{"id":"https://openalex.org/W2181662234","doi":null,"title":"Quantum Entanglement and Algebraic Group Actions","display_name":"Quantum Entanglement and Algebraic Group Actions","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2181662234","mag":"2181662234"},"language":"en","primary_location":{"id":"mag:2181662234","doi":null,"is_oa":false,"landing_page_url":"https://www.cs.ox.ac.uk/people/bob.coecke/Robert.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"volume":null,"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085159760","display_name":"Robert Furber","orcid":"https://orcid.org/0000-0001-6208-9782","observed_orcids":["https://orcid.org/0000-0001-6208-9782"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert Furber","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6208-9782","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085159760"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15708854,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.8496000170707703,"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":0.8496000170707703,"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":0.08139999955892563,"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":0.008999999612569809,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"quantum entanglement","score":0.9980000257492065},{"id":"https://openalex.org/keywords/algebraic-group-actions","display_name":"algebraic group actions","score":0.9309999942779541},{"id":"https://openalex.org/keywords/pure-states","display_name":"pure states","score":0.6890000104904175},{"id":"https://openalex.org/keywords/algebraic-closure","display_name":"algebraic closure","score":0.4869999885559082},{"id":"https://openalex.org/keywords/quotient-spaces","display_name":"quotient spaces","score":0.4860000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7722011804580688},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.7163178324699402},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5933200716972351},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5789271593093872},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5728833079338074},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5521001815795898},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5363465547561646},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.5019524097442627},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4910721778869629},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4874003529548645},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4596107006072998},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4477177858352661},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4238511025905609},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.4182840585708618},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38362979888916016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3684072494506836},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3452061414718628},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14734289050102234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1457599401473999},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10987913608551025},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07616263628005981},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0641060471534729},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2181662234","doi":null,"is_oa":false,"landing_page_url":"https://www.cs.ox.ac.uk/people/bob.coecke/Robert.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1495410784","https://openalex.org/W1534413569","https://openalex.org/W1539838732","https://openalex.org/W1549880792","https://openalex.org/W1574151794","https://openalex.org/W1596185498","https://openalex.org/W1596671514","https://openalex.org/W1631356911","https://openalex.org/W1640543104","https://openalex.org/W1974928788","https://openalex.org/W1977670750","https://openalex.org/W1978553093","https://openalex.org/W1986407511","https://openalex.org/W2005813528","https://openalex.org/W2020725861","https://openalex.org/W2032795441","https://openalex.org/W2070102357","https://openalex.org/W2079320104","https://openalex.org/W2082864593","https://openalex.org/W2120713972","https://openalex.org/W2135830616","https://openalex.org/W2154434103","https://openalex.org/W2175098281","https://openalex.org/W3101000757","https://openalex.org/W3105874181"],"related_works":["https://openalex.org/W77083448","https://openalex.org/W3103000235","https://openalex.org/W7100463418","https://openalex.org/W1900931176","https://openalex.org/W2981467930","https://openalex.org/W6929156796","https://openalex.org/W2798037770","https://openalex.org/W2991460863","https://openalex.org/W1976051534","https://openalex.org/W2130189713"],"abstract_inverted_index":{"In":[0],"the":[1,13,30,53,56,67,89,99,106,121,126],"following":[2,19],"we":[3],"discuss":[4,118],"how":[5],"algebraic":[6,92],"group":[7,93],"actions":[8,94],"can":[9],"be":[10,111],"applied":[11],"to":[12,65],"study":[14],"of":[15,33,52,58,108,112,120,123],"quantum":[16],"entanglement.":[17],"The":[18],"facts":[20],"are":[21],"new:":[22],"\u2022":[23,49,69,97],"A":[24,50],"method":[25],"for":[26,29],"calculating":[27],"equations":[28,54],"SLOCC":[31,80,103],"class":[32,104],"any":[34,133],"pure":[35],"state,":[36,61],"with":[37],"no":[38],"restrictions":[39],"on":[40],"dimensions":[41],"other":[42],"than":[43],"those":[44],"imposed":[45],"by":[46,125],"computational":[47],"speed.":[48],"calculation":[51],"defining":[55],"closure":[57,85,107],"one":[59],"4-partite":[60],"as":[62],"an":[63],"example":[64],"illustrate":[66],"method.":[68],"To":[70],"my":[71],"knowledge,":[72],"it":[73],"has":[74],"not":[75,130],"previously":[76],"been":[77],"observed":[78],"that":[79,101],"classes":[81],"equal":[82],"if":[83],"their":[84],"is":[86,95],"equal,":[87],"although":[88],"fact":[90,100],"about":[91],"known.":[96],"Similarly,":[98],"a":[102],"inside":[105],"another":[109],"must":[110],"strictly":[113],"smaller":[114],"dimension.":[115],"We":[116],"also":[117],"quotients":[119],"space":[122],"states":[124],"action,":[127],"but":[128],"do":[129],"actually":[131],"compute":[132],"or":[134],"prove":[135],"new":[136],"theorems":[137],"in":[138],"this":[139],"area.":[140]},"counts_by_year":[],"updated_date":"2025-11-06T04:12:42.849631","created_date":"2016-06-24T00:00:00"}
