{"id":"https://openalex.org/W7212281124","doi":"https://doi.org/10.48550/arxiv.2609.11930","title":"Hierarchy of R\u00e9nyi Coherent Information in Stabilizer Codes","display_name":"Hierarchy of R\u00e9nyi Coherent Information in Stabilizer Codes","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212281124","doi":"https://doi.org/10.48550/arxiv.2609.11930"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11930","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11930","pdf_url":"https://arxiv.org/pdf/2609.11930","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":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.11930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102697454","display_name":"Akash Vijay","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I4405252470","display_name":"Anthony J. Leggett Institute for Condensed Matter Theory","ror":"https://ror.org/02zvy6a06","country_code":"US","type":"facility","lineage":["https://openalex.org/I157725225","https://openalex.org/I4405252470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vijay, Akash","raw_affiliation_strings":["Department of Physics and Institute for Condensed Matter Theory , University of Illinois Urbana-Champaign , Urbana , Illinois 61801 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Institute for Condensed Matter Theory , University of Illinois Urbana-Champaign , Urbana , Illinois 61801 , USA","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I4405252470"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065010171","display_name":"Luis Colmen\u00e1rez","orcid":"https://orcid.org/0000-0002-5946-7591","observed_orcids":["https://orcid.org/0000-0002-5946-7591"]},"institutions":[{"id":"https://openalex.org/I171892758","display_name":"Forschungszentrum J\u00fclich","ror":"https://ror.org/02nv7yv05","country_code":"DE","type":"facility","lineage":["https://openalex.org/I1305996414","https://openalex.org/I171892758"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Colmenarez, Luis","raw_affiliation_strings":["Institute for Quantum Information , RWTH Aachen University , 52056 Aachen , Germany","Institute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum J\u00fclich , 52428 J\u00fclich , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information , RWTH Aachen University , 52056 Aachen , Germany","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Institute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum J\u00fclich , 52428 J\u00fclich , Germany","institution_ids":["https://openalex.org/I171892758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5151334231","display_name":"Jong Yeon Lee","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I125608817","display_name":"Korea Institute for Advanced Study","ror":"https://ror.org/041hz9568","country_code":"KR","type":"facility","lineage":["https://openalex.org/I125608817"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I4405252470","display_name":"Anthony J. Leggett Institute for Condensed Matter Theory","ror":"https://ror.org/02zvy6a06","country_code":"US","type":"facility","lineage":["https://openalex.org/I157725225","https://openalex.org/I4405252470"]}],"countries":["KR","US"],"is_corresponding":false,"raw_author_name":"Lee, Jong Yeon","raw_affiliation_strings":["Department of Physics and Institute for Condensed Matter Theory , University of Illinois Urbana-Champaign , Urbana , Illinois 61801 , USA","Korea Institute for Advanced Study , Seoul 02455 , South Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Institute for Condensed Matter Theory , University of Illinois Urbana-Champaign , Urbana , Illinois 61801 , USA","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I4405252470"]},{"raw_affiliation_string":"Korea Institute for Advanced Study , Seoul 02455 , South Korea","institution_ids":["https://openalex.org/I125608817"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":6,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9496999979019165,"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":0.9496999979019165,"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":0.03269999846816063,"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"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.008700000122189522,"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/stabilizer-codes","display_name":"stabilizer codes","score":0.9539999961853027},{"id":"https://openalex.org/keywords/renyi-entropy","display_name":"R\u00e9nyi entropy","score":0.9359999895095825},{"id":"https://openalex.org/keywords/pauli-noise","display_name":"Pauli noise","score":0.777999997138977},{"id":"https://openalex.org/keywords/post-selection","display_name":"post-selection","score":0.6660000085830688},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"quantum channel capacity","score":0.5680000185966492},{"id":"https://openalex.org/keywords/coherent-information","display_name":"coherent information","score":0.46799999475479126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6407999992370605},{"id":"https://openalex.org/C184049767","wikidata":"https://www.wikidata.org/wiki/Q5141355","display_name":"Coherent information","level":5,"score":0.5436000227928162},{"id":"https://openalex.org/C64775481","wikidata":"https://www.wikidata.org/wiki/Q3798613","display_name":"Quantum mutual information","level":5,"score":0.4961000084877014},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.49129998683929443},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.4828999936580658},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.47350001335144043},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4108999967575073},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.40400001406669617},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3917999863624573},{"id":"https://openalex.org/C152026323","wikidata":"https://www.wikidata.org/wiki/Q1032070","display_name":"Coherent states","level":3,"score":0.3765000104904175},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.3531000018119812},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.35269999504089355},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.3303000032901764},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.29809999465942383},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2897999882698059},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.28200000524520874},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.27889999747276306},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2734000086784363},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2563000023365021}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11930","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11930","pdf_url":"https://arxiv.org/pdf/2609.11930","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.11930","doi":"https://doi.org/10.48550/arxiv.2609.11930","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11930","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.11930","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11930","pdf_url":"https://arxiv.org/pdf/2609.11930","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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1432373144","display_name":null,"funder_award_id":"W911NF-21-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G1895100257","display_name":null,"funder_award_id":"W911NF-23- 2-0216","funder_id":"https://openalex.org/F4320333051","funder_display_name":"Intelligence Advanced Research Projects Activity"},{"id":"https://openalex.org/G3165068977","display_name":null,"funder_award_id":"W911NF-21-1-0007","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G3904860572","display_name":null,"funder_award_id":"W911NF-23-2-0216","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"},{"id":"https://openalex.org/F4320333051","display_name":"Intelligence Advanced Research Projects Activity","ror":"https://ror.org/01v3fsc55"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212281124.pdf","grobid_xml":"https://content.openalex.org/works/W7212281124.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1791650288","https://openalex.org/W2068143801","https://openalex.org/W2088636071","https://openalex.org/W2171133411","https://openalex.org/W2290247654","https://openalex.org/W4385576694","https://openalex.org/W4391462085","https://openalex.org/W4392576632","https://openalex.org/W4398766446","https://openalex.org/W4404829411","https://openalex.org/W4408106593","https://openalex.org/W4408216530","https://openalex.org/W4416385783","https://openalex.org/W4416390678","https://openalex.org/W4416781456","https://openalex.org/W7117554438","https://openalex.org/W7117579252","https://openalex.org/W7160651303"],"related_works":["https://openalex.org/W1863348671","https://openalex.org/W4408106593","https://openalex.org/W7171501897","https://openalex.org/W4414891640","https://openalex.org/W7223566163","https://openalex.org/W4416982405","https://openalex.org/W2002090857","https://openalex.org/W4391462085","https://openalex.org/W2115616752","https://openalex.org/W1985989979"],"abstract_inverted_index":{"R\u00e9nyi":[0,35,44,111],"coherent":[1,10,78,139,167,200,215,221],"information,":[2,11],"a":[3,31,89,100,105,143,190],"computable":[4],"proxy":[5],"for":[6,61,65,158],"the":[7,43,48,76,110,124,131,134,137,165,198,209,213,219],"von":[8,53],"Neumann":[9,54],"is":[12,80,115,123,130,136,202],"widely":[13],"used":[14],"to":[15,99,142,204],"study":[16],"mixed-state":[17],"phases":[18],"of":[19,33,51,197,208],"matter":[20],"and":[21,46,104,128,133,152,181,193],"decodability":[22],"transitions":[23],"in":[24,42,82,117],"noisy":[25],"quantum":[26,191],"error-correcting":[27],"codes.":[28,63],"However,":[29],"being":[30],"difference":[32,113,135],"two":[34],"entropies,":[36],"it":[37],"need":[38],"not":[39],"be":[40],"monotonic":[41],"index,":[45],"lacks":[47],"operational":[49,170],"meaning":[50,171],"its":[52],"counterpart.":[55],"Here":[56],"we":[57,73,163],"address":[58],"both":[59],"issues":[60],"stabilizer":[62,120],"First,":[64],"Pauli":[66,161],"noise":[67],"generated":[68],"by":[69],"independent":[70,93,153],"Bernoulli":[71],"events,":[72],"prove":[74],"that":[75,195],"R\u00e9nyi-$n$":[77,138,166,199,214],"information":[79,140,168,201,216,222],"nondecreasing":[81,116],"$n":[83],"\\in":[84],"\\mathbb{Z}^+$.":[85],"This":[86],"follows":[87],"from":[88],"general":[90],"theorem:":[91],"if":[92],"random":[94],"bits":[95],"are":[96],"mapped":[97],"linearly":[98],"fine":[101],"label":[102,107],"$T$":[103,122],"coarse":[106],"$C$,":[108],"then":[109],"entropy":[112],"$H_n(C)-H_n(T)$":[114],"$n$.":[118],"For":[119],"codes,":[121],"joint":[125],"syndrome--logical":[126],"class":[127],"$C$":[129],"syndrome,":[132],"up":[141],"constant.":[144],"The":[145],"same":[146],"theorem":[147],"covers":[148],"classical":[149],"linear":[150],"codes":[151],"detector":[154],"error":[155],"models.":[156],"Second,":[157],"arbitrary":[159],"stochastic":[160],"noise,":[162],"give":[164],"an":[169],"via":[172],"postselection":[173],"on":[174],"matching":[175],"syndromes":[176],"between":[177],"one":[178],"data":[179],"block":[180],"$n-1$":[182],"auxiliary":[183],"blocks.":[184],"We":[185],"determine":[186],"when":[187],"this":[188],"defines":[189],"channel":[192],"show":[194],"saturation":[196],"equivalent":[203],"asymptotically":[205],"perfect":[206],"recovery":[207],"postselected":[210],"channel.":[211],"Moreover,":[212],"also":[217],"upper-bounds":[218],"ordinary":[220],"achievable":[223],"after":[224],"any":[225],"syndrome-conditioned":[226],"recovery.":[227]},"counts_by_year":[{"year":2026,"cited_by_count":6}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}