{"id":"https://openalex.org/W3209192400","doi":"https://doi.org/10.1145/3485628","title":"MIP* = RE","display_name":"MIP* = RE","publication_year":2021,"publication_date":"2021-10-25","ids":{"openalex":"https://openalex.org/W3209192400","doi":"https://doi.org/10.1145/3485628","mag":"3209192400"},"language":"en","primary_location":{"id":"doi:10.1145/3485628","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3485628","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3485628","source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications of the ACM","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3485628","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043930796","display_name":"Zhengfeng Ji","orcid":"https://orcid.org/0000-0002-7659-3178"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Zhengfeng Ji","raw_affiliation_strings":["University of Technology Sydney, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"University of Technology Sydney, Sydney, Australia","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083428352","display_name":"Anand Natarajan","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anand Natarajan","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019616211","display_name":"Thomas Vidick","orcid":"https://orcid.org/0000-0002-6405-365X"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thomas Vidick","raw_affiliation_strings":["California Institute of Technology, Pasadena, CA"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology, Pasadena, CA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015430753","display_name":"John C. Wright","orcid":"https://orcid.org/0000-0002-6926-1837"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Wright","raw_affiliation_strings":["University of Texas at Austin, Austin, TX"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin, Austin, TX","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085540097","display_name":"Henry Yuen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Henry Yuen","raw_affiliation_strings":["Colombia University, New York, NY"],"affiliations":[{"raw_affiliation_string":"Colombia University, New York, NY","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5043930796"],"corresponding_institution_ids":["https://openalex.org/I114017466"],"apc_list":null,"apc_paid":null,"fwci":16.0545,"has_fulltext":true,"cited_by_count":164,"citation_normalized_percentile":{"value":0.99363124,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"64","issue":"11","first_page":"131","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9987000226974487,"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/T10237","display_name":"Cryptography and Data Security","score":0.9962000250816345,"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":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6645320057868958},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6604989767074585},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.6501657962799072},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6501460671424866},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.6252338886260986},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.6067733764648438},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5783358812332153},{"id":"https://openalex.org/keywords/quantum-complexity-theory","display_name":"Quantum complexity theory","score":0.46867045760154724},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.4672035574913025},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.44121211767196655},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.43457192182540894},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4181438982486725},{"id":"https://openalex.org/keywords/recursively-enumerable-language","display_name":"Recursively enumerable language","score":0.41110673546791077},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39602142572402954},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3337476849555969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27491942048072815},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27326256036758423},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.22966361045837402},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.13549470901489258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13510432839393616}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6645320057868958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6604989767074585},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.6501657962799072},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6501460671424866},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.6252338886260986},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.6067733764648438},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5783358812332153},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.46867045760154724},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4672035574913025},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.44121211767196655},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.43457192182540894},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4181438982486725},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.41110673546791077},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39602142572402954},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3337476849555969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27491942048072815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27326256036758423},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.22966361045837402},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.13549470901489258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13510432839393616},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3485628","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3485628","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3485628","source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications of the ACM","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:102605","is_oa":true,"landing_page_url":null,"pdf_url":"https://authors.library.caltech.edu/102605/","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1145/3485628","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3485628","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3485628","source":{"id":"https://openalex.org/S103482838","display_name":"Communications of the ACM","issn_l":"0001-0782","issn":["0001-0782","1557-7317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications of the ACM","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1352987678","display_name":null,"funder_award_id":"FA9550-18-1-0161","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1404197429","display_name":null,"funder_award_id":"W911NF-17-1-04","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2050599915","display_name":null,"funder_award_id":"PHY-173390","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2077426331","display_name":null,"funder_award_id":"W911NF-17-1-0433","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G230078430","display_name":null,"funder_award_id":"FA9550-16","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2403330605","display_name":null,"funder_award_id":"PHY-1733907","funder_id":"https://openalex.org/F4320334224","funder_display_name":"Institute for Quantum Information and Matter, California Institute of Technology"},{"id":"https://openalex.org/G2684148513","display_name":null,"funder_award_id":"12500028","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G2894089465","display_name":null,"funder_award_id":"PHY-1125565","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G3297071621","display_name":null,"funder_award_id":"FA9550-18-1-016","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G3392305090","display_name":null,"funder_award_id":"-16-1-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3462782470","display_name":null,"funder_award_id":"1250002","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G3549753986","display_name":null,"funder_award_id":"CCF-1553477","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3616359867","display_name":null,"funder_award_id":"FA9550-16-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3673415204","display_name":null,"funder_award_id":"FA9550-18-1-01","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3747832099","display_name":null,"funder_award_id":"1125565","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4493575176","display_name":null,"funder_award_id":"GBMF-1250","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G4533172783","display_name":null,"funder_award_id":"PHY-1733907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G507237395","display_name":null,"funder_award_id":"1733907","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5175037542","display_name":null,"funder_award_id":"FA9550-16-1-0495","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5783856802","display_name":null,"funder_award_id":"2019-06636","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6487893095","display_name":null,"funder_award_id":"FA9550-18-1-016","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G768684073","display_name":null,"funder_award_id":"W911NF-17-1-0433","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7691558364","display_name":null,"funder_award_id":"PHY-1733907","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7830237364","display_name":null,"funder_award_id":"BMF-1250002","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"},{"id":"https://openalex.org/G8163048266","display_name":null,"funder_award_id":"FA9550-18-1-0161","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G8415630618","display_name":"CAREER: Interactions with Untrusted Quantum Devices","funder_award_id":"1553477","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8838030021","display_name":null,"funder_award_id":"PHY-1125565","funder_id":"https://openalex.org/F4320334224","funder_display_name":"Institute for Quantum Information and Matter, California Institute of Technology"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G999948053","display_name":null,"funder_award_id":"GBMF-12500028","funder_id":"https://openalex.org/F4320306202","funder_display_name":"Gordon and Betty Moore Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306202","display_name":"Gordon and Betty Moore Foundation","ror":"https://ror.org/006wxqw41"},{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320309949","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320334224","display_name":"Institute for Quantum Information and Matter, California Institute of Technology","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/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3209192400.pdf","grobid_xml":"https://content.openalex.org/works/W3209192400.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1483568252","https://openalex.org/W1991877988","https://openalex.org/W2009005793","https://openalex.org/W2028815089","https://openalex.org/W2034154168","https://openalex.org/W2039308336","https://openalex.org/W2044199052","https://openalex.org/W2045356657","https://openalex.org/W2051051926","https://openalex.org/W2071520502","https://openalex.org/W2148791594","https://openalex.org/W2328912295","https://openalex.org/W2627090645","https://openalex.org/W2951124766","https://openalex.org/W2995328993","https://openalex.org/W3100584152","https://openalex.org/W4256317935","https://openalex.org/W6600366268","https://openalex.org/W7048190923"],"related_works":["https://openalex.org/W4297966919","https://openalex.org/W2019646940","https://openalex.org/W2952003478","https://openalex.org/W2570053645","https://openalex.org/W4234189135","https://openalex.org/W2045590835","https://openalex.org/W4301013907","https://openalex.org/W2953001340","https://openalex.org/W2170336571","https://openalex.org/W2072410898"],"abstract_inverted_index":{"Note":[0],"from":[1],"the":[2,32,39,59,70,84,92,100,112,131,143,157,165,172,183,212],"Research":[3,7],"Highlights":[4,8],"Co-Chairs:":[5],"A":[6],"paper":[9,21],"appearing":[10],"in":[11,24,38,83,164,211],"Communications":[12],"is":[13,22,27,179],"usually":[14],"peer-reviewed":[15],"prior":[16],"to":[17,78,114,130,138,156],"publication.":[18],"The":[19,54,124,205],"following":[20],"unusual":[23],"that":[25,64,76,97,162,175,178],"it":[26],"still":[28],"under":[29],"review.":[30],"However,":[31],"result":[33,174,206],"has":[34],"generated":[35],"enormous":[36],"excitement":[37],"research":[40],"community,":[41],"and":[42,111,135,142,219],"came":[43],"strongly":[44],"nominated":[45],"by":[46,51,190],"SIGACT,":[47],"a":[48,153,191],"nomination":[49],"seconded":[50],"external":[52],"reviewers.":[53],"complexity":[55,86],"class":[56,105,109,122],"NP":[57],"characterizes":[58],"collection":[60],"of":[61,72,91,94,102,126,140,145,159,167,214],"computational":[62,74],"problems":[63,75,210],"have":[65,88],"efficiently":[66,188],"verifiable":[67],"solutions.":[68],"With":[69],"goal":[71],"classifying":[73],"seem":[77],"lie":[79],"beyond":[80],"NP,":[81],"starting":[82],"1980s":[85],"theorists":[87],"considered":[89],"extensions":[90,128],"notion":[93,158],"efficient":[95,160],"verification":[96,161],"allow":[98],"for":[99],"use":[101],"randomness":[103],"(the":[104,108,121],"MA),":[106],"interaction":[107],"IP),":[110],"possibility":[113],"interact":[115],"with":[116,197],"multiple":[117],"proofs,":[118],"or":[119],"provers":[120,202],"MIP).":[123],"study":[125,152,166],"these":[127],"led":[129],"celebrated":[132],"PCP":[133],"theorem":[134],"its":[136],"applications":[137],"hardness":[139],"approximation":[141],"design":[144],"cryptographic":[146],"protocols.":[147],"In":[148],"this":[149],"work,":[150],"we":[151],"fourth":[154],"modification":[155],"originates":[163],"quantum":[168,215],"entanglement.":[169,204],"We":[170],"prove":[171],"surprising":[173],"every":[176],"problem":[177],"recursively":[180],"enumerable,":[181],"including":[182],"Halting":[184],"problem,":[185],"can":[186],"be":[187],"verified":[189],"classical":[192],"probabilistic":[193],"polynomial-time":[194],"verifier":[195],"interacting":[196],"two":[198],"all-powerful":[199],"but":[200],"noncommunicating":[201],"sharing":[203],"resolves":[207],"long-standing":[208],"open":[209],"foundations":[213],"mechanics":[216],"(Tsirelson's":[217],"problem)":[218],"operator":[220],"algebras":[221],"(Connes'":[222],"embedding":[223],"problem).":[224]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":52},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":54},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":12}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2021-11-08T00:00:00"}