{"id":"https://openalex.org/W2012134026","doi":"https://doi.org/10.1007/s11704-008-0017-8","title":"Entanglement of formation and concurrence for mixed states","display_name":"Entanglement of formation and concurrence for mixed states","publication_year":2008,"publication_date":"2008-06-01","ids":{"openalex":"https://openalex.org/W2012134026","doi":"https://doi.org/10.1007/s11704-008-0017-8","mag":"2012134026"},"language":"en","primary_location":{"id":"doi:10.1007/s11704-008-0017-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11704-008-0017-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11704-008-0017-8.pdf","source":{"id":"https://openalex.org/S134228058","display_name":"Frontiers of Computer Science in China","issn_l":"1673-7350","issn":["1673-7350","1673-7466"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers of Computer Science in China","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11704-008-0017-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110017525","display_name":"Xiu-Hong Gao","orcid":null},"institutions":[{"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"],"is_corresponding":true,"raw_author_name":"Xiuhong Gao","raw_affiliation_strings":["Department of Mathematics, Capital Normal University, Beijing, 100037, China","Department of Mathematics, Capital Normal University, Beijing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Capital Normal University, Beijing, 100037, China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"Department of Mathematics, Capital Normal University, Beijing, China#TAB#","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109884242","display_name":"Albeverio Sergio","orcid":null},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Albeverio Sergio","raw_affiliation_strings":["Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Bonn, D-53115, Germany","Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn , Bonn, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Bonn, D-53115, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn , Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056073614","display_name":"Kai Chen","orcid":"https://orcid.org/0000-0001-9833-8197"},"institutions":[{"id":"https://openalex.org/I4210103894","display_name":"Hefei National Center for Physical Sciences at Nanoscale","ror":"https://ror.org/01jeedh73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366","https://openalex.org/I4210103894"]},{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Chen","raw_affiliation_strings":["Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China","Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei, China"],"affiliations":[{"raw_affiliation_string":"Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China","institution_ids":["https://openalex.org/I4210103894","https://openalex.org/I126520041"]},{"raw_affiliation_string":"Hefei National Laboratory for Physical Sciences at Microscale, Department of Modern Physics, University of Science and Technology of China, Hefei, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087659431","display_name":"Shao-Ming Fei","orcid":"https://orcid.org/0000-0003-2412-8626"},"institutions":[{"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"]},{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Shaoming Fei","raw_affiliation_strings":["Department of Mathematics, Capital Normal University, Beijing, 100037, China","Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Bonn, D-53115, Germany","Capital Normal University","Universit\u00e4t Bonn"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Capital Normal University, Beijing, 100037, China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"Institut f\u00fcr Angewandte Mathematik, Universit\u00e4t Bonn, Bonn, D-53115, Germany","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"Capital Normal University","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"Universit\u00e4t Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080139681","display_name":"Xianqing Li\u2010Jost","orcid":null},"institutions":[{"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/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/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"funder","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xianqing Li-Jost","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Leipzig, D-04103, Germany","Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Leipzig, D-04103, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany#TAB#","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5110017525"],"corresponding_institution_ids":["https://openalex.org/I96852419"],"apc_list":null,"apc_paid":null,"fwci":0.5721,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.77246559,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"2","issue":"2","first_page":"114","last_page":"128"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9994999766349792,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/concurrence","display_name":"Concurrence","score":0.9848830103874207},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.8728859424591064},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.8025009632110596},{"id":"https://openalex.org/keywords/multipartite-entanglement","display_name":"Multipartite entanglement","score":0.7194252014160156},{"id":"https://openalex.org/keywords/multipartite","display_name":"Multipartite","score":0.6467068791389465},{"id":"https://openalex.org/keywords/squashed-entanglement","display_name":"Squashed entanglement","score":0.5099979639053345},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4653623402118683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4189996123313904},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.38563379645347595},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3599233329296112},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.33751118183135986},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2087785005569458},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.14413318037986755},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1048210859298706},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.0526852011680603}],"concepts":[{"id":"https://openalex.org/C2777843375","wikidata":"https://www.wikidata.org/wiki/Q5159090","display_name":"Concurrence","level":4,"score":0.9848830103874207},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.8728859424591064},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.8025009632110596},{"id":"https://openalex.org/C71799126","wikidata":"https://www.wikidata.org/wiki/Q6934832","display_name":"Multipartite entanglement","level":5,"score":0.7194252014160156},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.6467068791389465},{"id":"https://openalex.org/C32270708","wikidata":"https://www.wikidata.org/wiki/Q7582152","display_name":"Squashed entanglement","level":4,"score":0.5099979639053345},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4653623402118683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4189996123313904},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.38563379645347595},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3599233329296112},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33751118183135986},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2087785005569458},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.14413318037986755},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1048210859298706},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0526852011680603}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11704-008-0017-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11704-008-0017-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11704-008-0017-8.pdf","source":{"id":"https://openalex.org/S134228058","display_name":"Frontiers of Computer Science in China","issn_l":"1673-7350","issn":["1673-7350","1673-7466"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers of Computer Science in China","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11704-008-0017-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11704-008-0017-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11704-008-0017-8.pdf","source":{"id":"https://openalex.org/S134228058","display_name":"Frontiers of Computer Science in China","issn_l":"1673-7350","issn":["1673-7350","1673-7466"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers of Computer Science in China","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5099999904632568,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2012134026.pdf","grobid_xml":"https://content.openalex.org/works/W2012134026.grobid-xml"},"referenced_works_count":74,"referenced_works":["https://openalex.org/W191718607","https://openalex.org/W1486543895","https://openalex.org/W1488435683","https://openalex.org/W1503422408","https://openalex.org/W1519530038","https://openalex.org/W1631356911","https://openalex.org/W1645624772","https://openalex.org/W1668368460","https://openalex.org/W1686382731","https://openalex.org/W1847580993","https://openalex.org/W1964728833","https://openalex.org/W1967782504","https://openalex.org/W1973442807","https://openalex.org/W1976720922","https://openalex.org/W1977064951","https://openalex.org/W1981812212","https://openalex.org/W1983265741","https://openalex.org/W1990542948","https://openalex.org/W1991882851","https://openalex.org/W1994369874","https://openalex.org/W1997212407","https://openalex.org/W1998865215","https://openalex.org/W1999733856","https://openalex.org/W2000407553","https://openalex.org/W2002598418","https://openalex.org/W2010664024","https://openalex.org/W2011208902","https://openalex.org/W2016939883","https://openalex.org/W2017069819","https://openalex.org/W2022476106","https://openalex.org/W2025107796","https://openalex.org/W2028549339","https://openalex.org/W2028704934","https://openalex.org/W2033093400","https://openalex.org/W2033612015","https://openalex.org/W2033909248","https://openalex.org/W2034272048","https://openalex.org/W2043671058","https://openalex.org/W2043836237","https://openalex.org/W2048468143","https://openalex.org/W2048680711","https://openalex.org/W2051684182","https://openalex.org/W2052896584","https://openalex.org/W2058355389","https://openalex.org/W2060887031","https://openalex.org/W2062183829","https://openalex.org/W2062292260","https://openalex.org/W2066331763","https://openalex.org/W2070163893","https://openalex.org/W2073781628","https://openalex.org/W2083492510","https://openalex.org/W2084875624","https://openalex.org/W2088076417","https://openalex.org/W2090807706","https://openalex.org/W2094271988","https://openalex.org/W2096089357","https://openalex.org/W2106985682","https://openalex.org/W2116898717","https://openalex.org/W2120002077","https://openalex.org/W2124094144","https://openalex.org/W2132578652","https://openalex.org/W2136544478","https://openalex.org/W2148576428","https://openalex.org/W2764347725","https://openalex.org/W2802073130","https://openalex.org/W2949433943","https://openalex.org/W2951432180","https://openalex.org/W2952721131","https://openalex.org/W3037891773","https://openalex.org/W3098486124","https://openalex.org/W3098579017","https://openalex.org/W3098707786","https://openalex.org/W3105109009","https://openalex.org/W4249299939"],"related_works":["https://openalex.org/W3106188946","https://openalex.org/W3098500157","https://openalex.org/W1986700247","https://openalex.org/W2211029024","https://openalex.org/W2963019433","https://openalex.org/W4301378338","https://openalex.org/W2577598364","https://openalex.org/W4383092955","https://openalex.org/W4287271129","https://openalex.org/W2312357241"],"abstract_inverted_index":{"We":[0,18],"review":[1],"some":[2,20],"results":[3,48],"on":[4,49],"analytical":[5],"computations":[6],"of":[7,14,22,29,36],"the":[8,23,27,40,53],"measures":[9],"for":[10,26,39,52],"quantum":[11],"entanglement:":[12],"entanglement":[13,28],"formation":[15,30],"and":[16,35,44],"concurrence.":[17],"introduce":[19],"estimations":[21],"lower":[24,37,50],"bounds":[25,38,51],"in":[31,42],"bipartite":[32,43],"mixed":[33],"states,":[34],"concurrence":[41,54],"tripartite":[45],"systems.":[46,61],"The":[47],"are":[55],"also":[56],"generalized":[57],"to":[58],"arbitrary":[59],"multipartite":[60]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}