{"id":"https://openalex.org/W4210940067","doi":"https://doi.org/10.3390/e24020247","title":"A Characterization of Maximally Entangled Two-Qubit States","display_name":"A Characterization of Maximally Entangled Two-Qubit States","publication_year":2022,"publication_date":"2022-02-07","ids":{"openalex":"https://openalex.org/W4210940067","doi":"https://doi.org/10.3390/e24020247","pmid":"https://pubmed.ncbi.nlm.nih.gov/35205540"},"language":"en","primary_location":{"id":"doi:10.3390/e24020247","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020247","pdf_url":"https://www.mdpi.com/1099-4300/24/2/247/pdf?version=1644886315","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/1099-4300/24/2/247/pdf?version=1644886315","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052017764","display_name":"Junjun Duan","orcid":null},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junjun Duan","raw_affiliation_strings":["School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040077842","display_name":"Lin Zhang","orcid":"https://orcid.org/0000-0001-6220-4218"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lin Zhang","raw_affiliation_strings":["School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":"https://orcid.org/0000-0001-6220-4218","affiliations":[{"raw_affiliation_string":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091560903","display_name":"Quan Qian","orcid":"https://orcid.org/0000-0003-0051-7440"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quan Qian","raw_affiliation_strings":["School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087659431","display_name":"Shao-Ming Fei","orcid":"https://orcid.org/0000-0003-2412-8626"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]},{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Shao-Ming Fei","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","School of Mathematical Sciences, Capital Normal University, Beijing 100048, China"],"raw_orcid":"https://orcid.org/0000-0003-2412-8626","affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]},{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing 100048, China","institution_ids":["https://openalex.org/I96852419"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5040077842"],"corresponding_institution_ids":["https://openalex.org/I50760025"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.4645,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67074209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"24","issue":"2","first_page":"247","last_page":"247"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","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/T10020","display_name":"Quantum Information and Cryptography","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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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":0.9995999932289124,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/qubit","display_name":"Qubit","score":0.7307802438735962},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.6453106999397278},{"id":"https://openalex.org/keywords/cluster-state","display_name":"Cluster state","score":0.45612043142318726},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.4552924931049347},{"id":"https://openalex.org/keywords/one-way-quantum-computer","display_name":"One-way quantum computer","score":0.43595874309539795},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4230727553367615},{"id":"https://openalex.org/keywords/w-state","display_name":"W state","score":0.4186600148677826},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33423537015914917},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3258148431777954},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3242955803871155},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.11045652627944946},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.06373301148414612}],"concepts":[{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.7307802438735962},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6453106999397278},{"id":"https://openalex.org/C158456648","wikidata":"https://www.wikidata.org/wiki/Q5136706","display_name":"Cluster state","level":4,"score":0.45612043142318726},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.4552924931049347},{"id":"https://openalex.org/C19271316","wikidata":"https://www.wikidata.org/wiki/Q7092353","display_name":"One-way quantum computer","level":5,"score":0.43595874309539795},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4230727553367615},{"id":"https://openalex.org/C20593774","wikidata":"https://www.wikidata.org/wiki/Q7958522","display_name":"W state","level":4,"score":0.4186600148677826},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33423537015914917},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3258148431777954},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3242955803871155},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.11045652627944946},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.06373301148414612}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e24020247","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020247","pdf_url":"https://www.mdpi.com/1099-4300/24/2/247/pdf?version=1644886315","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:35205540","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35205540","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:2202.03321","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.03321","pdf_url":"https://arxiv.org/pdf/2202.03321","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:fa4f325c26c44c7883e988cbe089b102","is_oa":true,"landing_page_url":"https://doaj.org/article/fa4f325c26c44c7883e988cbe089b102","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 2, p 247 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/2/247/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24020247","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 2; Pages: 247","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8871273","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8871273","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/e24020247","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24020247","pdf_url":"https://www.mdpi.com/1099-4300/24/2/247/pdf?version=1644886315","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/G2693165179","display_name":"\u8054\u5408\u91cf\u5b50\u6d4b\u91cf\u3001\u975e\u7ecf\u5178\u5173\u8054\u53ca\u91cf\u5b50\u4fe1\u606f\u76f8\u5173\u7814\u7a76","funder_award_id":"11971140","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4210940067.pdf"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W87766535","https://openalex.org/W1979369481","https://openalex.org/W2032971769","https://openalex.org/W2034920898","https://openalex.org/W2134984950","https://openalex.org/W2144126354","https://openalex.org/W2328660023","https://openalex.org/W2804172638","https://openalex.org/W2897050953","https://openalex.org/W3020341346","https://openalex.org/W3041649645","https://openalex.org/W3136303371","https://openalex.org/W6603563847"],"related_works":["https://openalex.org/W1981099706","https://openalex.org/W2048020554","https://openalex.org/W2065708769","https://openalex.org/W4399151291","https://openalex.org/W2784205599","https://openalex.org/W1974094588","https://openalex.org/W2376150306","https://openalex.org/W4290740036","https://openalex.org/W2005315265","https://openalex.org/W2019827680"],"abstract_inverted_index":{"As":[0],"already":[1],"known":[2],"by":[3],"Rana's":[4],"result,":[5],"all":[6],"eigenvalues":[7,33],"of":[8,26,34,49,81],"any":[9],"partial-transposed":[10,35,51],"bipartite":[11,27],"state":[12,52,62],"fall":[13],"within":[14],"the":[15,31,46,79,82],"closed":[16],"interval":[17],"[-12,1].":[18],"In":[19],"this":[20,67],"note,":[21],"we":[22,43],"study":[23],"a":[24,40,60,75],"family":[25],"quantum":[28],"states":[29,36],"where":[30],"minimal":[32,47],"are":[37,85],"-12.":[38],"For":[39],"two-qubit":[41,61],"system,":[42],"find":[44],"that":[45],"eigenvalue":[48],"its":[50],"is":[53,63],"-12":[54],"if":[55,58],"and":[56],"only":[57],"such":[59],"maximally":[64],"entangled.":[65],"However":[66],"result":[68],"does":[69],"not":[70],"hold":[71],"in":[72],"general":[73],"for":[74],"two-qudit":[76],"system":[77],"when":[78],"dimensions":[80],"underlying":[83],"space":[84],"larger":[86],"than":[87],"two.":[88]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
