{"id":"https://openalex.org/W4406167076","doi":"https://doi.org/10.22331/q-2025-01-08-1583","title":"No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords","display_name":"No quantum solutions to linear constraint systems in odd dimension from Pauli group and diagonal Cliffords","publication_year":2025,"publication_date":"2025-01-08","ids":{"openalex":"https://openalex.org/W4406167076","doi":"https://doi.org/10.22331/q-2025-01-08-1583"},"language":"en","primary_location":{"id":"doi:10.22331/q-2025-01-08-1583","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1583","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1583/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-2025-01-08-1583/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029029670","display_name":"Markus Frembs","orcid":"https://orcid.org/0000-0001-6653-4652"},"institutions":[{"id":"https://openalex.org/I11701301","display_name":"Griffith University","ror":"https://ror.org/02sc3r913","country_code":"AU","type":"education","lineage":["https://openalex.org/I11701301"]},{"id":"https://openalex.org/I4210091585","display_name":"Quantum (Australia)","ror":"https://ror.org/00bp6rb10","country_code":"AU","type":"company","lineage":["https://openalex.org/I4210091585"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Markus Frembs","raw_affiliation_strings":["Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, QLD 4222, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, QLD 4222, Australia","institution_ids":["https://openalex.org/I11701301","https://openalex.org/I4210091585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011282980","display_name":"Cihan Okay","orcid":"https://orcid.org/0000-0001-8097-5227"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Cihan Okay","raw_affiliation_strings":["Department of Mathematics, Bilkent University, Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059815173","display_name":"Ho Yiu Chung","orcid":"https://orcid.org/0000-0003-4319-5664"},"institutions":[{"id":"https://openalex.org/I168864056","display_name":"Bilkent University","ror":"https://ror.org/02vh8a032","country_code":"TR","type":"education","lineage":["https://openalex.org/I168864056"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Ho Yiu Chung","raw_affiliation_strings":["Department of Mathematics, Bilkent University, Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bilkent University, Ankara, Turkey","institution_ids":["https://openalex.org/I168864056"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029029670"],"corresponding_institution_ids":["https://openalex.org/I11701301","https://openalex.org/I4210091585"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":2.1251,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.83670087,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"9","issue":null,"first_page":"1583","last_page":"1583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9995999932289124,"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":0.9995999932289124,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.7912485599517822},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7314830422401428},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6677677035331726},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6513031125068665},{"id":"https://openalex.org/keywords/pauli-exclusion-principle","display_name":"Pauli exclusion principle","score":0.5866925716400146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.53582763671875},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5124788284301758},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47828635573387146},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40724316239356995},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4069535732269287},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.33698487281799316},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10902127623558044}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7912485599517822},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7314830422401428},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6677677035331726},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6513031125068665},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.5866925716400146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.53582763671875},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5124788284301758},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47828635573387146},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40724316239356995},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4069535732269287},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33698487281799316},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10902127623558044}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2025-01-08-1583","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1583","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1583/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:doaj.org/article:dd1064c919774caf835363a0a05029db","is_oa":true,"landing_page_url":"https://doaj.org/article/dd1064c919774caf835363a0a05029db","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 9, p 1583 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2025-01-08-1583","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2025-01-08-1583","pdf_url":"https://quantum-journal.org/papers/q-2025-01-08-1583/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/G2034298839","display_name":null,"funder_award_id":"FT180100317","funder_id":"https://openalex.org/F4320306192","funder_display_name":"Silicon Valley Community Foundation"},{"id":"https://openalex.org/G5854263488","display_name":null,"funder_award_id":"FA9550-21-1-0002","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G96397972","display_name":null,"funder_award_id":"FQXi-RFP-1807","funder_id":"https://openalex.org/F4320311357","funder_display_name":"Foundational Questions Institute"}],"funders":[{"id":"https://openalex.org/F4320306192","display_name":"Silicon Valley Community Foundation","ror":"https://ror.org/001ader08"},{"id":"https://openalex.org/F4320306689","display_name":"Fetzer Institute","ror":"https://ror.org/02t1yaf39"},{"id":"https://openalex.org/F4320311357","display_name":"Foundational Questions Institute","ror":"https://ror.org/016en1t86"},{"id":"https://openalex.org/F4320323792","display_name":"Bilkent \u00dcniversitesi","ror":"https://ror.org/02vh8a032"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406167076.pdf","grobid_xml":"https://content.openalex.org/works/W4406167076.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W24440755","https://openalex.org/W1490521149","https://openalex.org/W1569796039","https://openalex.org/W1933312167","https://openalex.org/W1966003503","https://openalex.org/W1969246646","https://openalex.org/W1976554830","https://openalex.org/W1991877988","https://openalex.org/W2007155307","https://openalex.org/W2012760578","https://openalex.org/W2033376433","https://openalex.org/W2052146120","https://openalex.org/W2055874354","https://openalex.org/W2122187744","https://openalex.org/W2151462437","https://openalex.org/W2409179138","https://openalex.org/W2409246750","https://openalex.org/W2483974103","https://openalex.org/W2502748465","https://openalex.org/W2512564998","https://openalex.org/W2798308216","https://openalex.org/W2944733072","https://openalex.org/W2952786109","https://openalex.org/W2963458829","https://openalex.org/W3039749731","https://openalex.org/W3096796582","https://openalex.org/W3100446014","https://openalex.org/W3102418387","https://openalex.org/W3104728484","https://openalex.org/W3105331568","https://openalex.org/W3105574871","https://openalex.org/W3183885798","https://openalex.org/W3209192400","https://openalex.org/W4243055393","https://openalex.org/W4299395000","https://openalex.org/W4313418235","https://openalex.org/W4394672652"],"related_works":["https://openalex.org/W3006983566","https://openalex.org/W2052382920","https://openalex.org/W2024371448","https://openalex.org/W4392297203","https://openalex.org/W2352949123","https://openalex.org/W1611230162","https://openalex.org/W2747066503","https://openalex.org/W1572121409","https://openalex.org/W2951304272","https://openalex.org/W2383259341"],"abstract_inverted_index":{"Linear":[0],"constraint":[1],"systems":[2,37],"(LCS)":[3],"have":[4,69],"proven":[5],"to":[6,36,85,102],"be":[7],"a":[8,106],"surprisingly":[9],"prolific":[10],"tool":[11],"in":[12,22,54,73,108],"the":[13,30,34,74,78,92,95,117],"study":[14],"of":[15,38,88,105,126],"non-classical":[16],"correlations":[17],"and":[18,132],"various":[19],"related":[20],"issues":[21],"quantum":[23,86,103],"foundations.":[24],"Many":[25],"results":[26],"are":[27],"known":[28,49],"for":[29],"Boolean":[31,75],"case,":[32,76],"yet":[33],"generalisation":[35],"odd":[39,55,109],"dimension":[40],"is":[41,47],"largely":[42],"open.":[43],"In":[44,65],"particular,":[45],"it":[46],"not":[48],"whether":[50],"there":[51],"exist":[52],"LCS":[53,89,107],"dimension,":[56],"which":[57],"admit":[58],"finite-dimensional":[59],"quantum,":[60],"but":[61],"no":[62],"classical":[63],"solutions.":[64],"recent":[66],"work,":[67],"\\cite{QassimWallman2020}":[68],"shown":[70],"that":[71],"unlike":[72],"where":[77],"<mml:math":[79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>n</mml:mi></mml:math>-qubit":[80],"Pauli":[81,97,131],"group":[82,98],"gives":[83,100],"rise":[84,101],"solutions":[87,104],"such":[90],"as":[91],"Mermin-Peres":[93],"square,":[94],"n-qudit":[96],"never":[99],"dimension.":[110],"Here,":[111],"we":[112,122],"generalise":[113],"this":[114],"result":[115],"towards":[116],"Clifford":[118,134],"hierarchy.":[119],"More":[120],"precisely,":[121],"consider":[123],"tensor":[124],"products":[125],"groups":[127],"generated":[128],"by":[129],"(single-qudit)":[130],"diagonal":[133],"operators.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}