{"id":"https://openalex.org/W7220705461","doi":"https://doi.org/10.48550/arxiv.2610.06533","title":"Closed-Form Arbitrary-Gap R\u00e9nyi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs","display_name":"Closed-Form Arbitrary-Gap R\u00e9nyi Nonadditivity Above Any Positive Order via Direct Products of Free Groups and High-Girth Graphs","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220705461","doi":"https://doi.org/10.48550/arxiv.2610.06533"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06533","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06533","pdf_url":"https://arxiv.org/pdf/2610.06533","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/2610.06533","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098970270","display_name":"Guocheng Zhen","orcid":"https://orcid.org/0009-0001-4039-6762","observed_orcids":["https://orcid.org/0009-0001-4039-6762"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4405261251","display_name":"The Hong Kong University of Science and Technology (Guangzhou)","ror":"https://ror.org/050h0vm43","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405261251"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Zhen, Guocheng","raw_affiliation_strings":["Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I4405261251"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5157673263","display_name":"Ranyiliu Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4400600918","display_name":"Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area","ror":"https://ror.org/03qb6k992","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4400600918"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Ranyiliu","raw_affiliation_strings":["Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area , Shenzhen 518045 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area , Shenzhen 518045 , China","institution_ids":["https://openalex.org/I4400600918"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100327887","display_name":"Xin Wang","orcid":"https://orcid.org/0000-0002-0641-3186","observed_orcids":["https://orcid.org/0000-0002-0641-3186"]},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]},{"id":"https://openalex.org/I4405261251","display_name":"The Hong Kong University of Science and Technology (Guangzhou)","ror":"https://ror.org/050h0vm43","country_code":"CN","type":"education","lineage":["https://openalex.org/I4405261251"]}],"countries":["CN","HK"],"is_corresponding":false,"raw_author_name":"Wang, Xin","raw_affiliation_strings":["Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Thrust of Artificial Intelligence , Information Hub , The Hong Kong University of Science and Technology (Guangzhou) , Guangdong 511453 , China","institution_ids":["https://openalex.org/I200769079","https://openalex.org/I4405261251"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9643999934196472,"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"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9643999934196472,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.014399999752640724,"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":0.00839999970048666,"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-channels","display_name":"quantum channels","score":0.7620000243186951},{"id":"https://openalex.org/keywords/bell-nonlocality","display_name":"Bell nonlocality","score":0.7409999966621399},{"id":"https://openalex.org/keywords/von-neumann-entropy","display_name":"von Neumann entropy","score":0.6349999904632568},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"quantum channel capacity","score":0.3779999911785126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7398999929428101},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.714900016784668},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.5770000219345093},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5740000009536743},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.554099977016449},{"id":"https://openalex.org/C2778217198","wikidata":"https://www.wikidata.org/wiki/Q556977","display_name":"Cutoff","level":2,"score":0.48980000615119934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43869999051094055},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.42890000343322754},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.3912000060081482},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.337799996137619},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.3321000039577484},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3215999901294708},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3043000102043152},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28630000352859497},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.28529998660087585},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.28459998965263367}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.06533","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06533","pdf_url":"https://arxiv.org/pdf/2610.06533","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.2610.06533","doi":"https://doi.org/10.48550/arxiv.2610.06533","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06533","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:2610.06533","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06533","pdf_url":"https://arxiv.org/pdf/2610.06533","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/G2052179644","display_name":null,"funder_award_id":"92576114","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8274973648","display_name":null,"funder_award_id":"12447107","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220705461.pdf","grobid_xml":"https://content.openalex.org/works/W7220705461.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W2074878962","https://openalex.org/W2087806988","https://openalex.org/W3083194718","https://openalex.org/W4416395259","https://openalex.org/W7169625508","https://openalex.org/W7204478320","https://openalex.org/W7204865273","https://openalex.org/W7213563897","https://openalex.org/W7214038988","https://openalex.org/W7214111786"],"related_works":["https://openalex.org/W7213563897","https://openalex.org/W4401692638","https://openalex.org/W7203743418","https://openalex.org/W2108699676","https://openalex.org/W7169625508","https://openalex.org/W7099398667","https://openalex.org/W7214038988","https://openalex.org/W4416395259","https://openalex.org/W1972266216","https://openalex.org/W2005612588"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,30,107,126],"closed-form":[3],"finite-dimensional":[4],"construction":[5,76,96],"of":[6,17,38,90],"quantum":[7],"channels":[8],"with":[9,86,116,133],"real":[10],"algebraic":[11],"entries":[12],"exhibiting":[13],"arbitrarily":[14],"large":[15],"violations":[16],"minimum-output":[18],"R\u00e9nyi":[19,27],"entropy":[20],"additivity":[21,63],"uniformly":[22],"above":[23],"any":[24],"prescribed":[25],"positive":[26,118],"order,":[28,125],"using":[29,138],"different":[31],"finite":[32],"realization":[33],"based":[34],"on":[35],"direct":[36],"products":[37],"free":[39],"groups":[40],"and":[41,50,56,81,92,105,142],"fixed-field":[42],"high-girth":[43],"graphs.":[44],"More":[45],"precisely,":[46],"for":[47,60,70,101],"every":[48,102],"$p_0>0$":[49],"$g>0$,":[51],"we":[52],"construct":[53],"one":[54,57],"channel":[55,132],"Bell":[58],"input":[59,83,140],"which":[61],"the":[62,75,87,113,117,122],"gap":[64,104,114,134],"is":[65],"greater":[66,135],"than":[67,136],"$g$":[68],"simultaneously":[69],"all":[71],"$p\\in[p_0,\\infty]$.":[72],"With":[73],"$r=\\lceil2g\\rceil$,":[74],"uses":[77,97],"$15r$":[78],"output":[79,99,144],"qubits":[80,100,141],"$O(r2^{30r}+r^2(1+p_0^{-1}))$":[82],"qubits.":[84,145],"Compared":[85],"stated":[88],"parameters":[89],"Shou":[91],"Gorshkov":[93],"\\cite{ShouGorshkov2026},":[94],"our":[95],"fewer":[98],"target":[103],"has":[106],"smaller":[108],"asymptotic":[109],"input-qubit":[110],"bound":[111],"as":[112],"grows":[115],"cutoff":[119],"fixed.":[120],"At":[121],"von":[123],"Neumann":[124],"separate":[127],"specialization":[128],"gives":[129],"an":[130],"explicit":[131],"$1/1024$":[137],"$37608898$":[139],"$8$":[143]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}