{"id":"https://openalex.org/W4402761170","doi":"https://doi.org/10.3390/e26090804","title":"Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States","display_name":"Robustness of Entanglement for Dicke-W and Greenberger-Horne-Zeilinger Mixed States","publication_year":2024,"publication_date":"2024-09-21","ids":{"openalex":"https://openalex.org/W4402761170","doi":"https://doi.org/10.3390/e26090804","pmid":"https://pubmed.ncbi.nlm.nih.gov/39330137"},"language":"en","primary_location":{"id":"doi:10.3390/e26090804","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090804","pdf_url":"https://www.mdpi.com/1099-4300/26/9/804/pdf","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/1099-4300/26/9/804/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113397629","display_name":"Ling-Hui Zhu","orcid":null},"institutions":[{"id":"https://openalex.org/I4400573310","display_name":"Hangzhou City University","ror":"https://ror.org/01wck0s05","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573310"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ling-Hui Zhu","raw_affiliation_strings":["School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China","institution_ids":["https://openalex.org/I4400573310"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100297954","display_name":"Zhu Zhen","orcid":null},"institutions":[{"id":"https://openalex.org/I4400573310","display_name":"Hangzhou City University","ror":"https://ror.org/01wck0s05","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573310"]},{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen Zhu","raw_affiliation_strings":["College of Information Engineering, Zhejiang University of Technology, Hangzhou 310014, China","School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Engineering, Zhejiang University of Technology, Hangzhou 310014, China","institution_ids":["https://openalex.org/I55712492"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China","institution_ids":["https://openalex.org/I4400573310"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109684335","display_name":"Guo-Lin Lv","orcid":null},"institutions":[{"id":"https://openalex.org/I4400573310","display_name":"Hangzhou City University","ror":"https://ror.org/01wck0s05","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573310"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guo-Lin Lv","raw_affiliation_strings":["College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310027, China","School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science & Electronic Engineering, Zhejiang University, Hangzhou 310027, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China","institution_ids":["https://openalex.org/I4400573310"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075111243","display_name":"Chong\u2010Qiang Ye","orcid":"https://orcid.org/0000-0003-0282-1155"},"institutions":[{"id":"https://openalex.org/I4400573310","display_name":"Hangzhou City University","ror":"https://ror.org/01wck0s05","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573310"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chong-Qiang Ye","raw_affiliation_strings":["School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China","institution_ids":["https://openalex.org/I4400573310"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100386496","display_name":"Xiaoyu Chen","orcid":"https://orcid.org/0000-0002-8576-1751"},"institutions":[{"id":"https://openalex.org/I4400573310","display_name":"Hangzhou City University","ror":"https://ror.org/01wck0s05","country_code":null,"type":"education","lineage":["https://openalex.org/I4400573310"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Yu Chen","raw_affiliation_strings":["School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China"],"raw_orcid":"https://orcid.org/0000-0002-8576-1751","affiliations":[{"raw_affiliation_string":"School of Information and Electrical Engineering, Hangzhou City University, Hangzhou 310015, China","institution_ids":["https://openalex.org/I4400573310"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13657887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"9","first_page":"804","last_page":"804"},"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":0.9994999766349792,"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":0.9994000196456909,"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":0.914269745349884},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6811545491218567},{"id":"https://openalex.org/keywords/entanglement-witness","display_name":"Entanglement witness","score":0.6184248924255371},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5995778441429138},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.5793476104736328},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4914332628250122},{"id":"https://openalex.org/keywords/squashed-entanglement","display_name":"Squashed entanglement","score":0.46739017963409424},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.45255860686302185},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.44423890113830566},{"id":"https://openalex.org/keywords/multipartite-entanglement","display_name":"Multipartite entanglement","score":0.4303876757621765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26897650957107544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11703532934188843}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.914269745349884},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6811545491218567},{"id":"https://openalex.org/C206003972","wikidata":"https://www.wikidata.org/wiki/Q5380097","display_name":"Entanglement witness","level":5,"score":0.6184248924255371},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5995778441429138},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.5793476104736328},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4914332628250122},{"id":"https://openalex.org/C32270708","wikidata":"https://www.wikidata.org/wiki/Q7582152","display_name":"Squashed entanglement","level":4,"score":0.46739017963409424},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45255860686302185},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.44423890113830566},{"id":"https://openalex.org/C71799126","wikidata":"https://www.wikidata.org/wiki/Q6934832","display_name":"Multipartite entanglement","level":5,"score":0.4303876757621765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26897650957107544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11703532934188843},{"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},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26090804","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090804","pdf_url":"https://www.mdpi.com/1099-4300/26/9/804/pdf","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:39330137","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39330137","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:11431323","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11431323","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11431323/pdf/entropy-26-00804.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:d6e7293d2d4e4c4cb11d4833dc5145d7","is_oa":false,"landing_page_url":"https://doaj.org/article/d6e7293d2d4e4c4cb11d4833dc5145d7","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 9, p 804 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26090804","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26090804","pdf_url":"https://www.mdpi.com/1099-4300/26/9/804/pdf","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/G156402513","display_name":"\u8fde\u7eed\u53d8\u91cf\u91cf\u5b50\u76f8\u5e72\u6027\u7814\u7a76","funder_award_id":"61871347","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/W4402761170.pdf","grobid_xml":"https://content.openalex.org/works/W4402761170.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W1519530038","https://openalex.org/W1559409009","https://openalex.org/W1607705556","https://openalex.org/W1623920228","https://openalex.org/W1963952399","https://openalex.org/W1975854896","https://openalex.org/W1978553093","https://openalex.org/W1984004232","https://openalex.org/W2017154611","https://openalex.org/W2017352994","https://openalex.org/W2019004690","https://openalex.org/W2023306990","https://openalex.org/W2039161940","https://openalex.org/W2051618454","https://openalex.org/W2058226548","https://openalex.org/W2060887031","https://openalex.org/W2062258079","https://openalex.org/W2062292260","https://openalex.org/W2063693490","https://openalex.org/W2067448156","https://openalex.org/W2072232105","https://openalex.org/W2088324731","https://openalex.org/W2094271988","https://openalex.org/W2103713333","https://openalex.org/W2132909821","https://openalex.org/W2144126354","https://openalex.org/W2406368573","https://openalex.org/W2413270780","https://openalex.org/W2613778173","https://openalex.org/W2614264617","https://openalex.org/W2809121551","https://openalex.org/W2886612138","https://openalex.org/W3000501171","https://openalex.org/W3002433437","https://openalex.org/W3037737784","https://openalex.org/W3038000163","https://openalex.org/W3102972224","https://openalex.org/W3111899370","https://openalex.org/W3137595724","https://openalex.org/W4376126806","https://openalex.org/W6631222095"],"related_works":["https://openalex.org/W2051172288","https://openalex.org/W2090456009","https://openalex.org/W4298151829","https://openalex.org/W2163823377","https://openalex.org/W4394656853","https://openalex.org/W1670210972","https://openalex.org/W2949206259","https://openalex.org/W2075028353","https://openalex.org/W2154907676","https://openalex.org/W3037985932"],"abstract_inverted_index":{"Quantum":[0],"entanglement":[1,14,24,36,52,58,102,156],"is":[2,19,48,75],"a":[3],"fundamental":[4],"characteristic":[5],"of":[6,13,26,35,37,57,59,71,86,101,103,121,135,152,155],"quantum":[7,28],"mechanics,":[8],"and":[9,39,61,79,88,105,109,111,115,123,137,143,145,149],"understanding":[10],"the":[11,23,33,51,68,84,99,119,131,147],"robustness":[12,34,100,154],"across":[15],"different":[16,45,66],"mixed":[17,42,63,107],"states":[18,43,64,90,108,125,139],"crucial":[20],"for":[21],"comprehending":[22],"properties":[25],"general":[27],"states.":[29],"In":[30],"this":[31],"paper,":[32],"Dicke-W":[38,60],"Greenberger-Horne-Zeilinger":[40],"(GHZ)":[41],"under":[44],"mixing":[46],"ratios":[47],"calculated":[49],"using":[50],"witness":[53],"method.":[54],"The":[55],"robustnesses":[56],"GHZ":[62,106],"are":[65],"when":[67],"probability":[69,85,120,133],"ratio":[70,134],"Dicke":[72,87,104,122,136],"to":[73,95],"W":[74,89,124,138],"greater":[76,91],"than":[77,81,92,127],"32":[78],"less":[80,126],"32.":[82],"For":[83,118],"or":[93],"equal":[94,132],"32,":[96,128],"we":[97,129],"study":[98],"analyze":[110,146],"calculate":[112,144],"their":[113,153],"upper":[114,148],"lower":[116,150],"bounds.":[117],"take":[130],"as":[140],"an":[141],"example":[142],"bounds":[151],"in":[157],"detail.":[158]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}