{"id":"https://openalex.org/W2783984805","doi":"https://doi.org/10.22331/q-2019-01-06-115","title":"Locally Maximally Entangled States of Multipart Quantum Systems","display_name":"Locally Maximally Entangled States of Multipart Quantum Systems","publication_year":2019,"publication_date":"2019-01-06","ids":{"openalex":"https://openalex.org/W2783984805","doi":"https://doi.org/10.22331/q-2019-01-06-115","mag":"2783984805"},"language":"en","primary_location":{"id":"doi:10.22331/q-2019-01-06-115","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-01-06-115","pdf_url":"https://quantum-journal.org/papers/q-2019-01-06-115/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-2019-01-06-115/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jim Bryan","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jim Bryan","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Samuel Leutheusser","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Samuel Leutheusser","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada"],"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Zinovy Reichstein","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zinovy Reichstein","raw_affiliation_strings":["Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C., V6T 1Z1, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mark Van Raamsdonk","orcid":null},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mark Van Raamsdonk","raw_affiliation_strings":["Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C., V6T 1Z2, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I141945490"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.5897,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.87359017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"3","issue":null,"first_page":"115","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.6822999715805054,"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"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.6822999715805054,"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/T11804","display_name":"Quantum many-body systems","score":0.06859999895095825,"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":0.06260000169277191,"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/unitary-state","display_name":"Unitary state","score":0.7134000062942505},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5895000100135803},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5831999778747559},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5637000203132629},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5476999878883362},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5224999785423279},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.5065000057220459},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5062999725341797}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7134000062942505},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5831999778747559},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5637000203132629},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5476999878883362},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5224999785423279},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5138000249862671},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.5065000057220459},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5062999725341797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48339998722076416},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.46540001034736633},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.41280001401901245},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3488999903202057},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.34459999203681946},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2953000068664551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29330000281333923},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2700999975204468},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26409998536109924},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2583000063896179}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2019-01-06-115","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-01-06-115","pdf_url":"https://quantum-journal.org/papers/q-2019-01-06-115/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:1801.03508","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.03508","pdf_url":"https://arxiv.org/pdf/1801.03508","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:3dad17cfbc954601887e8b06191953aa","is_oa":true,"landing_page_url":"https://doaj.org/article/3dad17cfbc954601887e8b06191953aa","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"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 115 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2019-01-06-115","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2019-01-06-115","pdf_url":"https://quantum-journal.org/papers/q-2019-01-06-115/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":[],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2783984805.pdf","grobid_xml":"https://content.openalex.org/works/W2783984805.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1572341022","https://openalex.org/W1616276250","https://openalex.org/W1900931176","https://openalex.org/W1934222401","https://openalex.org/W1974928788","https://openalex.org/W1977053640","https://openalex.org/W1986320748","https://openalex.org/W2005470559","https://openalex.org/W2015302454","https://openalex.org/W2017373958","https://openalex.org/W2051311955","https://openalex.org/W2059010572","https://openalex.org/W2063545024","https://openalex.org/W2072157476","https://openalex.org/W2088077267","https://openalex.org/W2093189259","https://openalex.org/W2111107703","https://openalex.org/W2122458733","https://openalex.org/W2252329211","https://openalex.org/W2276254339","https://openalex.org/W2511875207","https://openalex.org/W2517466239","https://openalex.org/W2591283100","https://openalex.org/W2594448544","https://openalex.org/W2615304149","https://openalex.org/W2744074143","https://openalex.org/W2775797465","https://openalex.org/W4230212166","https://openalex.org/W4232991715","https://openalex.org/W4249726483"],"related_works":[],"abstract_inverted_index":{"For":[0],"a":[1,5,26,63,105,122,148,153,164,221],"multipart":[2,227],"quantum":[3,186],"system,":[4],"locally":[6],"maximally":[7,18],"entangled":[8,19],"(LME)":[9],"state":[10,223],"is":[11,17,25,236],"one":[12],"where":[13,233],"each":[14],"elementary":[15],"subsystem":[16,73,142],"with":[20,141],"its":[21,72],"complement.":[22],"This":[23],"paper":[24],"sequel":[27],"to~[J.":[28],"Bryan,":[29],"Z.":[30],"Reichstein":[31],"and":[32,59,78,108,120,229],"M.":[33],"Van":[34],"Raamsdonk,":[35],"Existence":[36],"of":[37,71,82,111,125,156,180,185,200,208],"Locally":[38],"Maximally":[39],"Entangled":[40],"Quantum":[41],"States":[42],"via":[43],"Geometric":[44],"Invariant":[45],"Theory,":[46],"Ann.":[47],"Henri":[48],"Poincar\u00e9":[49],"19":[50],"(2018),":[51],"no.":[52],"8,":[53],"2491-2511.":[54],"MR3830220],":[55],"which":[56],"gives":[57],"necessary":[58],"sufficient":[60],"conditions":[61],"for":[62,98,128,138,152,167,177],"system":[64,228],"to":[65,94,117,197],"admit":[66],"LME":[67,91,129,136,158,170],"states":[68,92,137],"in":[69,224],"terms":[70],"dimensions<mml:math":[74,143],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mo":[75,144],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>\u2026</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo":[76],"stretchy=\"false\">)</mml:mo></mml:math>,":[77],"computes":[79],"the":[80,83,112,178,206,209],"dimension":[81,207],"space<mml:math":[84],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mrow":[85,191],"class=\"MJX-TeXAtom-ORD\"><mml:mi":[86,192,214,218],"class=\"MJX-tex-caligraphic\"":[87,193],"mathvariant=\"script\">S</mml:mi></mml:mrow><mml:mrow":[88,194],"class=\"MJX-TeXAtom-ORD\"><mml:mi>L</mml:mi><mml:mi>M</mml:mi><mml:mi>E</mml:mi></mml:mrow></mml:msub><mml:mrow":[89,195],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi>K</mml:mi></mml:math>of":[90],"up":[93],"local":[95],"unitary":[96],"transformations":[97],"all":[99,135,231],"non-empty":[100],"cases.":[101],"Here":[102],"we":[103,133,204],"provide":[104],"pedagogical":[106],"overview":[107],"physical":[109],"interpretation":[110],"underlying":[113],"mathematics":[114],"that":[115],"leads":[116],"these":[118],"results":[119,173],"give":[121,147,205],"large":[123],"class":[124,155],"explicit":[126],"constructions":[127],"states.":[130,159,171],"In":[131],"particular,":[132],"construct":[134],"tripartite":[139],"systems":[140],"stretchy=\"false\">(</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi><mml:mo":[145],"stretchy=\"false\">)</mml:mo></mml:math>and":[146],"general":[149],"representation-theoretic":[150],"construction":[151,162],"special":[154],"stabilizer":[157,210,235],"The":[160],"latter":[161],"provides":[163],"common":[165],"framework":[166],"many":[168],"known":[169],"Our":[172],"have":[174],"direct":[175],"implications":[176],"problem":[179],"characterizing":[181],"SLOCC":[182,201],"equivalence":[183],"classes":[184],"states,":[187],"since":[188],"points":[189],"in<mml:math":[190],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi>K</mml:mi></mml:math>correspond":[196],"natural":[198],"families":[199],"classes.":[202],"Finally,":[203],"subgroup<mml:math":[211],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>S</mml:mi><mml:mo>\u2282</mml:mo><mml:mi>SL</mml:mi><mml:mo>\u2061</mml:mo><mml:mo":[212],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mrow":[213],"mathvariant=\"double-struck\">C</mml:mi></mml:mrow><mml:mo":[215,219],"stretchy=\"false\">)</mml:mo><mml:mo>\u00d7</mml:mo><mml:mo>\u22ef</mml:mo><mml:mo>\u00d7</mml:mo><mml:mi>SL</mml:mi><mml:mo>\u2061</mml:mo><mml:mo":[216],"stretchy=\"false\">(</mml:mo><mml:msub><mml:mi>d</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:mrow":[217],"stretchy=\"false\">)</mml:mo></mml:math>for":[220],"generic":[222],"an":[225],"arbitrary":[226],"identify":[230],"cases":[232],"this":[234],"trivial.":[237]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2018-01-26T00:00:00"}