{"id":"https://openalex.org/W4289524281","doi":"https://doi.org/10.3390/e24081064","title":"Separability Criteria Based on the Weyl Operators","display_name":"Separability Criteria Based on the Weyl Operators","publication_year":2022,"publication_date":"2022-08-02","ids":{"openalex":"https://openalex.org/W4289524281","doi":"https://doi.org/10.3390/e24081064","pmid":"https://pubmed.ncbi.nlm.nih.gov/36010728"},"language":"en","primary_location":{"id":"doi:10.3390/e24081064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081064","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1064/pdf?version=1659430216","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":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/8/1064/pdf?version=1659430216","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034868367","display_name":"Xiaofen Huang","orcid":"https://orcid.org/0000-0003-0942-5921"},"institutions":[{"id":"https://openalex.org/I152033890","display_name":"Hainan Normal University","ror":"https://ror.org/031dhcv14","country_code":"CN","type":"education","lineage":["https://openalex.org/I152033890"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaofen Huang","raw_affiliation_strings":["Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, China","School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, China","institution_ids":["https://openalex.org/I152033890"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China","institution_ids":["https://openalex.org/I152033890"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041120070","display_name":"Tinggui Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I152033890","display_name":"Hainan Normal University","ror":"https://ror.org/031dhcv14","country_code":"CN","type":"education","lineage":["https://openalex.org/I152033890"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tinggui Zhang","raw_affiliation_strings":["Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, China","School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Data Science and Smart Education, Ministry of Education, Hainan Normal University, Haikou 571158, China","institution_ids":["https://openalex.org/I152033890"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China","institution_ids":["https://openalex.org/I152033890"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083106050","display_name":"Ming\u2010Jing Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ming-Jing Zhao","raw_affiliation_strings":["School of Science, Beijing Information Science and Technology University, Beijing 100192, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Beijing Information Science and Technology University, Beijing 100192, China","institution_ids":["https://openalex.org/I78675632"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027271530","display_name":"Naihuan Jing","orcid":"https://orcid.org/0000-0002-2156-2569"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Naihuan Jing","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA","Department of Mathematics, Shanghai University, Shanghai 200444, China"],"raw_orcid":"https://orcid.org/0000-0002-2156-2569","affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai 200444, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041120070"],"corresponding_institution_ids":["https://openalex.org/I152033890"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2777,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62536254,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"24","issue":"8","first_page":"1064","last_page":"1064"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":1.0,"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/T10020","display_name":"Quantum Information and Cryptography","score":1.0,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9991000294685364,"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/T11414","display_name":"Quantum optics and atomic interactions","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.8175231218338013},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5831198692321777},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5793569087982178},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5061871409416199},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.4714183509349823},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4470392167568207},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4283018112182617},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3784066140651703},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3609854280948639},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2689061760902405},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2519378662109375}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.8175231218338013},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5831198692321777},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5793569087982178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5061871409416199},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4714183509349823},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4470392167568207},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4283018112182617},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3784066140651703},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3609854280948639},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2689061760902405},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2519378662109375},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e24081064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081064","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1064/pdf?version=1659430216","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:36010728","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36010728","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:arXiv.org:2208.04789","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2208.04789","pdf_url":"https://arxiv.org/pdf/2208.04789","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":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:a58e6a79c4444b69b971964e1fd4ff5a","is_oa":true,"landing_page_url":"https://doaj.org/article/a58e6a79c4444b69b971964e1fd4ff5a","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 24, Iss 8, p 1064 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/8/1064/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24081064","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; Volume 24; Issue 8; Pages: 1064","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9407106","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9407106","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.3390/e24081064","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081064","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1064/pdf?version=1659430216","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/G173642446","display_name":null,"funder_award_id":"12126314","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3577722885","display_name":null,"funder_award_id":"12126351","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7206151321","display_name":null,"funder_award_id":"12171044","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7339724017","display_name":null,"funder_award_id":"12061029","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8091462602","display_name":null,"funder_award_id":"11861031","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/W4289524281.pdf","grobid_xml":"https://content.openalex.org/works/W4289524281.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W1486543895","https://openalex.org/W1519530038","https://openalex.org/W1589119750","https://openalex.org/W1963952399","https://openalex.org/W1978553093","https://openalex.org/W1981815566","https://openalex.org/W1983045379","https://openalex.org/W1983058105","https://openalex.org/W1997678118","https://openalex.org/W2016409581","https://openalex.org/W2020725861","https://openalex.org/W2025990522","https://openalex.org/W2028549339","https://openalex.org/W2034920898","https://openalex.org/W2051051926","https://openalex.org/W2058183617","https://openalex.org/W2060887031","https://openalex.org/W2061421380","https://openalex.org/W2066766456","https://openalex.org/W2072108220","https://openalex.org/W2074848738","https://openalex.org/W2081744538","https://openalex.org/W2090831313","https://openalex.org/W2093508461","https://openalex.org/W2144126354","https://openalex.org/W2148576428","https://openalex.org/W2404301959","https://openalex.org/W2473272119","https://openalex.org/W2486050317","https://openalex.org/W2764347725","https://openalex.org/W2794648121","https://openalex.org/W2952721131","https://openalex.org/W2963083276","https://openalex.org/W3002609932","https://openalex.org/W3099305558","https://openalex.org/W3099973342","https://openalex.org/W3101129372","https://openalex.org/W3101325319","https://openalex.org/W3105751024","https://openalex.org/W3122850579","https://openalex.org/W4211081440","https://openalex.org/W4220851483","https://openalex.org/W4229457787","https://openalex.org/W6631222095","https://openalex.org/W6811472462"],"related_works":["https://openalex.org/W2258058860","https://openalex.org/W2065830994","https://openalex.org/W2092555887","https://openalex.org/W1964921276","https://openalex.org/W2741523612","https://openalex.org/W2102682197","https://openalex.org/W2101135880","https://openalex.org/W2135584473","https://openalex.org/W2071709897","https://openalex.org/W2939685112"],"abstract_inverted_index":{"Entanglement":[0],"as":[1],"a":[2,25],"vital":[3],"resource":[4],"for":[5,65,87],"information":[6],"processing":[7],"can":[8],"be":[9],"described":[10],"by":[11],"special":[12],"properties":[13],"of":[14,29,47],"the":[15,19,30,48,52,58,66,79],"quantum":[16,31,88],"state.":[17],"Using":[18],"well-known":[20],"Weyl":[21,80],"basis":[22],"we":[23],"propose":[24],"new":[26],"Bloch":[27],"decomposition":[28,39],"state":[32],"and":[33,71],"study":[34],"its":[35],"separability":[36,49],"problem.":[37],"This":[38],"enables":[40],"us":[41],"to":[42,82],"find":[43],"an":[44,84],"alternative":[45],"characterization":[46],"based":[50],"on":[51],"correlation":[53],"matrix.":[54],"We":[55,76],"show":[56],"that":[57],"criterion":[59],"is":[60],"effective":[61],"in":[62],"detecting":[63,85],"entanglement":[64],"isotropic":[67],"states,":[68],"Bell-diagonal":[69],"states":[70],"some":[72],"PPT":[73],"entangled":[74],"states.":[75],"also":[77],"use":[78],"operators":[81],"construct":[83],"operator":[86],"teleportation.":[89]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}