{"id":"https://openalex.org/W2948990656","doi":"https://doi.org/10.22331/q-2019-12-02-203","title":"Separability for mixed states with operator Schmidt rank two","display_name":"Separability for mixed states with operator Schmidt rank two","publication_year":2019,"publication_date":"2019-12-02","ids":{"openalex":"https://openalex.org/W2948990656","doi":"https://doi.org/10.22331/q-2019-12-02-203","mag":"2948990656"},"language":"en","primary_location":{"id":"doi:10.22331/q-2019-12-02-203","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-12-02-203","pdf_url":"https://quantum-journal.org/papers/q-2019-12-02-203/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2019-12-02-203/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Gemma De las Cuevas","orcid":"https://orcid.org/0000-0002-0977-7727"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Gemma De las Cuevas","raw_affiliation_strings":["Institute for Theoretical Physics, Technikerstr. 21a, A-6020 Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-0977-7727","affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, Technikerstr. 21a, A-6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Tom Drescher","orcid":"https://orcid.org/0000-0001-7647-5916"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tom Drescher","raw_affiliation_strings":["Department of Mathematics, Technikerstr. 13, A-6020 Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0001-7647-5916","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technikerstr. 13, A-6020 Innsbruck, Austria","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Tim Netzer","orcid":"https://orcid.org/0000-0002-7000-6200"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tim Netzer","raw_affiliation_strings":["Department of Mathematics, Technikerstr. 13, A-6020 Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0002-7000-6200","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technikerstr. 13, A-6020 Innsbruck, Austria","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.4506,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65273573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"3","issue":null,"first_page":"203","last_page":"203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.2888000011444092,"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/T11804","display_name":"Quantum many-body systems","score":0.2888000011444092,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.2515999972820282,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.10869999974966049,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6983000040054321},{"id":"https://openalex.org/keywords/multipartite","display_name":"Multipartite","score":0.6517000198364258},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6308000087738037},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6057000160217285},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5023000240325928},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.48100000619888306},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.45899999141693115},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.40059998631477356},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.38960000872612}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.830299973487854},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6983000040054321},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.6517000198364258},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6308000087738037},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6057000160217285},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.550599992275238},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5023000240325928},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.48100000619888306},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.45899999141693115},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4453999996185303},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.38960000872612},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.37689998745918274},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36629998683929443},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C55795843","wikidata":"https://www.wikidata.org/wiki/Q614178","display_name":"Separable state","level":5,"score":0.3334999978542328},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.3287999927997589},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C71799126","wikidata":"https://www.wikidata.org/wiki/Q6934832","display_name":"Multipartite entanglement","level":5,"score":0.3174000084400177},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.30489999055862427},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.29350000619888306},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2892000079154968},{"id":"https://openalex.org/C2992500303","wikidata":"https://www.wikidata.org/wiki/Q5680845","display_name":"Operator matrix","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C134440745","wikidata":"https://www.wikidata.org/wiki/Q1186765","display_name":"Ladder operator","level":4,"score":0.2797999978065491},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C73052347","wikidata":"https://www.wikidata.org/wiki/Q5282616","display_name":"Displacement operator","level":5,"score":0.2639999985694885}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2019-12-02-203","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-12-02-203","pdf_url":"https://quantum-journal.org/papers/q-2019-12-02-203/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.05373","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.05373","pdf_url":"https://arxiv.org/pdf/1903.05373","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:doaj.org/article:d87b48a5270543bab2879cb38f0863af","is_oa":true,"landing_page_url":"https://doaj.org/article/d87b48a5270543bab2879cb38f0863af","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 3, p 203 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2019-12-02-203","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-12-02-203","pdf_url":"https://quantum-journal.org/papers/q-2019-12-02-203/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3148599713","display_name":null,"funder_award_id":"P 29496-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2948990656.pdf","grobid_xml":"https://content.openalex.org/works/W2948990656.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1519530038","https://openalex.org/W1550516781","https://openalex.org/W1644115585","https://openalex.org/W1729990846","https://openalex.org/W1945057103","https://openalex.org/W1972445258","https://openalex.org/W1990758844","https://openalex.org/W1992787289","https://openalex.org/W2003954610","https://openalex.org/W2015775929","https://openalex.org/W2044630019","https://openalex.org/W2048223511","https://openalex.org/W2061987651","https://openalex.org/W2094092037","https://openalex.org/W2118148754","https://openalex.org/W2119368733","https://openalex.org/W2123829027","https://openalex.org/W2138677859","https://openalex.org/W2230452386","https://openalex.org/W2481251364","https://openalex.org/W2525822570","https://openalex.org/W2762614478","https://openalex.org/W2775797465","https://openalex.org/W2810998922","https://openalex.org/W2811425173","https://openalex.org/W2954726043","https://openalex.org/W2964347283","https://openalex.org/W2971766044","https://openalex.org/W2990961515","https://openalex.org/W3037737784"],"related_works":[],"abstract_inverted_index":{"The":[0],"operator":[1,37,68],"Schmidt":[2,38],"rank":[3,39],"is":[4,41,105],"the":[5,29,62,72,88,141],"minimum":[6],"number":[7],"of":[8,18,28,50,64,74,79,84,101,114,136,143,148,157],"terms":[9],"required":[10],"to":[11],"express":[12],"a":[13,16,25,48,75,112],"state":[14,35],"as":[15,47,111,138],"sum":[17,49,113],"elementary":[19],"tensor":[20],"factors.":[21],"Here":[22],"we":[23,91],"provide":[24],"new":[26],"proof":[27,58],"fact":[30],"that":[31,93,125],"any":[32,94],"bipartite":[33],"mixed":[34],"with":[36],"two":[40,51,104],"separable,":[42,106],"and":[43,67,70,82,107,133],"can":[44,108,128,152],"be":[45,109],"written":[46,110],"positive":[52,118],"semidefinite":[53,119],"matrices":[54,120],"per":[55,121],"site.":[56,122],"Our":[57],"uses":[59],"results":[60],"from":[61],"theory":[63],"free":[65],"spectrahedra":[66],"systems,":[69],"illustrates":[71],"use":[73],"connection":[76],"between":[77],"decompositions":[78,83],"quantum":[80],"states":[81,127],"nonnegative":[85],"matrices.":[86],"In":[87,145],"multipartite":[89],"case,":[90],"prove":[92],"Hermitian":[95],"Matrix":[96],"Product":[97],"Density":[98],"Operator":[99],"(MPDO)":[100],"bond":[102,149],"dimension":[103,150],"at":[115],"most":[116],"four":[117],"This":[123],"implies":[124],"these":[126],"only":[129],"contain":[130,153],"classical":[131,158],"correlations,":[132],"very":[134],"few":[135],"them,":[137],"measured":[139],"by":[140],"entanglement":[142],"purification.":[144],"contrast,":[146],"MPDOs":[147],"three":[151],"an":[154],"unbounded":[155],"amount":[156],"correlations.":[159]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2019-06-14T00:00:00"}
