{"id":"https://openalex.org/W1662052389","doi":null,"title":"Entangling power, cartan decomposition, and braiding operators","display_name":"Entangling power, cartan decomposition, and braiding operators","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1662052389","mag":"1662052389"},"language":"en","primary_location":{"id":"mag:1662052389","doi":null,"is_oa":false,"landing_page_url":"http://content.lib.utah.edu/utils/getfile/collection/etd2/id/103/filename/928.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306522422","display_name":"PhDT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PhDT","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/A5111491485","display_name":"Yong-Shi Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yong-Shi Wu","raw_affiliation_strings":["The University of Utah#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Utah#TAB#","institution_ids":["https://openalex.org/I223532165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070831680","display_name":"Aaron David Ballard","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I223532165","display_name":"University of Utah","ror":"https://ror.org/03r0ha626","country_code":"US","type":"education","lineage":["https://openalex.org/I223532165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron David Ballard","raw_affiliation_strings":["The University of Utah#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Utah#TAB#","institution_ids":["https://openalex.org/I223532165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I223532165"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09217762,"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":0.7461000084877014,"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":0.7461000084877014,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.1462000012397766,"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":0.04820000007748604,"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/entangling-power","display_name":"entangling power","score":0.9990000128746033},{"id":"https://openalex.org/keywords/linear-entropy","display_name":"linear entropy","score":0.8059999942779541},{"id":"https://openalex.org/keywords/von-neumann-entropy","display_name":"von Neumann entropy","score":0.8600000143051147},{"id":"https://openalex.org/keywords/cartan-decomposition","display_name":"Cartan decomposition","score":0.7799999713897705},{"id":"https://openalex.org/keywords/su-8","display_name":"SU-8","score":0.8569999933242798},{"id":"https://openalex.org/keywords/three-qubit-entanglement","display_name":"three-qubit entanglement","score":0.8159999847412109},{"id":"https://openalex.org/keywords/ghz-states","display_name":"GHZ states","score":0.9240000247955322},{"id":"https://openalex.org/keywords/yang-baxter-equation","display_name":"Yang-Baxter equation","score":0.9750000238418579},{"id":"https://openalex.org/keywords/bell-states","display_name":"Bell states","score":0.7979999780654907},{"id":"https://openalex.org/keywords/topological-quantum-computation","display_name":"topological quantum computation","score":0.8939999938011169},{"id":"https://openalex.org/keywords/unitary-operators","display_name":"unitary operators","score":0.5019999742507935}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.7100484371185303},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6430966258049011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.635857105255127},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.47881513833999634},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4643796682357788},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.4530676007270813},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3961450457572937},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32061728835105896},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2931479215621948},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.27832478284835815},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18987157940864563}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:1662052389","doi":null,"is_oa":false,"landing_page_url":"http://content.lib.utah.edu/utils/getfile/collection/etd2/id/103/filename/928.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306522422","display_name":"PhDT","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"PhDT","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1608643664","https://openalex.org/W1631356911","https://openalex.org/W1977278339","https://openalex.org/W2000281602","https://openalex.org/W2005028755","https://openalex.org/W2005468889","https://openalex.org/W2005952170","https://openalex.org/W2015444455","https://openalex.org/W2029289973","https://openalex.org/W2037061784","https://openalex.org/W2060849535","https://openalex.org/W2066365197","https://openalex.org/W2073781628","https://openalex.org/W2093687880","https://openalex.org/W2147733222","https://openalex.org/W2158605123","https://openalex.org/W2167050139","https://openalex.org/W2172159049","https://openalex.org/W2265094020","https://openalex.org/W2397826713","https://openalex.org/W2991588408","https://openalex.org/W3102596210"],"related_works":["https://openalex.org/W2795564260","https://openalex.org/W2064767171","https://openalex.org/W2397826713","https://openalex.org/W2078612070","https://openalex.org/W2011854288","https://openalex.org/W2023575638","https://openalex.org/W2011944497","https://openalex.org/W2952922174","https://openalex.org/W6960015068","https://openalex.org/W7100349226"],"abstract_inverted_index":{"The":[0,32,104,291,322],"main":[1],"part":[2],"of":[3,10,18,51,71,79,85,101,122,155,159,167,197,204,208,217,221,258,289,293,309,314,328,332,343,395],"this":[4,62],"dissertation":[5],"starts":[6],"with":[7,173,319],"a":[8,48,83,142,188,214,225,248,268,376],"generalization":[9],"the":[11,16,29,52,80,86,102,111,115,120,129,153,165,174,181,194,205,209,218,235,240,244,251,256,275,297,320,329,339,348,362,368,372,381,393],"entangling":[12,33,195,236,283,298,311,330,378],"power,":[13,379],"which":[14,315,344],"quantifies":[15],"ability":[17],"unitary":[19],"operators":[20,170,198,229,284,333],"to":[21,95,114,118,144,163,223,280,285,305,347,355,392],"generate":[22,335],"entangled":[23],"states":[24,45,337,370],"by":[25],"their":[26],"action":[27,257],"on":[28,128,176,384],"computational":[30,340,373],"basis.":[31],"power":[34,74,299],"has":[35,375],"been":[36],"defined":[37,76],"for":[38,99,185,228,287],"an":[39,68],"evenly":[40],"split":[41],"bipartite":[42],"system,":[43],"whose":[44,90],"live":[46],"in":[47,77,147,171,199,230,277,296],"Hilbert":[49],"space":[50,113,117],"form":[53,92],"H1\u2297":[54],"H2":[55],"where":[56,133],"dimH1=":[57],"dimH2":[58,138],".":[59],"I":[60,178,211],"generalize":[61],"so":[63],"that":[64,192,334,361,366],"we":[65,126,233,272],"can":[66],"consider":[67],"odd":[69],"number":[70,292],"qubits.":[72],"Entangling":[73],"is":[75,108,152,162,253,266,300],"terms":[78],"linear":[81,105],"entropy,":[82,89],"linearization":[84],"von":[87],"Neumann":[88],"polynomial":[91],"allows":[93],"one":[94,313],"derive":[96],"simpler":[97],"expressions":[98],"functions":[100],"entropy.":[103],"entropy":[106],"measure":[107,119],"lifted":[109],"from":[110,303,338,371],"state":[112],"operator":[116],"entanglement":[121,146,168,252],"operators.":[123],"In":[124],"particular,":[125],"focus":[127,175],"three":[130,385],"qubit":[131,149,242],"case,":[132],"dimH1":[134],"=":[135,139],"2":[136],"and":[137,243,271,351],"4,":[140],"as":[141,238,247],"step":[143],"understanding":[145],"many":[148,342],"systems.":[150],"This":[151],"content":[154],"Chapter":[156,160],"3.\r\nThe":[157],"goal":[158],"4":[161],"explore":[164],"structure":[166],"producing":[169],"SU(2n),":[172],"SU(8).":[177,231,290],"first":[179,241],"review":[180],"magic":[182,226],"matrix":[183,191,227],"formalism":[184],"two-qubit":[186,364],"operators,":[187,312],"well":[189],"known":[190],"captures":[193],"capability":[196],"SU(4),":[200,261],"using":[201],"only":[202],"3":[203],"15":[206],"parameters":[207,294],"group.":[210],"then":[212,301,325],"use":[213,274],"recursive":[215],"definition":[216],"Cartan":[219],"decomposition":[220,276],"SU(2n)":[222],"construct":[224],"Because":[232],"view":[234],"operation":[237],"between":[239],"other":[245],"two":[246,278],"single":[249],"subsystem,":[250],"invariant":[254],"under":[255],"SU(2)":[259],"\u2297":[260,264],"but":[262],"SU(8)/SU(2)":[263],"SU(4)":[265],"not":[267,317],"symmetric":[269],"space,":[270],"must":[273],"stages":[279],"capture":[281],"enough":[282],"account":[286],"all":[288],"appearing":[295],"reduced":[302],"63":[304],"8,":[306],"keeping":[307],"track":[308],"7":[310],"does":[316,387],"commute":[318],"others.":[321],"next":[323],"chapter":[324],"presents":[326],"calculations":[327],"powers":[331],"GHZ":[336,382],"basis,":[341],"are":[345],"solutions":[346],"Yang-Baxter":[349],"equation":[350],"have":[352],"strong":[353],"connections":[354],"topological":[356],"quantum":[357],"computing.":[358],"We":[359],"find":[360],"Kauffman-Lomonaco":[363],"gate":[365,383],"produces":[367],"Bell":[369],"basis":[374],"maximal":[377],"while":[380],"qubits":[386],"not,":[388],"adding":[389],"another":[390],"piece":[391],"puzzle":[394],"entanglement.":[396]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}