{"id":"https://openalex.org/W4400494337","doi":"https://doi.org/10.22331/q-2024-07-10-1402","title":"Algebra of Nonlocal Boxes and the Collapse of Communication Complexity","display_name":"Algebra of Nonlocal Boxes and the Collapse of Communication Complexity","publication_year":2024,"publication_date":"2024-07-10","ids":{"openalex":"https://openalex.org/W4400494337","doi":"https://doi.org/10.22331/q-2024-07-10-1402"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-07-10-1402","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-07-10-1402","pdf_url":"https://quantum-journal.org/papers/q-2024-07-10-1402/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2024-07-10-1402/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057359374","display_name":"Pierre Botteron","orcid":"https://orcid.org/0000-0002-3861-0934"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre Botteron","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I17866349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034032202","display_name":"Anne Broadbent","orcid":"https://orcid.org/0000-0003-1911-0093"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]},{"id":"https://openalex.org/I75381157","display_name":"Wilfrid Laurier University","ror":"https://ror.org/00fn7gb05","country_code":"CA","type":"education","lineage":["https://openalex.org/I75381157"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Anne Broadbent","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Canada","Nexus for Quantum Technologies, University of Ottawa, Canada","University of Ottawa [Ottawa] (75 Laurier Avenue East, Ottawa, ON K1N 6N5 - Canada)"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"Nexus for Quantum Technologies, University of Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]},{"raw_affiliation_string":"University of Ottawa [Ottawa] (75 Laurier Avenue East, Ottawa, ON K1N 6N5 - Canada)","institution_ids":["https://openalex.org/I153718931","https://openalex.org/I75381157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086364729","display_name":"Reda Chhaibi","orcid":"https://orcid.org/0000-0002-0085-0086"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Reda Chhaibi","raw_affiliation_strings":["Institut Universitaire de France (IUF), France","Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut Universitaire de France (IUF), France","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I17866349"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041561607","display_name":"Ion Nechita","orcid":"https://orcid.org/0000-0003-3016-7795"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210109170","display_name":"Laboratoire de Physique Th\u00e9orique","ror":"https://ror.org/01w0hda30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210109170","https://openalex.org/I4388446414","https://openalex.org/I4405258862"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ion Nechita","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique, Universit\u00e9 de Toulouse, CNRS, France"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique, Universit\u00e9 de Toulouse, CNRS, France","institution_ids":["https://openalex.org/I4210109170","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086690346","display_name":"Cl\u00e9ment Pellegrini","orcid":"https://orcid.org/0000-0001-8072-4284"},"institutions":[{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405259414","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cl\u00e9ment Pellegrini","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France"],"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse, Universit\u00e9 de Toulouse, France","institution_ids":["https://openalex.org/I84500057","https://openalex.org/I17866349"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5057359374"],"corresponding_institution_ids":["https://openalex.org/I17866349","https://openalex.org/I84500057"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.6751,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.73991019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"8","issue":null,"first_page":"1402","last_page":"1402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9993000030517578,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9993000030517578,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/algorithm","display_name":"Algorithm","score":0.6466282606124878},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5141663551330566},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39967846870422363},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.37612754106521606}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6466282606124878},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5141663551330566},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39967846870422363},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.37612754106521606}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2024-07-10-1402","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-07-10-1402","pdf_url":"https://quantum-journal.org/papers/q-2024-07-10-1402/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:HAL:hal-04687878v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04687878","pdf_url":"https://hal.science/hal-04687878/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, 2024, 8, pp.1402. &#x27E8;10.22331/q-2024-07-10-1402&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:3edcf2e7f72a4bc6b9886d85c75b44d2","is_oa":true,"landing_page_url":"https://doaj.org/article/3edcf2e7f72a4bc6b9886d85c75b44d2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 8, p 1402 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2024-07-10-1402","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-07-10-1402","pdf_url":"https://quantum-journal.org/papers/q-2024-07-10-1402/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/G1092084723","display_name":null,"funder_award_id":"ANR-11-LABX-004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1436787102","display_name":null,"funder_award_id":"ANR-20-CE40-0024-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1688067019","display_name":"Quantum trajectories","funder_award_id":"ANR-20-CE40-0024","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2286017975","display_name":null,"funder_award_id":"Q-COAST ANR-19-CE48-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2402987151","display_name":null,"funder_award_id":"ANR-20-CE","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2627508364","display_name":null,"funder_award_id":"ALLRP","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G2815963884","display_name":null,"funder_award_id":"11-LABX-004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3054997996","display_name":null,"funder_award_id":"FR113029","funder_id":"https://openalex.org/F4320322675","funder_display_name":"Mitacs"},{"id":"https://openalex.org/G3174652392","display_name":null,"funder_award_id":"ANR-20-CE47-0014","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3335229504","display_name":null,"funder_award_id":"Avenir","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3807293409","display_name":null,"funder_award_id":"ANR-11-LABX-00","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3924576937","display_name":null,"funder_award_id":"13029","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G3969759488","display_name":null,"funder_award_id":"program","funder_id":"https://openalex.org/F4320322675","funder_display_name":"Mitacs"},{"id":"https://openalex.org/G400116904","display_name":null,"funder_award_id":"unknow","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G4036996791","display_name":null,"funder_award_id":"ANR-20-CE47-0014-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4553129391","display_name":null,"funder_award_id":"ANR-3IA","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4717139763","display_name":null,"funder_award_id":"ANR-20-CE40-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5221025394","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320328356","funder_display_name":"R\u00e9gion Occitanie Pyr\u00e9n\u00e9es-M\u00e9diterran\u00e9e"},{"id":"https://openalex.org/G563580206","display_name":null,"funder_award_id":"19-CE48-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6069716728","display_name":null,"funder_award_id":"FA9550-20-1-0375","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6268741103","display_name":null,"funder_award_id":"0014-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6558666582","display_name":null,"funder_award_id":"ANR-19-CE48-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7472618560","display_name":null,"funder_award_id":"ANR-3IA","funder_id":"https://openalex.org/F7608296345","funder_display_name":"Artificial and Natural Intelligence Toulouse Institute"},{"id":"https://openalex.org/G7786692064","display_name":null,"funder_award_id":"ANR-11-LABX-0040","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7980265494","display_name":null,"funder_award_id":"20-CE40-0008","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8284766523","display_name":null,"funder_award_id":"(NSERC)","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8554691130","display_name":null,"funder_award_id":"ALLRP 580876 - 22","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G893321756","display_name":null,"funder_award_id":"20-CE47-0014-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322675","display_name":"Mitacs","ror":"https://ror.org/00cjrc276"},{"id":"https://openalex.org/F4320328356","display_name":"R\u00e9gion Occitanie Pyr\u00e9n\u00e9es-M\u00e9diterran\u00e9e","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F7608296345","display_name":"Artificial and Natural Intelligence Toulouse Institute","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400494337.pdf","grobid_xml":"https://content.openalex.org/works/W4400494337.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W605043455","https://openalex.org/W1480673261","https://openalex.org/W1665582821","https://openalex.org/W1969016943","https://openalex.org/W1972771071","https://openalex.org/W1973027773","https://openalex.org/W1998660432","https://openalex.org/W2002501531","https://openalex.org/W2008236737","https://openalex.org/W2009329166","https://openalex.org/W2014283062","https://openalex.org/W2019557606","https://openalex.org/W2022083124","https://openalex.org/W2023476664","https://openalex.org/W2028815089","https://openalex.org/W2044285503","https://openalex.org/W2052476506","https://openalex.org/W2102039510","https://openalex.org/W2108732680","https://openalex.org/W2119210589","https://openalex.org/W2120979175","https://openalex.org/W2128006942","https://openalex.org/W2129072779","https://openalex.org/W2138230010","https://openalex.org/W2162381006","https://openalex.org/W2340242708","https://openalex.org/W2595673182","https://openalex.org/W2743259048","https://openalex.org/W2950628286","https://openalex.org/W2954849489","https://openalex.org/W3099100261","https://openalex.org/W3100427438","https://openalex.org/W3129084028","https://openalex.org/W3142070261","https://openalex.org/W4211154544","https://openalex.org/W4293775970","https://openalex.org/W4323310688","https://openalex.org/W4379015446","https://openalex.org/W4383907604","https://openalex.org/W4389781892","https://openalex.org/W4391811142","https://openalex.org/W4403559051"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W3107602296","https://openalex.org/W4394896187","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347"],"abstract_inverted_index":{"Communication":[0],"complexity":[1,204],"quantifies":[2],"how":[3],"difficult":[4],"it":[5,174],"is":[6,87,172],"for":[7,205],"two":[8,51],"distant":[9],"computers":[10],"to":[11,24,145,177,186,191],"evaluate":[12],"a":[13,92,96,152],"function<mml:math":[14],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>f</mml:mi><mml:mo":[15],"stretchy=\"false\">(</mml:mo><mml:mi>X</mml:mi><mml:mo>,</mml:mo><mml:mi>Y</mml:mi><mml:mo":[16],"stretchy=\"false\">)</mml:mo></mml:math>,":[17],"where":[18],"the":[19,25,32,50,63,75,100,117,126,129,146,149,159,183],"strings<mml:math":[20],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi></mml:math>and<mml:math":[21],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Y</mml:mi></mml:math>are":[22],"distributed":[23],"first":[26],"and":[27,134,139,161,190,193],"second":[28],"computer":[29],"respectively,":[30],"under":[31],"constraint":[33],"of":[34,77,81,90,99,102,116,119,128,131,148,151,163,168,208],"exchanging":[35],"as":[36,39],"few":[37],"bits":[38],"possible.":[40],"Surprisingly,":[41],"some":[42],"nonlocal":[43,104,122],"boxes,":[44,123,189],"which":[45],"are":[46,53],"resources":[47],"shared":[48],"by":[49],"computers,":[52],"so":[54],"powerful":[55],"that":[56,65,173,201],"they":[57],"allow":[58],"to<mml:math":[59],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>c</mml:mi><mml:mi>o</mml:mi><mml:mi>l</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>p</mml:mi><mml:mi>s</mml:mi><mml:mi>e</mml:mi></mml:math>communication":[60],"complexity,":[61],"in":[62],"sense":[64],"any":[66],"Boolean":[67],"function":[68],"f":[69],"can":[70],"be":[71],"correctly":[72],"estimated":[73],"with":[74],"exchange":[76],"only":[78],"one":[79],"bit":[80],"communication.":[82],"The":[83,166],"Popescu-Rohrlich":[84],"(PR)":[85],"box":[86],"an":[88,113],"example":[89],"such":[91],"collapsing":[93,103],"resource,":[94],"but":[95],"comprehensive":[97],"description":[98],"set":[101],"boxes":[105],"remains":[106],"elusive.In":[107],"this":[108,169],"work,":[109],"we":[110,135],"carry":[111],"out":[112],"algebraic":[114],"study":[115],"structure":[118],"wirings":[120],"connecting":[121],"thus":[124],"defining":[125],"notion":[127,147],"\"product":[130],"boxes\"<mml:math":[132],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>P</mml:mi><mml:mo>&amp;#x22A0;</mml:mo><mml:mi>Q</mml:mi></mml:math>,":[133],"show":[136],"related":[137],"associativity":[138],"commutativity":[140],"results.":[141],"This":[142],"gives":[143],"rise":[144],"\"orbit":[150],"box\",":[153],"unveiling":[154],"surprising":[155],"geometrical":[156],"properties":[157],"about":[158],"alignment":[160],"parallelism":[162],"distilled":[164],"boxes.":[165],"power":[167],"new":[170],"framework":[171],"allows":[175],"us":[176],"prove":[178],"previously-reported":[179],"numerical":[180],"observations":[181],"concerning":[182],"best":[184],"way":[185],"wire":[187],"consecutive":[188],"numerically":[192],"analytically":[194],"recover":[195],"recently-identified":[196],"noisy<mml:math":[197],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[198],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[199],"mathvariant=\"monospace\">PR</mml:mtext></mml:mrow></mml:math>boxes":[200],"collapse":[202],"communication":[203],"different":[206],"types":[207],"noise":[209],"models.":[210]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2025-10-10T00:00:00"}