{"id":"https://openalex.org/W2121374143","doi":"https://doi.org/10.3390/e16031484","title":"Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States","display_name":"Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States","publication_year":2014,"publication_date":"2014-03-14","ids":{"openalex":"https://openalex.org/W2121374143","doi":"https://doi.org/10.3390/e16031484","mag":"2121374143"},"language":"en","primary_location":{"id":"doi:10.3390/e16031484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16031484","pdf_url":"https://www.mdpi.com/1099-4300/16/3/1484/pdf?version=1424785351","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/16/3/1484/pdf?version=1424785351","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111917777","display_name":"D. M. Appleby","orcid":null},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"D. Appleby","raw_affiliation_strings":["School of Physics, University of Sydney, Sydney, NSW 2006, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics, University of Sydney, Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058674988","display_name":"Hoan Bui Dang","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Hoan Dang","raw_affiliation_strings":["University of Waterloo, 200 University Ave West, Waterloo, ON N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Waterloo, 200 University Ave West, Waterloo, ON N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103265089","display_name":"Christopher A. Fuchs","orcid":"https://orcid.org/0000-0003-0389-6204"},"institutions":[{"id":"https://openalex.org/I1306686416","display_name":"RTX (United States)","ror":"https://ror.org/0354t7b78","country_code":"US","type":"company","lineage":["https://openalex.org/I1306686416"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher Fuchs","raw_affiliation_strings":["Quantum Information Processing Group, Raytheon BBN Technologies, 10 Moulton Street, Cambridge, MA 02138, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantum Information Processing Group, Raytheon BBN Technologies, 10 Moulton Street, Cambridge, MA 02138, USA","institution_ids":["https://openalex.org/I1306686416"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058674988"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":12.6998,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.98570809,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"16","issue":"3","first_page":"1484","last_page":"1492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9984999895095825,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/orthonormal-basis","display_name":"Orthonormal basis","score":0.9113985300064087},{"id":"https://openalex.org/keywords/orthonormality","display_name":"Orthonormality","score":0.714747428894043},{"id":"https://openalex.org/keywords/mutually-unbiased-bases","display_name":"Mutually unbiased bases","score":0.653876006603241},{"id":"https://openalex.org/keywords/covariant-transformation","display_name":"Covariant transformation","score":0.589850664138794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5888450145721436},{"id":"https://openalex.org/keywords/uncertainty-principle","display_name":"Uncertainty principle","score":0.5793062448501587},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5092204809188843},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4864951968193054},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.4595351219177246},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4583756923675537},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4534563720226288},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32510003447532654},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22965043783187866},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.15268662571907043},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1505613923072815},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.09595352411270142}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.9113985300064087},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.714747428894043},{"id":"https://openalex.org/C158587675","wikidata":"https://www.wikidata.org/wiki/Q17160413","display_name":"Mutually unbiased bases","level":3,"score":0.653876006603241},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.589850664138794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5888450145721436},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.5793062448501587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5092204809188843},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4864951968193054},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4595351219177246},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4583756923675537},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4534563720226288},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32510003447532654},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22965043783187866},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.15268662571907043},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1505613923072815},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.09595352411270142},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e16031484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16031484","pdf_url":"https://www.mdpi.com/1099-4300/16/3/1484/pdf?version=1424785351","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d53af56037874466961b52d908ff56c5","is_oa":true,"landing_page_url":"https://doaj.org/article/d53af56037874466961b52d908ff56c5","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":"Entropy, Vol 16, Iss 3, Pp 1484-1492 (2014)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/16/3/1484/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e16031484","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 16; Issue 3; Pages: 1484-1492","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e16031484","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e16031484","pdf_url":"https://www.mdpi.com/1099-4300/16/3/1484/pdf?version=1424785351","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W170055115","https://openalex.org/W1480647633","https://openalex.org/W1491346439","https://openalex.org/W1509167021","https://openalex.org/W1544025753","https://openalex.org/W1574883946","https://openalex.org/W1591596752","https://openalex.org/W1593125407","https://openalex.org/W1651296189","https://openalex.org/W1665316997","https://openalex.org/W1886182640","https://openalex.org/W1977809994","https://openalex.org/W1989301452","https://openalex.org/W1998169277","https://openalex.org/W1999618182","https://openalex.org/W2002688185","https://openalex.org/W2003583756","https://openalex.org/W2039178006","https://openalex.org/W2039312417","https://openalex.org/W2041938419","https://openalex.org/W2046555850","https://openalex.org/W2057906938","https://openalex.org/W2061524924","https://openalex.org/W2081888852","https://openalex.org/W2094366212","https://openalex.org/W2131730048","https://openalex.org/W2144623882","https://openalex.org/W2147406322","https://openalex.org/W2182304189","https://openalex.org/W2600106234","https://openalex.org/W2949652296","https://openalex.org/W3099753513","https://openalex.org/W3101740473","https://openalex.org/W3103349989","https://openalex.org/W3103840197","https://openalex.org/W3105455910","https://openalex.org/W6636837599","https://openalex.org/W6637305494","https://openalex.org/W6639191846"],"related_works":["https://openalex.org/W2013801824","https://openalex.org/W1529452180","https://openalex.org/W1496788307","https://openalex.org/W2013322017","https://openalex.org/W3101372095","https://openalex.org/W2149054915","https://openalex.org/W1591253575","https://openalex.org/W1508480368","https://openalex.org/W2121374143","https://openalex.org/W2951235573"],"abstract_inverted_index":{"Recently":[0],"there":[1],"has":[2],"been":[3],"much":[4],"effort":[5],"in":[6,26,70,99,119],"the":[7,15,33,61,73,97,100,110,120],"quantum":[8,24],"information":[9],"community":[10],"to":[11,55,109],"prove":[12],"(or":[13],"disprove)":[14],"existence":[16,113],"of":[17,23,35,49,63,79,102,112],"symmetric":[18],"informationally":[19],"complete":[20,77],"(SIC)":[21],"sets":[22,78],"states":[25,95],"arbitrary":[27],"finite":[28],"dimension.":[29],"This":[30],"paper":[31],"strengthens":[32],"urgency":[34],"this":[36],"question":[37,111],"by":[38,45,114],"showing":[39],"that":[40],"if":[41],"SIC-sets":[42,86],"exist:":[43],"(1)":[44],"a":[46,116],"natural":[47],"measure":[48],"orthonormality,":[50],"they":[51],"are":[52,87],"as":[53,66],"close":[54],"being":[56],"an":[57],"orthonormal":[58],"basis":[59],"for":[60,76,96,122],"space":[62],"density":[64],"operators":[65],"possible;":[67],"and":[68,83,104],"(2)":[69],"prime":[71],"dimensions,":[72],"standard":[74],"construction":[75],"mutually":[80],"unbiased":[81],"bases":[82],"Weyl-Heisenberg":[84,123],"covariant":[85],"intimately":[88],"related:":[89],"The":[90],"latter":[91],"represent":[92],"minimum":[93],"uncertainty":[94],"former":[98],"sense":[101],"Wootters":[103],"Sussman.":[105],"Finally,":[106],"we":[107],"contribute":[108],"conjecturing":[115],"quadratic":[117],"redundancy":[118],"equations":[121],"SIC-sets.":[124]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2016-06-24T00:00:00"}
