{"id":"https://openalex.org/W3121902900","doi":"https://doi.org/10.13016/lokj-p4fa","title":"THE MEMBERSHIP PROBLEM FOR CONSTANT-SIZED QUANTUM CORRELATIONS IS UNDECIDABLE","display_name":"THE MEMBERSHIP PROBLEM FOR CONSTANT-SIZED QUANTUM CORRELATIONS IS UNDECIDABLE","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3121902900","doi":"https://doi.org/10.13016/lokj-p4fa","mag":"3121902900"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2101.11087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.11087","pdf_url":"https://arxiv.org/pdf/2101.11087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2101.11087","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051880407","display_name":"Honghao Fu","orcid":"https://orcid.org/0000-0002-1934-3391"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Honghao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063535590","display_name":"Carl A. Miller","orcid":"https://orcid.org/0000-0003-1917-1531"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Miller, Carl A.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102809836","display_name":"William Slofstra","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Slofstra, William","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9990000128746033,"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":0.9962999820709229,"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/undecidable-problem","display_name":"Undecidable problem","score":0.9584519267082214},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6100213527679443},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5649012327194214},{"id":"https://openalex.org/keywords/quantum-correlation","display_name":"Quantum correlation","score":0.5511316657066345},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.520167350769043},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.33278417587280273},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33217501640319824},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.3007161021232605},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2885015606880188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2866309881210327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21649014949798584},{"id":"https://openalex.org/keywords/open-quantum-system","display_name":"Open quantum system","score":0.18087291717529297},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.10573247075080872}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.9584519267082214},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6100213527679443},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5649012327194214},{"id":"https://openalex.org/C198377831","wikidata":"https://www.wikidata.org/wiki/Q7269027","display_name":"Quantum correlation","level":5,"score":0.5511316657066345},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.520167350769043},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33278417587280273},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33217501640319824},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.3007161021232605},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2885015606880188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2866309881210327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21649014949798584},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.18087291717529297},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.10573247075080872},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2101.11087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.11087","pdf_url":"https://arxiv.org/pdf/2101.11087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:drum.lib.umd.edu:1903/27361","is_oa":true,"landing_page_url":"http://hdl.handle.net/1903/27361","pdf_url":"http://hdl.handle.net/1903/27361","source":{"id":"https://openalex.org/S4306401518","display_name":"University Libraries (University of Maryland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"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":"Dissertation"},{"id":"doi:10.48550/arxiv.2101.11087","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2101.11087","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.13016/lokj-p4fa","is_oa":true,"landing_page_url":"https://doi.org/10.13016/lokj-p4fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2101.11087","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2101.11087","pdf_url":"https://arxiv.org/pdf/2101.11087","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3121902900.pdf","grobid_xml":"https://content.openalex.org/works/W3121902900.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W16784680","https://openalex.org/W642788305","https://openalex.org/W1541824250","https://openalex.org/W1557734813","https://openalex.org/W1973948469","https://openalex.org/W1975806059","https://openalex.org/W2005261058","https://openalex.org/W2008023303","https://openalex.org/W2012140001","https://openalex.org/W2015926343","https://openalex.org/W2033376433","https://openalex.org/W2043508110","https://openalex.org/W2108732680","https://openalex.org/W2116397277","https://openalex.org/W2128006942","https://openalex.org/W2129072779","https://openalex.org/W2133888859","https://openalex.org/W2135830616","https://openalex.org/W2409179138","https://openalex.org/W2530940551","https://openalex.org/W2796785994","https://openalex.org/W2892870078","https://openalex.org/W2947949186","https://openalex.org/W2950502875","https://openalex.org/W2952228226","https://openalex.org/W2963105196","https://openalex.org/W2963458829","https://openalex.org/W2988028196","https://openalex.org/W2995328993","https://openalex.org/W2999186103","https://openalex.org/W3008650101","https://openalex.org/W3099772093","https://openalex.org/W3101328089","https://openalex.org/W3102951940","https://openalex.org/W3104728484","https://openalex.org/W3104792351","https://openalex.org/W3106278932"],"related_works":["https://openalex.org/W4308697948","https://openalex.org/W2081424146","https://openalex.org/W2528105924","https://openalex.org/W1602699863","https://openalex.org/W1576005355","https://openalex.org/W1969102538","https://openalex.org/W4379209391","https://openalex.org/W2006745775","https://openalex.org/W4300124435","https://openalex.org/W2266217977"],"abstract_inverted_index":{"One":[0],"of":[1,8,20,38,50,58,61,77,104,111,117,136,141,171,187,191,207,217,223,232,245,261,264,282,294,316,330,337,347,366,370,375,379,392,395,397,408],"the":[2,21,39,59,74,85,94,102,109,115,118,129,133,139,142,154,185,188,205,262,266,321,327,334,338,344,356,364,367,376,383,387,390],"most":[3],"fundamental":[4],"and":[5,174,201],"counterintuitive":[6],"features":[7],"quantum":[9,22,25,78,106,151,156,172,192,371,422],"me-":[10],"chanics":[11],"is":[12,15,36,53,67,70,89,167,176,194,237,301,351,359,373,401,421],"entanglement,":[13],"which":[14,69],"central":[16],"to":[17,42,54,127,158,195,311,416],"many":[18],"demonstrations":[19],"advantage.":[23],"Studying":[24],"correlations":[26,137,152,173,193,222,247,308,331,350,372,396],"generated":[27],"by":[28,132,291],"local":[29,283],"measurements":[30],"on":[31,320],"an":[32,258],"entangled":[33,161,215,230,280,314],"physical":[34],"system":[35,157],"one":[37],"direct":[40],"ways":[41],"gain":[43],"insights":[44],"into":[45],"en-":[46],"tanglement.":[47],"The":[48,180],"focus":[49],"this":[51,235,276,299,303,409],"dissertation":[52],"get":[55,196],"better":[56],"understanding":[57],"hardness":[60,95,140,186,365,384],"determining":[62],"if":[63,418],"a":[64,105,163,168,208,213,224,238,278,292,295,398,413,419],"given":[65],"correlation":[66,107,209,293,420],"quantum,":[68],"also":[71],"known":[72,177],"as":[73,178],"membership":[75,87,143,189,244,345,368],"problem":[76,88,190,346,369],"correlations.":[79,380],"Previous":[80],"work":[81],"has":[82,146],"shown":[83,148],"that":[84,149,210,242,255,306,326,343,389,404],"general":[86],"computationally":[90,353],"undecidable.":[91],"Where":[92],"does":[93],"come":[96],"from?":[97],"Is":[98],"it":[99,175],"just":[100],"because":[101],"size":[103,206,226,358,400],"(i.e.,":[108],"number":[110],"real":[112],"values":[113],"in":[114,138,275],"description":[116,407],"correlation)":[119],"can":[120,211,227,248,288,411],"be":[121,159,249,289],"arbitrarily":[122,218],"large?":[123],"We":[124,252],"would":[125],"like":[126],"understand":[128],"role":[130],"played":[131],"varying":[134,328,377],"sizes":[135,329,378],"problem.":[144],"It":[145],"been":[147],"certain":[150,164],"require":[153],"measured":[155],"maximally":[160,214,279,313],"with":[162],"dimension.":[165,220,318],"This":[166],"unique":[169],"phenomenon":[170,236],"self-testing.":[179],"first":[181,253],"step":[182],"towards":[183],"answering":[184],"deeper":[197],"understandings":[198],"about":[199,204],"self-testing,":[200],"more":[202],"specifically,":[203],"self-test":[212,312],"state":[216,281],"large":[219],"If":[221],"fixed":[225,296,348,357],"self-":[228],"test":[229],"states":[231,315],"unbounded":[233,317],"dimension,":[234],"strong":[239],"evidence":[240],"suggesting":[241],"deciding":[243],"fixed-sized":[246],"very":[250],"hard.":[251],"show":[254,325,342],"there":[256],"exists":[257],"infinite":[259],"subset":[260],"set":[263,300,394,410],"all":[265],"prime":[267,273],"numbers":[268],"such":[269],"that,":[270],"for":[271],"each":[272],"p":[274],"set,":[277],"dimension":[284],"(p":[285],"\u2212":[286],"1)":[287],"self-tested":[290],"size.":[297],"Since":[298],"infinite,":[302],"result":[304],"implies":[305],"constant-sized":[307],"are":[309,332],"sufficient":[310],"Building":[319],"self-testing":[322],"result,":[323],"we":[324,341],"not":[333],"only":[335],"root":[336],"hardness.":[339],"Specifically,":[340],"finite-sized":[349],"still":[352],"undecidable":[354],"when":[355],"sufficiently":[360],"large.":[361],"That":[362],"is,":[363],"independent":[374],"In":[381],"fact,":[382],"arises":[385],"from":[386],"fact":[388],"structure":[391],"some":[393],"particular":[399],"so":[402],"complicated":[403],"no":[405],"finite":[406],"allow":[412],"Turing":[414],"machine":[415],"decide":[417],"or":[423],"not.":[424]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
