{"id":"https://openalex.org/W7225326171","doi":"https://doi.org/10.5281/zenodo.23971714","title":"Eberhard's 82.84% Detector Efficiency Threshold for Loophole-Free Bell Tests \u2014 E8 Intelligence Research","display_name":"Eberhard's 82.84% Detector Efficiency Threshold for Loophole-Free Bell Tests \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225326171","doi":"https://doi.org/10.5281/zenodo.23971714"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23971714","doi":"https://doi.org/10.5281/zenodo.23971714","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23971714","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23971714","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155309988","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5155309988"],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9814000129699707,"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":0.9814000129699707,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.006399999838322401,"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":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/loophole-free-bell-tests","display_name":"loophole-free Bell tests","score":0.9860000014305115},{"id":"https://openalex.org/keywords/singlet-state","display_name":"singlet state","score":0.9470000267028809},{"id":"https://openalex.org/keywords/chsh-inequality","display_name":"CHSH inequality","score":0.9599999785423279},{"id":"https://openalex.org/keywords/quantum-correlations","display_name":"quantum correlations","score":0.5230000019073486},{"id":"https://openalex.org/keywords/polarization-analyzer","display_name":"polarization analyzer","score":0.6539999842643738},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.367000013589859},{"id":"https://openalex.org/keywords/octagon","display_name":"octagon","score":0.6179999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6305000185966492},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C205049153","wikidata":"https://www.wikidata.org/wiki/Q2698605","display_name":"Polarization (electrochemistry)","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3986999988555908},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3919000029563904},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.38350000977516174},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3779999911785126},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3666999936103821},{"id":"https://openalex.org/C17648541","wikidata":"https://www.wikidata.org/wiki/Q2265984","display_name":"Efficiency","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C203103908","wikidata":"https://www.wikidata.org/wiki/Q3689728","display_name":"Spontaneous parametric down-conversion","level":4,"score":0.35989999771118164},{"id":"https://openalex.org/C128108043","wikidata":"https://www.wikidata.org/wiki/Q388525","display_name":"Bell's theorem","level":4,"score":0.3043999969959259},{"id":"https://openalex.org/C198377831","wikidata":"https://www.wikidata.org/wiki/Q7269027","display_name":"Quantum correlation","level":5,"score":0.29260000586509705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2919999957084656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28529998660087585},{"id":"https://openalex.org/C205507967","wikidata":"https://www.wikidata.org/wiki/Q900625","display_name":"Quantum efficiency","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C96473913","wikidata":"https://www.wikidata.org/wiki/Q7187858","display_name":"Photon polarization","level":3,"score":0.2648000121116638}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23971714","doi":"https://doi.org/10.5281/zenodo.23971714","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23971714","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23971715","doi":"https://doi.org/10.5281/zenodo.23971715","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23971715","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23971714","doi":"https://doi.org/10.5281/zenodo.23971714","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23971714","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225073220","https://openalex.org/W7225273059","https://openalex.org/W7225248784","https://openalex.org/W7225153823","https://openalex.org/W7225166607","https://openalex.org/W7225051877","https://openalex.org/W7225012935","https://openalex.org/W7225153058","https://openalex.org/W7203713674","https://openalex.org/W2011966438"],"abstract_inverted_index":{"FINDING:":[0],"Eberhard's":[1],"threshold":[2],"\u03b7":[3,67],"\u2265":[4,68],"2(\u221a2":[5,69,75,87],"\u2212":[6,45,70,76,80,88,92,100,125,145],"1)":[7,71,77,81,89,97],"\u2248":[8],"0.8284":[9],"is":[10,156,171],"the":[11,31,34,162,172,177,188],"minimum":[12],"detector":[13],"efficiency":[14],"for":[15,53],"a":[16,26,119],"loophole-free":[17],"Bell":[18],"test":[19],"with":[20],"maximally":[21],"entangled":[22],"photon":[23],"pairs":[24],"\u2014":[25,110],"pure":[27],"number":[28],"arising":[29],"from":[30],"geometry":[32],"of":[33,158,176,187],"singlet-state":[35],"correlation":[36],"function.":[37],"MATH:":[38],"-":[39,47,60,72,84,102,121,133,140,150,167],"Singlet":[40],"state:":[41],"|\u03c8\u207b\u27e9":[42],"=":[43,51,78,82,90,94,98,113,116,127,129,131,136,138,143,154,160,169],"(1/\u221a2)(|H\u27e9\u2081|V\u27e9\u2082":[44],"|V\u27e9\u2081|H\u27e9\u2082)":[46],"Quantum":[48],"correlation:":[49],"E_Q(\u03b8)":[50],"\u2212cos(2\u03b8)":[52],"polarization":[54],"analyzers":[55],"at":[56],"relative":[57],"angle":[58,152,165],"\u03b8":[59],"Eberhard":[61],"inequality":[62],"(CHSH-type,":[63],"asymmetric":[64],"settings):":[65],"requires":[66],"Numerical":[73],"value:":[74],"2(1.41421356":[79],"0.82842712\u2026":[83],"Equivalent":[85],"forms:":[86],"2\u221a2":[91],"2":[93],"2/(\u221a2":[95],"+":[96],"(\u221a2":[99],"1)\u00b72":[101],"Also":[103],"expressible":[104],"as:":[105],"1/\u03c6\u00b2":[106,112],"\u00b7":[107],"(something)?":[108],"No":[109],"check:":[111],"0.381966;":[114],"2(\u221a2\u22121)":[115],"0.828427.":[117],"Not":[118],"\u03c6-power.":[120],"But":[122],"note:":[123],"\u221a2":[124,144],"1":[126,146],"0.41421356\u2026":[128],"tan(\u03c0/8)":[130,142],"tan(22.5\u00b0)":[132],"Therefore:":[134],"\u03b7_min":[135],"2\u00b7tan(\u03c0/8)":[137],"2\u00b7tan(22.5\u00b0)":[139],"And:":[141],"(exact":[147],"algebraic":[148],"identity)":[149],"The":[151],"\u03c0/8":[153,168],"22.5\u00b0":[155,170],"half":[157],"\u03c0/4":[159],"45\u00b0,":[161],"optimal":[163],"CHSH":[164],"CONNECTION:":[166],"fundamental":[173],"angular":[174],"unit":[175],"octago":[178],"Author:":[179],"Andrew":[180],"Stewart":[181],"Caldin,":[182],"Independent":[183],"Researcher,":[184],"UK.":[185],"Part":[186],"E8":[189],"Intelligence":[190],"Research":[191],"series.":[192],"Platform:":[193],"e8intelligence.com":[194]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}
