{"id":"https://openalex.org/W4293756338","doi":"https://doi.org/10.1137/21m140729x","title":"QMA-Hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge","display_name":"QMA-Hardness of Consistency of Local Density Matrices with Applications to Quantum Zero-Knowledge","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4293756338","doi":"https://doi.org/10.1137/21m140729x"},"language":"en","primary_location":{"id":"doi:10.1137/21m140729x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m140729x","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Anne Broadbent","raw_affiliation_strings":["University of Ottawa [Ottawa] (75 Laurier Avenue East, Ottawa, ON K1N 6N5 - Canada)"],"affiliations":[{"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":"last","author":{"id":"https://openalex.org/A5090313356","display_name":"Alex B. Grilo","orcid":"https://orcid.org/0000-0001-7374-7082"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alex Bredariol Grilo","raw_affiliation_strings":["QI - Information Quantique [LIP6] (France)"],"affiliations":[{"raw_affiliation_string":"QI - Information Quantique [LIP6] (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034032202"],"corresponding_institution_ids":["https://openalex.org/I153718931","https://openalex.org/I75381157"],"apc_list":null,"apc_paid":null,"fwci":1.7936,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87259031,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"51","issue":"4","first_page":"1400","last_page":"1450"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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/T10237","display_name":"Cryptography and Data Security","score":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9987999796867371,"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/T10270","display_name":"Blockchain Technology Applications and Security","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/zero-knowledge-proof","display_name":"Zero-knowledge proof","score":0.6635550260543823},{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.6500254273414612},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5889750123023987},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4861616790294647},{"id":"https://openalex.org/keywords/quantum-complexity-theory","display_name":"Quantum complexity theory","score":0.47010868787765503},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4554545283317566},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4455111622810364},{"id":"https://openalex.org/keywords/quantum-computer","display_name":"Quantum computer","score":0.4431869089603424},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4286026060581207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37541303038597107},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22927305102348328},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1210947334766388}],"concepts":[{"id":"https://openalex.org/C176329583","wikidata":"https://www.wikidata.org/wiki/Q191943","display_name":"Zero-knowledge proof","level":3,"score":0.6635550260543823},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.6500254273414612},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5889750123023987},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4861616790294647},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.47010868787765503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4554545283317566},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4455111622810364},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4431869089603424},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4286026060581207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37541303038597107},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22927305102348328},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1210947334766388},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m140729x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m140729x","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03773541v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03773541","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Computing, 2022, 51 (4), pp.1400-1450. ⟨10.1137/21M140729X⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6399999856948853,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W150248338","https://openalex.org/W1484557542","https://openalex.org/W1539572409","https://openalex.org/W1556171410","https://openalex.org/W1565012603","https://openalex.org/W1565801357","https://openalex.org/W1572495953","https://openalex.org/W1589034595","https://openalex.org/W1593955619","https://openalex.org/W1601001795","https://openalex.org/W1667728213","https://openalex.org/W1828812675","https://openalex.org/W1970606468","https://openalex.org/W1989051052","https://openalex.org/W1999502904","https://openalex.org/W2011039300","https://openalex.org/W2011112377","https://openalex.org/W2026979651","https://openalex.org/W2027471022","https://openalex.org/W2038517014","https://openalex.org/W2039072244","https://openalex.org/W2043007983","https://openalex.org/W2064263748","https://openalex.org/W2070421562","https://openalex.org/W2079913403","https://openalex.org/W2080578129","https://openalex.org/W2083019346","https://openalex.org/W2084019889","https://openalex.org/W2100827027","https://openalex.org/W2102632861","https://openalex.org/W2115105645","https://openalex.org/W2115354090","https://openalex.org/W2129261735","https://openalex.org/W2131575873","https://openalex.org/W2153671025","https://openalex.org/W2159924820","https://openalex.org/W2172643090","https://openalex.org/W2179731956","https://openalex.org/W2193371463","https://openalex.org/W2210183803","https://openalex.org/W2252150191","https://openalex.org/W2291524553","https://openalex.org/W2297990348","https://openalex.org/W2308553311","https://openalex.org/W2341328795","https://openalex.org/W2401610261","https://openalex.org/W2764347725","https://openalex.org/W2792324887","https://openalex.org/W2895657145","https://openalex.org/W2898776076","https://openalex.org/W2913430283","https://openalex.org/W2913761579","https://openalex.org/W2917473520","https://openalex.org/W2951183775","https://openalex.org/W2952170582","https://openalex.org/W2952228226","https://openalex.org/W2953217285","https://openalex.org/W2953790121","https://openalex.org/W2954045836","https://openalex.org/W2962977579","https://openalex.org/W2962997396","https://openalex.org/W2963124215","https://openalex.org/W2968094846","https://openalex.org/W2970305865","https://openalex.org/W2990348468","https://openalex.org/W2994531541","https://openalex.org/W3010534979","https://openalex.org/W3011699807","https://openalex.org/W3081357568","https://openalex.org/W3098258437","https://openalex.org/W3104165767","https://openalex.org/W3104729002","https://openalex.org/W3104805189","https://openalex.org/W3105421460","https://openalex.org/W3106278932","https://openalex.org/W3128541474","https://openalex.org/W4288332230"],"related_works":["https://openalex.org/W1970588133","https://openalex.org/W2022025391","https://openalex.org/W2163538620","https://openalex.org/W1567449721","https://openalex.org/W1546864018","https://openalex.org/W2951363717","https://openalex.org/W2134613344","https://openalex.org/W2158634152","https://openalex.org/W2915900549","https://openalex.org/W1971258940"],"abstract_inverted_index":{"We":[0,129,232,256],"provide":[1],"several":[2,224],"advances":[3,225],"to":[4,157,164,301],"the":[5,8,16,30,61,79,92,134,158,197,217,229,235,313],"understanding":[6],"of":[7,10,19,32,45,48,55,78,86,103,136,139,146,160,167,201,205,216,246,252,261,273],"class":[9],"quantum":[11,17,70,230,250,262,275,307],"Merlin--Arthur":[12],"(QMA)":[13],"proof":[14,242,260,280,286,296,310],"systems,":[15],"analogue":[18,251],"NP.":[20],"Our":[21],"central":[22],"contribution":[23],"is":[24,38,66,73,113,119,269],"proving":[25],"a":[26,171,238,249,253,259,267,274,306],"longstanding":[27],"conjecture":[28],"that":[29,72,111,173,185,266,283,294,303],"consistency":[31],"local":[33,49,81],"density":[34,51,82,199],"matrices":[35,52],"(CLDM)":[36],"problem":[37,62,88],"QMA-hard":[39,114],"under":[40,94,115],"Karp":[41,116],"reductions.":[42],"The":[43,84],"input":[44],"CLDM":[46,112],"consists":[47],"reduced":[50,198],"on":[53],"sets":[54],"at":[56],"most":[57],"$k$":[58,193],"qubits,":[59],"and":[60,91,123,142,154,281],"asks":[63],"if":[64],"there":[65],"an":[67,206,278],"$n$-qubit":[68],"global":[69],"state":[71],"locally":[74,176],"consistent":[75],"with":[76],"all":[77,245],"$k$-qubit":[80,203],"matrices.":[83],"containment":[85],"this":[87,127,131,181,220,289],"in":[89,212,226,228,271,277,312],"QMA":[90,183,304],"QMA-hardness":[93],"Turing":[95],"reductions":[96],"were":[97],"proved":[98],"by":[99,190],"Liu":[100,108],"[in":[101,144],"Proceeding":[102,145],"APPROX-RANDOM,":[104],"2006,":[105],"pp.":[106,149],"438--449].":[107],"also":[109],"conjectured":[110],"reductions,":[117],"which":[118,264],"desirable":[120],"for":[121,179,234,244],"applications,":[122],"we":[124,169,174,222,292],"finally":[125],"prove":[126],"conjecture.":[128],"establish":[130,302],"result":[132],"using":[133],"techniques":[135],"simulatable":[137,177],"codes":[138],"Grilo,":[140],"Slofstra,":[141],"Yuen":[143],"FOCS,":[147],"2019,":[148],"611--635],":[150],"simplifying":[151],"their":[152],"proofs":[153,178,184],"tailoring":[155],"them":[156],"context":[159],"QMA.":[161],"In":[162],"order":[163],"develop":[165],"applications":[166],"CLDM,":[168],"propose":[170],"framework":[172],"call":[175],"QMA:":[180],"provides":[182],"can":[186,209,298],"be":[187,210,299],"efficiently":[188],"verified":[189],"probing":[191],"only":[192],"qubits":[194],"and,":[195],"furthermore,":[196],"matrix":[200],"any":[202],"subsystem":[204],"accepting":[207],"witness":[208,276],"computed":[211],"polynomial":[213],"time,":[214],"independently":[215],"witness.":[218],"Within":[219],"framework,":[221],"show":[223,233,282,293],"zero-knowledge":[227,241,285,309],"setting.":[231,316],"first":[236],"time":[237],"commit-and-open":[239],"computational":[240],"system":[243,287,297,311],"QMA,":[247],"as":[248],"\u201csigma\u201d":[254],"protocol.":[255],"then":[257],"define":[258],"knowledge,":[263],"guarantees":[265],"prover":[268],"effectively":[270],"possession":[272],"interactive":[279],"our":[284,295],"satisfies":[288],"definition.":[290],"Finally,":[291],"used":[300],"has":[305],"noninteractive":[308],"secret":[314],"parameter":[315]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}