{"id":"https://openalex.org/W4319027742","doi":"https://doi.org/10.3390/e25020273","title":"Two Types of Trilocality of Probability and Correlation Tensors","display_name":"Two Types of Trilocality of Probability and Correlation Tensors","publication_year":2023,"publication_date":"2023-02-01","ids":{"openalex":"https://openalex.org/W4319027742","doi":"https://doi.org/10.3390/e25020273","pmid":"https://pubmed.ncbi.nlm.nih.gov/36832638"},"language":"en","primary_location":{"id":"doi:10.3390/e25020273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25020273","pdf_url":"https://www.mdpi.com/1099-4300/25/2/273/pdf?version=1675991201","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/25/2/273/pdf?version=1675991201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104104272","display_name":"Shu Xiao","orcid":null},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shu Xiao","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000025783","display_name":"Huaixin Cao","orcid":"https://orcid.org/0000-0002-2141-825X"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Huaixin Cao","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China"],"raw_orcid":"https://orcid.org/0000-0002-2141-825X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071304677","display_name":"Zhihua Guo","orcid":"https://orcid.org/0000-0002-2631-4919"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhihua Guo","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China","institution_ids":["https://openalex.org/I88830068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080172028","display_name":"Kanyuan Han","orcid":null},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kanyuan Han","raw_affiliation_strings":["School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an 710119, China","institution_ids":["https://openalex.org/I88830068"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000025783","https://openalex.org/A5071304677"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.6182,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.5807601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"25","issue":"2","first_page":"273","last_page":"273"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9821000099182129,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9603999853134155,"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/mathematics","display_name":"Mathematics","score":0.7788747549057007},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6706365346908569},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.5611037015914917},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5210311412811279},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4754497706890106},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.4465567171573639},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.4457719922065735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40237101912498474},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22437477111816406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22002065181732178},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08105868101119995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7788747549057007},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6706365346908569},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.5611037015914917},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5210311412811279},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4754497706890106},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.4465567171573639},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4457719922065735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40237101912498474},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22437477111816406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22002065181732178},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08105868101119995},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e25020273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25020273","pdf_url":"https://www.mdpi.com/1099-4300/25/2/273/pdf?version=1675991201","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:36832638","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36832638","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:9955690","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9955690","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC9955690/pdf/entropy-25-00273.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:e08f7ce24a9b4cc08b10cb7dc1c0872a","is_oa":true,"landing_page_url":"https://doaj.org/article/e08f7ce24a9b4cc08b10cb7dc1c0872a","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":"Entropy, Vol 25, Iss 2, p 273 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/25/2/273/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e25020273","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e25020273","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e25020273","pdf_url":"https://www.mdpi.com/1099-4300/25/2/273/pdf?version=1675991201","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1913030296","display_name":null,"funder_award_id":"12271325","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5576908386","display_name":null,"funder_award_id":"11871318","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4319027742.pdf","grobid_xml":"https://content.openalex.org/works/W4319027742.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1616015000","https://openalex.org/W1978553093","https://openalex.org/W1999854952","https://openalex.org/W2000157180","https://openalex.org/W2006670559","https://openalex.org/W2028965768","https://openalex.org/W2074573782","https://openalex.org/W2086947442","https://openalex.org/W2132764286","https://openalex.org/W2135830616","https://openalex.org/W2143891888","https://openalex.org/W2163464259","https://openalex.org/W2514258805","https://openalex.org/W2569675513","https://openalex.org/W2755176521","https://openalex.org/W2761908798","https://openalex.org/W2892957355","https://openalex.org/W2897264299","https://openalex.org/W2944528888","https://openalex.org/W2949106161","https://openalex.org/W2968047580","https://openalex.org/W3004967896","https://openalex.org/W3004998874","https://openalex.org/W3006125226","https://openalex.org/W3014204504","https://openalex.org/W3025109711","https://openalex.org/W3035661937","https://openalex.org/W3038000163","https://openalex.org/W3038067977","https://openalex.org/W3099619715","https://openalex.org/W3102213319","https://openalex.org/W3106526257","https://openalex.org/W3112239143","https://openalex.org/W3138890484","https://openalex.org/W4205334819","https://openalex.org/W4210830352","https://openalex.org/W4224286739","https://openalex.org/W4302423442","https://openalex.org/W6763895341"],"related_works":["https://openalex.org/W2164571009","https://openalex.org/W1978042415","https://openalex.org/W783893852","https://openalex.org/W3103693455","https://openalex.org/W3205718857","https://openalex.org/W1580435510","https://openalex.org/W1971514761","https://openalex.org/W1985684185","https://openalex.org/W3142700197","https://openalex.org/W2112972328"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"we":[3],"discuss":[4],"two":[5],"types":[6],"of":[7,9,105,130,147,151],"trilocality":[8],"probability":[10],"tensors":[11,21],"(PTs)":[12],"P=\u301aP(a1a2a3)\u301b":[13],"over":[14,24],"an":[15,25],"outcome":[16],"set":[17,27,104],"\u03a93":[18],"and":[19,34,39,47,82,98,119,153,158,166],"correlation":[20],"(CTs)":[22],"P=\u301aP(a1a2a3|x1x2x3)\u301b":[23],"outcome-input":[26],"\u03943":[28],"based":[29],"on":[30],"a":[31,52,67,75,90,99,103,112,127,136,142],"triangle":[32,91],"network":[33,92],"described":[35,65],"by":[36,66,93],"continuous":[37],"(integral)":[38],"discrete":[40],"(sum)":[41],"trilocal":[42],"hidden":[43],"variable":[44],"models":[45],"(C-triLHVMs":[46],"D-triLHVMs).":[48],"We":[49],"say":[50],"that":[51,74],"PT":[53,76,140],"(or":[54],"CT)":[55,78],"P":[56],"is":[57,72,79,114],"C-trilocal":[58,115,137,152,157],"(resp.":[59,69,77,102,116,138,156],"D-trilocal)":[60,117,139],"if":[61,81,84,118,121],"it":[62,85,122],"can":[63,86,123],"be":[64,87,124],"C-triLHVM":[68],"D-triLHVM).":[70],"It":[71],"proved":[73],"D-trilocal":[80,154,159],"only":[83,120],"realized":[88],"in":[89],"three":[94],"shared":[95],"separable":[96],"states":[97],"local":[100,106],"POVM":[101],"POVMs)":[107],"performed":[108],"at":[109],"each":[110],"node;":[111],"CT":[113],"written":[125],"as":[126,141],"convex":[128],"combination":[129],"the":[131,148],"product":[132],"deterministic":[133],"CTs":[134],"with":[135],"coefficient":[143],"tensor.":[144],"Some":[145],"properties":[146],"sets":[149],"consisting":[150],"PTs":[155],"CTs)":[160],"are":[161],"proved,":[162],"including":[163],"their":[164],"path-connectedness":[165],"partial":[167],"star-convexity.":[168]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}