{"id":"https://openalex.org/W7204865273","doi":"https://doi.org/10.48550/arxiv.2608.31081","title":"Deterministic Minimum-Output-Entropy Nonadditivity via Haagerup's Inequality and Near-Free Permutation Representations","display_name":"Deterministic Minimum-Output-Entropy Nonadditivity via Haagerup's Inequality and Near-Free Permutation Representations","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204865273","doi":"https://doi.org/10.48550/arxiv.2608.31081"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.31081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31081","pdf_url":"https://arxiv.org/pdf/2608.31081","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/2608.31081","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/A5081020461","display_name":"Chengkai Zhu","orcid":"https://orcid.org/0000-0001-5250-5885","observed_orcids":["https://orcid.org/0000-0001-5250-5885"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Chengkai","raw_affiliation_strings":["QudeLeap Research , Shanghai 200030 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QudeLeap Research , Shanghai 200030 , China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148841454","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":5,"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":0.9243000149726868,"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":0.9243000149726868,"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":0.0340999998152256,"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":0.009499999694526196,"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/minimum-output-entropy","display_name":"minimum output entropy","score":0.8309999704360962},{"id":"https://openalex.org/keywords/non-additivity","display_name":"non-additive effects","score":0.8289999961853027},{"id":"https://openalex.org/keywords/permutation-representations","display_name":"permutation representations","score":0.7839999794960022},{"id":"https://openalex.org/keywords/stinespring-dilation","display_name":"Stinespring dilation","score":0.6010000109672546},{"id":"https://openalex.org/keywords/quantum-channels","display_name":"quantum channels","score":0.5630000233650208},{"id":"https://openalex.org/keywords/quantum-information","display_name":"quantum information","score":0.3540000021457672}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8551999926567078},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.4959999918937683},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49480000138282776},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.46639999747276306},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4090000092983246},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3919000029563904},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3571999967098236},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C20017120","wikidata":"https://www.wikidata.org/wiki/Q922087","display_name":"Superadditivity","level":2,"score":0.3346000015735626},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.29429998993873596},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.271699994802475},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2551000118255615},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.31081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31081","pdf_url":"https://arxiv.org/pdf/2608.31081","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.2608.31081","doi":"https://doi.org/10.48550/arxiv.2608.31081","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.31081","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:2608.31081","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.31081","pdf_url":"https://arxiv.org/pdf/2608.31081","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204865273.pdf","grobid_xml":"https://content.openalex.org/works/W7204865273.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4416395259","https://openalex.org/W7169625508","https://openalex.org/W7204478320"],"related_works":["https://openalex.org/W7213563897","https://openalex.org/W2292498576","https://openalex.org/W7214038988","https://openalex.org/W2016648670","https://openalex.org/W3034166775","https://openalex.org/W3101780540","https://openalex.org/W7099186474","https://openalex.org/W2956393256","https://openalex.org/W1544448519","https://openalex.org/W1560695905"],"abstract_inverted_index":{"We":[0,93],"give":[1],"a":[2,29,61,141],"deterministic":[3,30,86,148],"realization":[4],"of":[5,14,89,124,134,155],"the":[6,51,84,97,104,112,121,125,130,137,146,156],"finite-dimensional":[7],"quadratic":[8],"certificate":[9],"underlying":[10],"Collins's":[11],"mixed-unitary":[12],"proof":[13],"minimum-output-entropy":[15],"nonadditivity.":[16],"For":[17],"every":[18,34],"fixed":[19],"integer":[20],"$K\\ge":[21],"2$":[22],"and":[23,60,91,110],"rational":[24],"$\u03b7>0$":[25],"satisfying":[26],"$\\log":[27],"K>2(3+\u03b7)^2$,":[28],"polynomial-time":[31],"algorithm,":[32],"for":[33],"sufficiently":[35],"large":[36],"target":[37],"size":[38],"$N$,":[39],"outputs":[40],"$K$":[41],"permutations":[42],"on":[43,103],"$N'=N+o_{K,\u03b7}(N)$":[44],"points.":[45],"Restricting":[46],"their":[47],"permutation":[48],"matrices":[49],"to":[50],"nontrivial":[52],"standard":[53,142],"representation":[54],"yields":[55],"real":[56],"orthogonal":[57],"Stinespring":[58],"blocks":[59],"channel":[62],"$\u03a6_{N'}:M_{N'-1}(\\mathbb{C})\\to":[63],"M_K(\\mathbb{C})$":[64],"such":[65],"that":[66,96,111],"\\[":[67],"2H_{\\min}(\u03a6_{N'})":[68],"-H_{\\min}(\u03a6_{N'}^{\\otimes":[69],"2})":[70],"\\ge":[71],"\\frac{\\log":[72],"K}{K}":[73],"-2\\log\\left(1+\\frac{(3+\u03b7)^2}{K}\\right)":[74],">0.":[75],"\\]":[76],"The":[77],"construction":[78],"combines":[79],"Haagerup's":[80],"length-two":[81],"inequality":[82],"with":[83],"simultaneous":[85],"spectral":[87,114],"approximation":[88],"O'Donnell":[90],"Wu.":[92],"further":[94],"show":[95],"constant":[98],"$3$":[99],"is":[100,116],"asymptotically":[101],"sharp":[102],"relevant":[105],"Hermitian":[106],"zero-diagonal":[107],"coefficient":[108],"class":[109],"finite":[113],"transfer":[115],"nearly":[117],"saturated,":[118],"thereby":[119],"isolating":[120],"finer":[122],"geometry":[123],"full":[126],"output":[127],"body":[128],"as":[129],"natural":[131],"next":[132],"level":[133],"refinement":[135],"beyond":[136],"scalar-radius":[138],"method.":[139],"Finally,":[140],"covariant":[143],"extension":[144],"converts":[145],"same":[147],"entropy":[149],"gap":[150],"exactly":[151],"into":[152],"self-tensor":[153],"superadditivity":[154],"one-shot":[157],"Holevo":[158],"quantity.":[159]},"counts_by_year":[{"year":2026,"cited_by_count":5}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
