{"id":"https://openalex.org/W3203384730","doi":"https://doi.org/10.22331/q-2023-01-19-900","title":"Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem","display_name":"Contextuality in composite systems: the role of entanglement in the Kochen-Specker theorem","publication_year":2023,"publication_date":"2023-01-19","ids":{"openalex":"https://openalex.org/W3203384730","doi":"https://doi.org/10.22331/q-2023-01-19-900","mag":"3203384730"},"language":"en","primary_location":{"id":"doi:10.22331/q-2023-01-19-900","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-01-19-900","pdf_url":"https://quantum-journal.org/papers/q-2023-01-19-900/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2023-01-19-900/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101920243","display_name":"Victoria J Wright","orcid":"https://orcid.org/0000-0003-3523-7553"},"institutions":[{"id":"https://openalex.org/I179630473","display_name":"Institute of Photonic Sciences","ror":"https://ror.org/03g5ew477","country_code":"ES","type":"facility","lineage":["https://openalex.org/I179630473","https://openalex.org/I4210132884","https://openalex.org/I4387153040","https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Victoria J Wright","raw_affiliation_strings":["ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Spain","institution_ids":["https://openalex.org/I179630473"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049520338","display_name":"Ravi Kunjwal","orcid":"https://orcid.org/0000-0002-3978-5971"},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Ravi Kunjwal","raw_affiliation_strings":["Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, CP 165, Universit\u00e9 libre de Bruxelles, 1050 Brussels, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, CP 165, Universit\u00e9 libre de Bruxelles, 1050 Brussels, Belgium","institution_ids":["https://openalex.org/I132053463"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.5223,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8062258,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":null,"first_page":"900","last_page":"900"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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":0.9987999796867371,"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/kochen\u2013specker-theorem","display_name":"Kochen\u2013Specker theorem","score":0.9800702333450317},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.8436594009399414},{"id":"https://openalex.org/keywords/no-go-theorem","display_name":"No-go theorem","score":0.6210081577301025},{"id":"https://openalex.org/keywords/bells-theorem","display_name":"Bell's theorem","score":0.6140294671058655},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.57463139295578},{"id":"https://openalex.org/keywords/quantum-nonlocality","display_name":"Quantum nonlocality","score":0.5551825165748596},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.530009388923645},{"id":"https://openalex.org/keywords/quantum-no-deleting-theorem","display_name":"Quantum no-deleting theorem","score":0.509131133556366},{"id":"https://openalex.org/keywords/bell-state","display_name":"Bell state","score":0.49508562684059143},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4145132005214691},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3698672652244568},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3406136929988861},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.32172197103500366},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.3087790012359619},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23543646931648254},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.1525643765926361},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.12334436178207397}],"concepts":[{"id":"https://openalex.org/C193588502","wikidata":"https://www.wikidata.org/wiki/Q528955","display_name":"Kochen\u2013Specker theorem","level":3,"score":0.9800702333450317},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.8436594009399414},{"id":"https://openalex.org/C68227491","wikidata":"https://www.wikidata.org/wiki/Q2914432","display_name":"No-go theorem","level":4,"score":0.6210081577301025},{"id":"https://openalex.org/C128108043","wikidata":"https://www.wikidata.org/wiki/Q388525","display_name":"Bell's theorem","level":4,"score":0.6140294671058655},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.57463139295578},{"id":"https://openalex.org/C138622882","wikidata":"https://www.wikidata.org/wiki/Q7269079","display_name":"Quantum nonlocality","level":4,"score":0.5551825165748596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.530009388923645},{"id":"https://openalex.org/C45483111","wikidata":"https://www.wikidata.org/wiki/Q7269076","display_name":"Quantum no-deleting theorem","level":5,"score":0.509131133556366},{"id":"https://openalex.org/C118704821","wikidata":"https://www.wikidata.org/wiki/Q2898260","display_name":"Bell state","level":4,"score":0.49508562684059143},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4145132005214691},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3698672652244568},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3406136929988861},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32172197103500366},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.3087790012359619},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23543646931648254},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.1525643765926361},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.12334436178207397},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2023-01-19-900","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-01-19-900","pdf_url":"https://quantum-journal.org/papers/q-2023-01-19-900/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2109.13594","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2109.13594","pdf_url":"https://arxiv.org/pdf/2109.13594","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/355103","is_oa":true,"landing_page_url":"http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/355103","pdf_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/355103/3/q-2023-01-19-900.pdf","source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 7","raw_type":"info:ulb-repo/semantics/openurl/article"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/354493","is_oa":true,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/354493/3/2109.13594.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv.org","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:04318ea7f9e941179f5854c58161925f","is_oa":true,"landing_page_url":"https://doaj.org/article/04318ea7f9e941179f5854c58161925f","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":"Quantum, Vol 7, p 900 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2023-01-19-900","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22331/q-2023-01-19-900","pdf_url":"https://quantum-journal.org/papers/q-2023-01-19-900/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1316516701","display_name":null,"funder_award_id":"SGR 1381","funder_id":"https://openalex.org/F4320334830","funder_display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca"},{"id":"https://openalex.org/G1466779151","display_name":null,"funder_award_id":"754510","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1908469581","display_name":null,"funder_award_id":"CEX2019-000910-S","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G5617805276","display_name":null,"funder_award_id":"SGR 1381","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G6079651610","display_name":null,"funder_award_id":"CERCA, AGAUR SGR 1381","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G6482940084","display_name":null,"funder_award_id":"CEX2019-000910-S","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"},{"id":"https://openalex.org/G6607828179","display_name":null,"funder_award_id":"AGAUR SGR 1381","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G6829033866","display_name":null,"funder_award_id":"CERCA, AGAUR SGR 1381 and QuantumCAT","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G7474895656","display_name":null,"funder_award_id":"754510","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7854272128","display_name":null,"funder_award_id":"AGAUR SGR 1381","funder_id":"https://openalex.org/F4320315803","funder_display_name":"Centres de Recerca de Catalunya"}],"funders":[{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320315803","display_name":"Centres de Recerca de Catalunya","ror":null},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320334830","display_name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","ror":"https://ror.org/01n4pqe45"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3203384730.pdf"},"referenced_works_count":69,"referenced_works":["https://openalex.org/W1499630255","https://openalex.org/W1914859158","https://openalex.org/W1923824182","https://openalex.org/W1971031870","https://openalex.org/W1974293884","https://openalex.org/W1977673587","https://openalex.org/W1990783708","https://openalex.org/W1992723105","https://openalex.org/W1996433234","https://openalex.org/W2009005793","https://openalex.org/W2014160297","https://openalex.org/W2015592342","https://openalex.org/W2016124611","https://openalex.org/W2019921462","https://openalex.org/W2024761964","https://openalex.org/W2033621353","https://openalex.org/W2039772562","https://openalex.org/W2039871263","https://openalex.org/W2040794877","https://openalex.org/W2045220263","https://openalex.org/W2052146120","https://openalex.org/W2058625806","https://openalex.org/W2062292260","https://openalex.org/W2065192689","https://openalex.org/W2065260707","https://openalex.org/W2070217890","https://openalex.org/W2075850288","https://openalex.org/W2079797445","https://openalex.org/W2089249635","https://openalex.org/W2091785906","https://openalex.org/W2092698230","https://openalex.org/W2122187744","https://openalex.org/W2129072779","https://openalex.org/W2135830616","https://openalex.org/W2144449223","https://openalex.org/W2145928944","https://openalex.org/W2156783697","https://openalex.org/W2227039197","https://openalex.org/W2228923719","https://openalex.org/W2243675715","https://openalex.org/W2468305475","https://openalex.org/W2567502636","https://openalex.org/W2748703062","https://openalex.org/W2753173407","https://openalex.org/W2760385998","https://openalex.org/W2771348173","https://openalex.org/W2781738013","https://openalex.org/W2801937927","https://openalex.org/W2888193378","https://openalex.org/W2982169647","https://openalex.org/W2983730483","https://openalex.org/W3030501679","https://openalex.org/W3098145670","https://openalex.org/W3098723739","https://openalex.org/W3098830176","https://openalex.org/W3099887839","https://openalex.org/W3100431838","https://openalex.org/W3100931082","https://openalex.org/W3101479050","https://openalex.org/W3102459651","https://openalex.org/W3104470344","https://openalex.org/W3105454500","https://openalex.org/W3105593544","https://openalex.org/W3121450020","https://openalex.org/W3135857312","https://openalex.org/W4238804566","https://openalex.org/W4244716531","https://openalex.org/W4295682181","https://openalex.org/W4305097924"],"related_works":["https://openalex.org/W2763106131","https://openalex.org/W1979760438","https://openalex.org/W3098268515","https://openalex.org/W3101783732","https://openalex.org/W1772523263","https://openalex.org/W4286955756","https://openalex.org/W2163464259","https://openalex.org/W3161181029","https://openalex.org/W3211755057","https://openalex.org/W4298135609"],"abstract_inverted_index":{"The":[0],"Kochen\u2013Specker":[1,55,162],"(KS)":[2],"theorem":[3,14,79,104,137],"reveals":[4],"the":[5,18,54,77,135,154,159,187,196],"nonclassicality":[6,19],"of":[7,20,53,66,76,134,161,174,189,198],"single":[8],"quantum":[9,22,199],"systems.":[10,23,82],"In":[11,83],"contrast,":[12],"Bell's":[13],"and":[15,28,46,139,158,163],"entanglement":[16,27,45,157],"concern":[17],"composite":[21],"Accordingly,":[24],"unlike":[25],"incompatibility,":[26],"Bell":[29,146],"non-locality":[30,47],"are":[31,48],"not":[32],"necessary":[33],"to":[34,51],"demonstrate":[35],"KS-contextuality.":[36],"However,":[37],"here":[38],"we":[39,58,123,178],"find":[40],"that":[41,60,101,125],"for":[42,80,95],"multiqubit":[43,81,107,127,190],"systems,":[44],"both":[49],"essential":[50],"proofs":[52],"theorem.":[56],"Firstly,":[57],"show":[59,124],"unentangled":[61,85],"measurements":[62],"(a":[63],"strict":[64],"superset":[65],"local":[67],"measurements)":[68],"can":[69,143],"never":[70],"yield":[71],"a":[72,106,126,130,145,193],"logical":[73],"(state-independent)":[74],"proof":[75,133],"KS":[78,136,175],"particular,":[84],"but":[86],"nonlocal":[87],"measurements\u2014whose":[88],"eigenstates":[89],"exhibit":[90],"''nonlocality":[91],"without":[92],"entanglement\"\u2014are":[93],"insufficient":[94],"such":[96],"proofs.":[97],"This":[98],"also":[99,152],"implies":[100],"proving":[102],"Gleason's":[103],"on":[105,186],"system":[108],"necessarily":[109],"requires":[110],"entangled":[111],"projections,":[112],"as":[113,192],"shown":[114],"by":[115,170],"Wallach":[116],"[Contemp":[117],"Math,":[118],"305:":[119],"291-298":[120],"(2002)].":[121],"Secondly,":[122],"state":[128,202],"admits":[129],"statistical":[131],"(state-dependent)":[132],"if":[138,141],"only":[140],"it":[142],"violate":[144],"inequality":[147],"with":[148,201],"projective":[149],"measurements.":[150],"We":[151],"establish":[153],"relationship":[155],"between":[156],"theorems":[160],"Gleason":[164],"more":[165],"generally":[166],"in":[167],"multiqudit":[168],"systems":[169],"constructing":[171],"new":[172,184],"examples":[173],"sets.":[176],"Finally,":[177],"discuss":[179],"how":[180],"our":[181],"results":[182],"shed":[183],"light":[185],"role":[188],"contextuality":[191],"resource":[194],"within":[195],"paradigm":[197],"computation":[200],"injection.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2025-10-10T00:00:00"}