{"id":"https://openalex.org/W2188305722","doi":null,"title":"MUTUALLY UNBIASED BASES 1","display_name":"MUTUALLY UNBIASED BASES 1","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2188305722","mag":"2188305722"},"language":"en","primary_location":{"id":"mag:2188305722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/quant-ph/0610216v1.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/quant-ph/0610216v1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063266138","display_name":"Ingemar Bengtsson","orcid":"https://orcid.org/0000-0002-4203-3180","observed_orcids":["https://orcid.org/0000-0002-4203-3180"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ingemar Bengtsson","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4203-3180","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5063266138"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.6650000214576721,"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":0.6650000214576721,"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":0.2727000117301941,"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":0.014399999752640724,"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/mutually-unbiased-bases","display_name":"mutually unbiased bases","score":1.0},{"id":"https://openalex.org/keywords/finite-dimensional-hilbert-space","display_name":"finite-dimensional Hilbert space","score":0.9549999833106995},{"id":"https://openalex.org/keywords/quantum-information","display_name":"quantum information","score":0.47099998593330383},{"id":"https://openalex.org/keywords/discrete-phase-space","display_name":"discrete phase space","score":0.3799999952316284}],"concepts":[{"id":"https://openalex.org/C158587675","wikidata":"https://www.wikidata.org/wiki/Q17160413","display_name":"Mutually unbiased bases","level":3,"score":0.9472372531890869},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.646765947341919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.523278534412384},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.47012197971343994},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4303811192512512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3909794092178345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.348610520362854},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3402400612831116},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33151212334632874},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07842963933944702}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2188305722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/quant-ph/0610216v1.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2188305722","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/quant-ph/0610216v1.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1509167021","https://openalex.org/W1556265897","https://openalex.org/W1624182979","https://openalex.org/W1841034626","https://openalex.org/W1983930529","https://openalex.org/W1995394259","https://openalex.org/W2011277039","https://openalex.org/W2014160297","https://openalex.org/W2015049075","https://openalex.org/W2031422325","https://openalex.org/W2035469609","https://openalex.org/W2039842791","https://openalex.org/W2046938896","https://openalex.org/W2058558225","https://openalex.org/W2094366212","https://openalex.org/W2103350111","https://openalex.org/W2131730048","https://openalex.org/W2133866430"],"related_works":["https://openalex.org/W1541494515","https://openalex.org/W7097790224","https://openalex.org/W2334026706","https://openalex.org/W1544467151","https://openalex.org/W1508480368","https://openalex.org/W2955975192","https://openalex.org/W3103441377","https://openalex.org/W6993045691","https://openalex.org/W2725819215","https://openalex.org/W7097236481"],"abstract_inverted_index":{"This":[0],"is":[1,25],"a":[2,20],"review":[3],"of":[4,7,23],"the":[5],"problem":[6],"Mutually":[8],"Unbiased":[9],"Bases":[10],"in":[11,33],"finite":[12],"dimensional":[13],"Hilbert":[14],"spaces,":[15],"real":[16],"and":[17,27],"complex.":[18],"Also":[19],"geometric":[21],"measure":[22],"\u201cmubness\u201d":[24],"introduced,":[26],"applied":[28],"to":[29],"some":[30],"explicit":[31],"calculations":[32],"six":[34],"di\uf8ee":[35]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}
