{"id":"https://openalex.org/W3101744433","doi":null,"title":"Fields of Quantum Reference Frames based on Different Representations of Rational Numbers as States of Qubit Strings","display_name":"Fields of Quantum Reference Frames based on Different Representations of Rational Numbers as States of Qubit Strings","publication_year":2006,"publication_date":"2006-11-13","ids":{"openalex":"https://openalex.org/W3101744433","mag":"3101744433"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.252.7210","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.7210","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/quant-ph/0611139v1.pdf","raw_type":"text"},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Paul Benioff","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Benioff","raw_affiliation_strings":["Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA","institution_ids":["https://openalex.org/I1282105669"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1282105669"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.6503999829292297,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.6503999829292297,"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.05640000104904175,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T13234","display_name":"advanced mathematical theories","score":0.03449999913573265,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/quantum-reference-frames","display_name":"quantum reference frames","score":0.9990000128746033},{"id":"https://openalex.org/keywords/rational-numbers","display_name":"rational numbers","score":0.7350000143051147},{"id":"https://openalex.org/keywords/cauchy-sequences","display_name":"Cauchy sequences","score":0.7749999761581421},{"id":"https://openalex.org/keywords/gauge-transformations","display_name":"gauge transformations","score":0.703000009059906},{"id":"https://openalex.org/keywords/complex-numbers","display_name":"complex numbers","score":0.6480000019073486},{"id":"https://openalex.org/keywords/frame-fields","display_name":"frame fields","score":0.5609999895095825},{"id":"https://openalex.org/keywords/quantum-foundations","display_name":"quantum foundations","score":0.3050000071525574}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5900912284851074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5823655724525452},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.5087538361549377},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.47420743107795715},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45609724521636963},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.44999396800994873},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.44253087043762207},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.4229293465614319},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40429452061653137},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3774442970752716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3584921061992645},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21885240077972412},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20784887671470642},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11064913868904114},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08734434843063354},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.252.7210","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.7210","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/quant-ph/0611139v1.pdf","raw_type":"text"},{"id":"pmh:oai:cds.cern.ch:999216","doi":null,"is_oa":false,"landing_page_url":"http://cds.cern.ch/record/999216","pdf_url":null,"source":{"id":"https://openalex.org/S4306402195","display_name":"CERN Document Server (European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","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":16,"referenced_works":["https://openalex.org/W2002554805","https://openalex.org/W2029568264","https://openalex.org/W2049436213","https://openalex.org/W2055993996","https://openalex.org/W2059309740","https://openalex.org/W2068677542","https://openalex.org/W2070481624","https://openalex.org/W2070707213","https://openalex.org/W2074699344","https://openalex.org/W2076068770","https://openalex.org/W2079289233","https://openalex.org/W2087461947","https://openalex.org/W2088811025","https://openalex.org/W2090624996","https://openalex.org/W2106528814","https://openalex.org/W2768335821"],"related_works":["https://openalex.org/W2152334162","https://openalex.org/W4394646796","https://openalex.org/W7100320528","https://openalex.org/W3106523108","https://openalex.org/W1632457453","https://openalex.org/W150352557","https://openalex.org/W2130366493","https://openalex.org/W6979294075","https://openalex.org/W48903221","https://openalex.org/W4309037153"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"fields":[3,128],"of":[4,12,50,55,64,73,80,100,125,141],"quantum":[5,52],"reference":[6,87],"frames":[7],"based":[8,39],"on":[9,40],"gauge":[10],"transformations":[11],"rational":[13,60,74],"string":[14,75],"states":[15,63,76],"are":[16,46,129,148],"described":[17],"in":[18,30,134],"a":[19,47,78,98,114],"way":[20],"that,":[21],"hopefully,":[22],"makes":[23],"them":[24],"more":[25],"understandable":[26],"than":[27],"their":[28],"description":[29],"an":[31],"earlier":[32],"paper.":[33],"The":[34],"approach":[35],"taken":[36],"here":[37],"is":[38,89],"three":[41],"main":[42],"points:":[43],"(1)":[44],"There":[45],"large":[48],"number":[49],"different":[51,139],"theory":[53],"representations":[54],"natural":[56],"numbers,":[57],"integers,":[58],"and":[59,103,110,122,132],"numbers":[61,112],"as":[62,113],"qubit":[65],"strings.":[66],"(2)":[67],"For":[68],"each":[69,92],"representation,":[70],"Cauchy":[71],"sequences":[72],"give":[77],"representation":[79,99],"the":[81,108,118,126,143],"real":[82,109],"(and":[83],"complex)":[84],"numbers.":[85],"A":[86],"frame":[88,96,144],"associated":[90],"to":[91,146],"representation.":[93],"(3)":[94],"Each":[95],"contains":[97],"all":[101],"mathematical":[102],"physical":[104],"theories":[105],"that":[106],"have":[107],"complex":[111],"scalar":[115],"base":[116],"for":[117],"theories.":[119],"These":[120],"points":[121],"other":[123],"aspects":[124],"resulting":[127],"then":[130],"discussed":[131],"justified":[133],"some":[135],"detail.":[136],"Also":[137],"two":[138],"methods":[140],"relating":[142],"field":[145],"physics":[147],"discussed.":[149],"1":[150]},"counts_by_year":[],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2020-11-23T00:00:00"}