{"id":"https://openalex.org/W7204911500","doi":"https://doi.org/10.48550/arxiv.2608.28897","title":"R\u00e9nyi Entanglement of Purification Is Non-additive","display_name":"R\u00e9nyi Entanglement of Purification Is Non-additive","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204911500","doi":"https://doi.org/10.48550/arxiv.2608.28897"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28897","pdf_url":"https://arxiv.org/pdf/2608.28897","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/2608.28897","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065567308","display_name":"Amir-Reza Negari","orcid":"https://orcid.org/0009-0007-1292-7187","observed_orcids":["https://orcid.org/0009-0007-1292-7187"]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Negari, Amir-Reza","raw_affiliation_strings":["Institute for Quantum Computing , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada","Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada","institution_ids":["https://openalex.org/I183974707"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061220756","display_name":"Zahra Baghali Khanian","orcid":"https://orcid.org/0000-0002-0892-7519","observed_orcids":["https://orcid.org/0000-0002-0892-7519"]},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Khanian, Zahra Baghali","raw_affiliation_strings":["Institute for Quantum Computing , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada","Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada","institution_ids":["https://openalex.org/I183974707"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9678000211715698,"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":0.9678000211715698,"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":0.019899999722838402,"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":0.004000000189989805,"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/entanglement-of-purification","display_name":"entanglement of purification","score":0.968999981880188},{"id":"https://openalex.org/keywords/renyi-entropy","display_name":"R\u00e9nyi entropy","score":0.9419999718666077},{"id":"https://openalex.org/keywords/non-additivity","display_name":"non-additive effects","score":0.7710000276565552},{"id":"https://openalex.org/keywords/additivity","display_name":"additivity","score":0.546999990940094},{"id":"https://openalex.org/keywords/two-qubit-states","display_name":"two-qubit states","score":0.7799999713897705},{"id":"https://openalex.org/keywords/total-correlation","display_name":"total correlation","score":0.6069999933242798},{"id":"https://openalex.org/keywords/tensor-products","display_name":"tensor products","score":0.5170000195503235},{"id":"https://openalex.org/keywords/von-neumann-entropy","display_name":"von Neumann entropy","score":0.7860000133514404}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.82669997215271},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.7718999981880188},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6134999990463257},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6060000061988831},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5766000151634216},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5562000274658203},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.5216000080108643},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5151000022888184},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.48500001430511475},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C142611142","wikidata":"https://www.wikidata.org/wiki/Q1433083","display_name":"R\u00e9nyi entropy","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.322299987077713},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31839999556541443},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C32270708","wikidata":"https://www.wikidata.org/wiki/Q7582152","display_name":"Squashed entanglement","level":4,"score":0.3050999939441681},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2946999967098236},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2793000042438507},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.26510000228881836},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28897","pdf_url":"https://arxiv.org/pdf/2608.28897","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.2608.28897","doi":"https://doi.org/10.48550/arxiv.2608.28897","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28897","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:2608.28897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28897","pdf_url":"https://arxiv.org/pdf/2608.28897","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/G3678198022","display_name":"New Routes from Topological Materials to Quantum Computing","funder_award_id":"rgpin-2018-04380","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G814497173","display_name":null,"funder_award_id":"RGPIN 2018","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320331473","display_name":"Ministry of Colleges and Universities","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204911500.pdf","grobid_xml":"https://content.openalex.org/works/W7204911500.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1560695905","https://openalex.org/W1563757785","https://openalex.org/W1568529095","https://openalex.org/W1798555910","https://openalex.org/W2003954610","https://openalex.org/W2016648670","https://openalex.org/W2062799611","https://openalex.org/W2070448530","https://openalex.org/W2071160621","https://openalex.org/W2077089904","https://openalex.org/W2092583681","https://openalex.org/W2092971644","https://openalex.org/W2140844418","https://openalex.org/W2347104449","https://openalex.org/W2809334181","https://openalex.org/W2943654704","https://openalex.org/W3091064147","https://openalex.org/W3101221511","https://openalex.org/W4283330948","https://openalex.org/W4416395259","https://openalex.org/W6891643117","https://openalex.org/W7161561996","https://openalex.org/W7169625508","https://openalex.org/W7204478320"],"related_works":["https://openalex.org/W7220748533","https://openalex.org/W1798555910","https://openalex.org/W7214321074","https://openalex.org/W7161561996","https://openalex.org/W1990674082","https://openalex.org/W4391972691","https://openalex.org/W4399930105","https://openalex.org/W4396670656","https://openalex.org/W1001253665","https://openalex.org/W1530320320"],"abstract_inverted_index":{"Entanglement":[0],"of":[1,7,41,71],"purification":[2],"is":[3,78],"a":[4,42,67],"fundamental":[5],"measure":[6],"total":[8],"correlations":[9],"whose":[10,76],"additivity":[11,17,90,111],"remains":[12,106],"unresolved.":[13],"We":[14,45,60],"study":[15],"its":[16],"for":[18,52,86],"classical":[19],"states":[20],"on":[21],"two":[22,39],"qubits":[23],"at":[24,56],"different":[25],"R\u00e9nyi":[26,58],"orders.":[27],"For":[28],"every":[29,57],"$\u03b1\\in[0,1)$,":[30],"we":[31,88,109],"prove":[32,89],"nonadditivity":[33],"within":[34,94],"this":[35,95],"family,":[36],"witnessed":[37],"by":[38],"copies":[40],"single":[43],"state.":[44],"first":[46],"solve":[47],"the":[48,53,63,81,101,114],"one-copy":[49],"optimization":[50,65],"exactly":[51],"entire":[54],"family":[55],"order.":[59],"then":[61],"restrict":[62],"two-copy":[64],"to":[66],"natural":[68],"finite":[69],"set":[70],"purifications":[72],"and":[73,108],"exhibit":[74],"one":[75],"entropy":[77],"strictly":[79],"below":[80],"product":[82],"value.":[83],"In":[84],"contrast,":[85],"$\u03b1\\in[2,\\infty]$":[87],"under":[91],"tensor":[92],"products":[93],"family.":[96,116],"The":[97],"interval":[98],"$\u03b1\\in[1,2)$,":[99],"including":[100],"von":[102],"Neumann":[103],"case":[104],"$\u03b1=1$,":[105],"open,":[107],"conjecture":[110],"there":[112],"throughout":[113],"same":[115]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}