{"id":"https://openalex.org/W4392341514","doi":"https://doi.org/10.22331/q-2026-01-27-1987","title":"A Computational Tsirelson&amp;apos;s Theorem for the Value of Compiled XOR Games","display_name":"A Computational Tsirelson&amp;apos;s Theorem for the Value of Compiled XOR Games","publication_year":2026,"publication_date":"2026-01-27","ids":{"openalex":"https://openalex.org/W4392341514","doi":"https://doi.org/10.22331/q-2026-01-27-1987"},"language":"en","primary_location":{"id":"doi:10.22331/q-2026-01-27-1987","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-01-27-1987","pdf_url":"https://quantum-journal.org/papers/q-2026-01-27-1987/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2026-01-27-1987/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056296606","display_name":"David Cui","orcid":"https://orcid.org/0000-0002-6101-5164"},"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":true,"raw_author_name":"David Cui","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007500399","display_name":"Giulio Malavolta","orcid":"https://orcid.org/0009-0009-9737-0094"},"institutions":[{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giulio Malavolta","raw_affiliation_strings":["Department of Computing Sciences, Bocconi University, 20136 Milano MI, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Computing Sciences, Bocconi University, 20136 Milano MI, Italy","institution_ids":["https://openalex.org/I71209653"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113131190","display_name":"Arthur Mehta","orcid":null},"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"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Arthur Mehta","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023960652","display_name":"Anand Natarajan","orcid":"https://orcid.org/0000-0001-6850-0798"},"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":["Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065585297","display_name":"Connor Paddock","orcid":"https://orcid.org/0000-0002-5742-2795"},"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/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Connor Paddock","raw_affiliation_strings":["Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada","Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON K1N 6N5, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103175989","display_name":"Simon Schmidt","orcid":"https://orcid.org/0000-0002-4863-5318"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Simon Schmidt","raw_affiliation_strings":["Faculty of Computer Science, Ruhr University Bochum, 44801 Bochum, Germany"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Ruhr University Bochum, 44801 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016087422","display_name":"Michael Walter","orcid":"https://orcid.org/0000-0002-3073-1408"},"institutions":[{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]},{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE","NL"],"is_corresponding":false,"raw_author_name":"Michael Walter","raw_affiliation_strings":["Faculty of Computer Science, Ruhr University Bochum, 44801 Bochum, Germany","Faculty of Physics and Faculty of Mathematics, Computer Science and Statistics, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 80539 M\u00fcnchen, Germany","Korteweg-de Vries Institute for Mathematics and QuSoft, University of Amsterdam, 1012 WP Amsterdam, Netherlands"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Ruhr University Bochum, 44801 Bochum, Germany","institution_ids":["https://openalex.org/I904495901"]},{"raw_affiliation_string":"Faculty of Physics and Faculty of Mathematics, Computer Science and Statistics, Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, 80539 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I8204097"]},{"raw_affiliation_string":"Korteweg-de Vries Institute for Mathematics and QuSoft, University of Amsterdam, 1012 WP Amsterdam, Netherlands","institution_ids":["https://openalex.org/I4210099082"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108825718","display_name":"Tina Zhang","orcid":"https://orcid.org/0000-0002-7229-6686"},"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":"Tina Zhang","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, United States","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5056296606"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00106464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"10","issue":null,"first_page":"1987","last_page":"1987"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11574","display_name":"Artificial Intelligence in Games","score":0.9847999811172485,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.9847999811172485,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.9739999771118164,"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":0.9682000279426575,"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/mathematical-economics","display_name":"Mathematical economics","score":0.5995734930038452},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5859826803207397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4875201880931854},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3316619396209717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3202623724937439},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15034624934196472}],"concepts":[{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5995734930038452},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5859826803207397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4875201880931854},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3316619396209717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3202623724937439},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15034624934196472},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2026-01-27-1987","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-01-27-1987","pdf_url":"https://quantum-journal.org/papers/q-2026-01-27-1987/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:2402.17301","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2402.17301","pdf_url":"https://arxiv.org/pdf/2402.17301","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":"","raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2402.17301","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:7e9c7b68768c4fc994fcd8fe7eb524e9","is_oa":true,"landing_page_url":"https://doaj.org/article/7e9c7b68768c4fc994fcd8fe7eb524e9","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 10, p 1987 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2402.17301","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2402.17301","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2026-01-27-1987","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-01-27-1987","pdf_url":"https://quantum-journal.org/papers/q-2026-01-27-1987/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/G1681793210","display_name":null,"funder_award_id":"KLEIN","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G18682879","display_name":null,"funder_award_id":"390781972","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"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/G4158264079","display_name":null,"funder_award_id":"17173","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5365867299","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5717916917","display_name":null,"funder_award_id":"39078197","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6955755495","display_name":null,"funder_award_id":"Germany","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"},{"id":"https://openalex.org/G6997071033","display_name":null,"funder_award_id":"10104","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7164833740","display_name":"Taming tensors: An optimization approach to computational invariant theory","funder_award_id":"OCENW.KLEIN.267","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4392341514.pdf","grobid_xml":"https://content.openalex.org/works/W4392341514.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Nonlocal":[0],"games":[1],"are":[2],"a":[3,41,45,87,109,118,169],"foundational":[4],"tool":[5],"for":[6,65,77,103,130,162,173],"understanding":[7],"entanglement":[8],"and":[9,44,90,123,167],"constructing":[10],"quantum":[11,19,49,81],"protocols":[12],"in":[13],"settings":[14],"with":[15],"multiple":[16],"spatially":[17],"separated":[18],"devices.":[20],"In":[21],"this":[22],"work,":[23],"we":[24,91,141],"continue":[25],"the":[26,56,80,98,104,114,131,135,151],"study":[27],"initiated":[28],"by":[29,59,86,95,121],"Kalai":[30,60],"et":[31,61],"al.":[32,62],"(STOC":[33],"&amp;apos;23)":[34],"of":[35,73,134,154],"compiled":[36,105,152,164],"nonlocal":[37],"games,":[38,79,157],"played":[39],"between":[40],"classical":[42],"verifier":[43],"single":[46],"cryptographically":[47],"limited":[48],"device.":[50],"Our":[51],"main":[52],"result":[53,94],"is":[54,63,83,181],"that":[55,76,97],"compiler":[57],"proposed":[58],"sound":[64],"any":[66,163,174],"two-player":[67],"XOR":[68,78,156,165,175],"game.":[69,137],"A":[70],"celebrated":[71],"theorem":[72],"Tsirelson":[74],"shows":[75],"value":[82,153],"exactly":[84],"given":[85],"semidefinite":[88],"program,":[89],"obtain":[92,142],"our":[93,139],"showing":[96],"SDP":[99],"upper":[100],"bound":[101],"holds":[102],"game":[106],"up":[107],"to":[108],"negligible":[110],"error":[111],"arising":[112],"from":[113,177],"compilation.":[115],"This":[116],"answers":[117],"question":[119],"raised":[120],"Natarajan":[122],"Zhang":[124],"(FOCS":[125],"&amp;apos;23),":[126],"who":[127],"showed":[128],"soundness":[129],"specific":[132],"case":[133],"CHSH":[136],"Using":[138],"techniques,":[140],"several":[143],"additional":[144],"results,":[145],"including":[146],"(1)":[147],"tight":[148],"bounds":[149],"on":[150],"parallel-repeated":[155],"(2)":[158],"operator":[159,179],"self-testing":[160],"statements":[161],"game,":[166,176],"(3)":[168],"\u201cnice&amp;apos;&amp;apos;":[170],"sum-of-squares":[171],"certificate":[172],"which":[178],"rigidity":[180],"manifest.":[182]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2024-03-05T00:00:00"}
