{"id":"https://openalex.org/W2522257371","doi":"https://doi.org/10.3390/e18090342","title":"The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices","display_name":"The Differential Entropy of the Joint Distribution of Eigenvalues of Random Density Matrices","publication_year":2016,"publication_date":"2016-09-21","ids":{"openalex":"https://openalex.org/W2522257371","doi":"https://doi.org/10.3390/e18090342","mag":"2522257371"},"language":"en","primary_location":{"id":"doi:10.3390/e18090342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090342","pdf_url":"https://www.mdpi.com/1099-4300/18/9/342/pdf?version=1474458930","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/9/342/pdf?version=1474458930","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100880774","display_name":"Laizhen Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I100188998","display_name":"Harbin University of Science and Technology","ror":"https://ror.org/04e6y1282","country_code":"CN","type":"education","lineage":["https://openalex.org/I100188998"]},{"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":"Laizhen Luo","raw_affiliation_strings":["School of Applied Science, Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China","School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Applied Science, Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China","institution_ids":["https://openalex.org/I100188998"]},{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001373585","display_name":"Jiamei Wang","orcid":"https://orcid.org/0000-0003-3724-0561"},"institutions":[{"id":"https://openalex.org/I92178344","display_name":"Anhui University of Technology","ror":"https://ror.org/02qdtrq21","country_code":"CN","type":"education","lineage":["https://openalex.org/I92178344"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiamei Wang","raw_affiliation_strings":["Department of Mathematics, Anhui University of Technology, Ma\u2019Anshan 243032, China","Department of Mathematics, Anhui University of Technology, Ma'Anshan 243032, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anhui University of Technology, Ma\u2019Anshan 243032, China","institution_ids":["https://openalex.org/I92178344"]},{"raw_affiliation_string":"Department of Mathematics, Anhui University of Technology, Ma'Anshan 243032, China","institution_ids":["https://openalex.org/I92178344"]}]},{"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":false,"raw_author_name":"Lin Zhang","raw_affiliation_strings":["Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011890541","display_name":"Shifang Zhang","orcid":"https://orcid.org/0000-0002-2805-1446"},"institutions":[{"id":"https://openalex.org/I111753288","display_name":"Fujian Normal University","ror":"https://ror.org/020azk594","country_code":"CN","type":"education","lineage":["https://openalex.org/I111753288"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shifang Zhang","raw_affiliation_strings":["College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350018, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350018, China","institution_ids":["https://openalex.org/I111753288"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5001373585"],"corresponding_institution_ids":["https://openalex.org/I92178344"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3295,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.67317125,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"9","first_page":"342","last_page":"342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11716","display_name":"Random Matrices and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.7090911269187927},{"id":"https://openalex.org/keywords/differential-entropy","display_name":"Differential entropy","score":0.7024967670440674},{"id":"https://openalex.org/keywords/wishart-distribution","display_name":"Wishart distribution","score":0.6597901582717896},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.5909410715103149},{"id":"https://openalex.org/keywords/joint-entropy","display_name":"Joint entropy","score":0.5463108420372009},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.5081796646118164},{"id":"https://openalex.org/keywords/generalized-relative-entropy","display_name":"Generalized relative entropy","score":0.46795332431793213},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.4657503068447113},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.41269057989120483},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3891216218471527},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.35905593633651733},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.3534892499446869},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.2975732088088989},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.2294662594795227},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17287176847457886},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.1631338894367218},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1529991328716278},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15220052003860474}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7090911269187927},{"id":"https://openalex.org/C124551494","wikidata":"https://www.wikidata.org/wiki/Q3055345","display_name":"Differential entropy","level":4,"score":0.7024967670440674},{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.6597901582717896},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.5909410715103149},{"id":"https://openalex.org/C106752470","wikidata":"https://www.wikidata.org/wiki/Q1364826","display_name":"Joint entropy","level":3,"score":0.5463108420372009},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.5081796646118164},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.46795332431793213},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.4657503068447113},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.41269057989120483},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3891216218471527},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.35905593633651733},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3534892499446869},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.2975732088088989},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2294662594795227},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17287176847457886},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.1631338894367218},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1529991328716278},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15220052003860474},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e18090342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090342","pdf_url":"https://www.mdpi.com/1099-4300/18/9/342/pdf?version=1474458930","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":"pmh:oai:doaj.org/article:81c4e012c57f4bbda244dbb2aa97b93b","is_oa":true,"landing_page_url":"https://doaj.org/article/81c4e012c57f4bbda244dbb2aa97b93b","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 18, Iss 9, p 342 (2016)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/9/342/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18090342","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 18; Issue 9; Pages: 342","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e18090342","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18090342","pdf_url":"https://www.mdpi.com/1099-4300/18/9/342/pdf?version=1474458930","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/G1561590163","display_name":null,"funder_award_id":"11301124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4459146105","display_name":null,"funder_award_id":"11371114","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6556454279","display_name":null,"funder_award_id":"11401007","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8204703214","display_name":null,"funder_award_id":"11301077","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/W2522257371.pdf","grobid_xml":"https://content.openalex.org/works/W2522257371.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W570992628","https://openalex.org/W1524987324","https://openalex.org/W1918063455","https://openalex.org/W1973335304","https://openalex.org/W1974637548","https://openalex.org/W1984182532","https://openalex.org/W1987513148","https://openalex.org/W1989339003","https://openalex.org/W1995875735","https://openalex.org/W1995999485","https://openalex.org/W2002610419","https://openalex.org/W2006991014","https://openalex.org/W2027976682","https://openalex.org/W2095222927","https://openalex.org/W2104271427","https://openalex.org/W2186100613","https://openalex.org/W2267889756","https://openalex.org/W2409978206","https://openalex.org/W2478708596","https://openalex.org/W2503558649","https://openalex.org/W2796546714","https://openalex.org/W2798707604","https://openalex.org/W3023808427","https://openalex.org/W3037637275","https://openalex.org/W3099510091","https://openalex.org/W3100793034","https://openalex.org/W3104522527","https://openalex.org/W3106417833","https://openalex.org/W4205593870","https://openalex.org/W4242849907"],"related_works":["https://openalex.org/W4392203663","https://openalex.org/W4252827860","https://openalex.org/W2962805415","https://openalex.org/W2008835467","https://openalex.org/W3080500608","https://openalex.org/W2608546004","https://openalex.org/W3099553964","https://openalex.org/W3100954629","https://openalex.org/W2242607083","https://openalex.org/W2092814302"],"abstract_inverted_index":{"We":[0],"derive":[1],"exactly":[2],"the":[3,7,21,25,40,44,54,58,72],"differential":[4,22,55],"entropy":[5,23,56,74],"of":[6,10,12,24,28,30,46,57,61,64,79],"joint":[8,26,59],"distribution":[9,27,60],"eigenvalues":[11,29],"Wishart":[13],"matrices.":[14],"Based":[15],"on":[16],"this":[17],"result,":[18],"we":[19,52,70],"calculate":[20],"random":[31,65],"mixed":[32,66],"quantum":[33,67],"states,":[34],"which":[35],"is":[36],"induced":[37],"by":[38],"taking":[39],"partial":[41],"trace":[42],"over":[43],"environment":[45],"Haar-distributed":[47],"bipartite":[48],"pure":[49],"states.":[50,68],"Then,":[51],"investigate":[53,71],"diagonal":[62],"entries":[63],"Finally,":[69],"relative":[73],"between":[75],"these":[76],"two":[77],"kinds":[78],"distributions.":[80]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
