{"id":"https://openalex.org/W7225759235","doi":"https://doi.org/10.5281/zenodo.24114802","title":"Grouped endpoint forms and a sharp interior law for the Werner distillability inequalities","display_name":"Grouped endpoint forms and a sharp interior law for the Werner distillability inequalities","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225759235","doi":"https://doi.org/10.5281/zenodo.24114802"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24114802","doi":"https://doi.org/10.5281/zenodo.24114802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24114802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24114802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093491483","display_name":"Yancun Yan","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yan, Yancun","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0006-7775-7329","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5093491483"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9437999725341797,"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":0.9437999725341797,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.042399998754262924,"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":0.0020000000949949026,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769599974155426},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.6640999913215637},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6395999789237976},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6208000183105469},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5216000080108643},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.507099986076355},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4311999976634979},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4108000099658966},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3709999918937683},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.36000001430511475},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C2779696439","wikidata":"https://www.wikidata.org/wiki/Q7512811","display_name":"Signature (topology)","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C33222762","wikidata":"https://www.wikidata.org/wiki/Q321119","display_name":"Identity function","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.2711000144481659},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.262800008058548},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.25949999690055847}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24114802","doi":"https://doi.org/10.5281/zenodo.24114802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24114802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24114803","doi":"https://doi.org/10.5281/zenodo.24114803","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24114803","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24114802","doi":"https://doi.org/10.5281/zenodo.24114802","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24114802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Preprint":[0],"and":[1,10,78,125,162,187,205,219,271,303,309,320,339,348],"verification":[2],"scripts":[3,296],"for":[4,15,63,74,126,146,157,172,222,229,236,272],"the":[5,16,51,95,131,143,151,176,188,208,226,247,255,259,262,280,291,299,315,322,346],"paper":[6],"\"Grouped":[7],"endpoint":[8,96,144,227],"forms":[9,97],"a":[11,57,86,103,158,183,284],"sharp":[12,132,169],"interior":[13],"law":[14],"Werner":[17,58],"distillability":[18],"inequalities\".":[19],"For":[20,42,201],"an":[21,72,115,217],"operator":[22,323],"C":[23,160,181],"on":[24,92,138,232,240],"H_1":[25],"\u2297":[26,28],"\u2026":[27],"H_k,":[29],"let":[30],"q_k(\u2212t,C)":[31,81,134],"=":[32,148,238,274],"\u03a3_J":[33],"(\u2212t)^{|J|}":[34],"\u2016Tr_J":[35],"C\u2016\u00b2,":[36],"over":[37,121],"sets":[38],"J":[39],"of":[40,48,54,56,94,98,180,244,261,287,305,317,321,350],"factors.":[41],"rank":[43,127,278],"at":[44,107,128,268,276],"most":[45,129],"two,":[46,109,130],"nonnegativity":[47],"q_k(\u22121/2,C)":[49],"is":[50,68,140],"Schmidt-rank-two":[52],"test":[53],"undistillability":[55],"state":[59],"from":[60],"k":[61,64,147,174,231,237,267,273],"copies;":[62],"\u2265":[65,135,166,195],"4":[66,275,308],"it":[67,155],"open.":[69],"We":[70],"prove":[71,225],"identity,":[73],"every":[75,173,192,223,230,269,277,351],"k,":[76,224],"t":[77],"operator,":[79],"writing":[80],"\u2212":[82],"(1\u22122t)(1\u2212t)^{k\u22121}":[83,136],"\u2016C\u2016\u00b2":[84,137],"as":[85],"combination,":[87],"with":[88,117,197,203,210,345],"explicit":[89,300],"weights":[90],"nonnegative":[91],"[0,1/2],":[93],"all":[99,122],"factor":[100,104],"groupings;":[101],"if":[102,161,164],"has":[105],"dimension":[106],"least":[108],"no":[110],"other":[111],"constant":[112],"admits":[113],"such":[114],"identity":[116,189,218],"C-independent":[118],"weights.":[119],"So,":[120],"local":[123],"dimensions":[124],"bound":[133,170],"[0,1/2]":[139],"equivalent":[141],"to":[142,191,341],"inequality;":[145],"4,":[149,239],"given":[150,246],"computer-assisted":[152],"three-copy":[153,248],"endpoint,":[154],"holds":[156,171,253],"fixed":[159],"only":[163],"q_4(\u22121/2,C)":[165],"0.":[167],"The":[168,250],"when":[175,254,279],"range":[177,204,256,281],"or":[178],"co-range":[179,206],"contains":[182],"fully":[184],"product":[185],"vector,":[186],"extends":[190],"real":[193],"m":[194],"1,":[196],"1/m":[198],"replacing":[199],"1/2.":[200],"operators":[202],"in":[207,258,283,325],"strings":[209],"exactly":[211],"one":[212,243],"digit":[213],"2,":[214],"we":[215],"give":[216],"pair":[220],"bounds":[221],"inequality":[228,251],"symmetric":[233],"sectors":[234],"and,":[235],"further":[241],"classes,":[242],"them":[245],"endpoint.":[249],"also":[252],"lies":[257,282],"span":[260,286],"vectors":[263],"|j\u27e9^{\u2297k}":[264],"(for":[265],"even":[266],"rank),":[270],"three-dimensional":[285],"W-type":[288],"vectors.":[289],"Files:":[290],"preprint":[292],"(PDF);":[293],"ten":[294],"Python":[295],"that":[297],"check":[298],"weights,":[301],"identities":[302],"examples":[304],"Sections":[306],"3,":[307],"6\u20138":[310],"(exact":[311],"rational":[312],"arithmetic,":[313],"except":[314],"checks":[316,338],"Section":[318],"7":[319],"C_0":[324],"Proposition":[326],"8.3,":[327],"which":[328,333],"use":[329],"floating":[330],"point);":[331],"README.md,":[332],"says":[334],"what":[335],"each":[336],"script":[337],"how":[340],"run":[342],"it;":[343],"MANIFEST.tsv":[344],"size":[347],"SHA-256":[349],"file.":[352]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}