"case":[81],"channels.":[84],"Channel":[85],"effect":[89,142,193],"in":[90,105,251],"which":[91,106],"one":[92],"can":[93],"synthesize":[94],"set":[96],"channels,":[98],"\u201cchannel":[100,103],"combining\u201d":[101],"splitting,\u201d":[104],"fraction":[108,131],"synthesized":[111],"channels":[112,121,159,196],"perfect":[114,158],"transmission,":[117,127],"while":[118],"other":[120],"completely":[123],"useless":[124,165],"good":[130],"equal":[132],"capacity":[135],"channel.":[138],"then":[143,204],"leads":[144],"simple":[147],"scheme":[148],"transmission:":[151],"send":[152],"information":[154,185],"bits":[155,162],"through":[156,163],"\u201cfrozen\u201d":[161],"ones.":[166],"main":[168],"technical":[169],"contributions":[170],"threefold.":[175],"First,":[176],"we":[177,271],"leverage":[178],"several":[179],"known":[180],"results":[181],"from":[182],"literature":[186],"demonstrate":[188,242],"occurs":[194],"We":[203,240],"construct":[205],"linear":[206],"polar":[207],"based":[209],"on":[210],"effect,":[212],"encoding":[215],"complexity":[216],"<i":[218,222,226,231],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[219,223,227,232],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">O</i>":[220],"(":[221],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[224,228,233],"log":[225],"),":[229],"where":[230],"blocklength":[236,263],"code.":[239,266],"also":[241],"successive":[246],"cancellation":[247],"decoder":[248],"works":[249],"well,":[250],"sense":[253],"word":[256],"error":[257],"rate":[258],"decays":[259],"exponentially":[260],"For":[267],"last":[269],"result,":[270],"Sen's":[273],"recent":[274],"\u201cnoncommutative":[275],"union":[276],"bound\u201d":[277],"holds":[279],"sequence":[282],"projectors":[284],"applied":[285],"state.":[289]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2020-11-23T00:00:00"}
