{"id":"https://openalex.org/W7162440975","doi":"https://doi.org/10.3390/e28060590","title":"Concurrence Percolation Behavior in Diluted Quantum Networks","display_name":"Concurrence Percolation Behavior in Diluted Quantum Networks","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162440975","doi":"https://doi.org/10.3390/e28060590","pmid":"https://pubmed.ncbi.nlm.nih.gov/42352100"},"language":"en","primary_location":{"id":"doi:10.3390/e28060590","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060590","pdf_url":null,"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://doi.org/10.3390/e28060590","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137020087","display_name":"Gaogao Dong","orcid":"https://orcid.org/0000-0003-4425-7724"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gaogao Dong","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China"],"raw_orcid":"https://orcid.org/0000-0003-4425-7724","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137006450","display_name":"Yili Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yili Shen","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005324379","display_name":"Xinqi Hu","orcid":"https://orcid.org/0009-0008-5018-1934"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinqi Hu","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China"],"raw_orcid":"https://orcid.org/0009-0008-5018-1934","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100742778","display_name":"Ruijin Du","orcid":"https://orcid.org/0000-0002-1530-7676"},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruijin Du","raw_affiliation_strings":["School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China"],"raw_orcid":"https://orcid.org/0000-0002-1530-7676","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China","institution_ids":["https://openalex.org/I115592961"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I115592961"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.52969972,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"6","first_page":"590","last_page":"590"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.45329999923706055,"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":0.45329999923706055,"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":0.09520000219345093,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.08510000258684158,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-decoherence","display_name":"Quantum decoherence","score":0.6089000105857849},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.5986999869346619},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5788000226020813},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.48980000615119934},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.4731999933719635},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4453999996185303},{"id":"https://openalex.org/keywords/percolation","display_name":"Percolation (cognitive psychology)","score":0.3982999920845032},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.3944999873638153}],"concepts":[{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.6089000105857849},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5986999869346619},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5982999801635742},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.48980000615119934},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.4731999933719635},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4246000051498413},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3944999873638153},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.3817000091075897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33230000734329224},{"id":"https://openalex.org/C2777843375","wikidata":"https://www.wikidata.org/wiki/Q5159090","display_name":"Concurrence","level":4,"score":0.32350000739097595},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.30489999055862427},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.304500013589859},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3003999888896942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2831999957561493},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.28209999203681946},{"id":"https://openalex.org/C206040425","wikidata":"https://www.wikidata.org/wiki/Q4748511","display_name":"Amplitude damping channel","level":5,"score":0.27149999141693115},{"id":"https://openalex.org/C2986219828","wikidata":"https://www.wikidata.org/wiki/Q1193095","display_name":"Coupling strength","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C15867958","wikidata":"https://www.wikidata.org/wiki/Q5280413","display_name":"Directed percolation","level":4,"score":0.2565000057220459}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e28060590","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060590","pdf_url":null,"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:42352100","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42352100","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":"Journal Article"},{"id":"pmh:oai:doaj.org/article:43d44dad130c46dfb13975f815630366","is_oa":false,"landing_page_url":"https://doaj.org/article/43d44dad130c46dfb13975f815630366","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 28, Iss 6, p 590 (2026)","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13297787","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13297787/","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/e28060590","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e28060590","pdf_url":null,"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/G7671115447","display_name":null,"funder_award_id":"72474086","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8646177056","display_name":null,"funder_award_id":"62373169","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1560341753","https://openalex.org/W1986513834","https://openalex.org/W2025550035","https://openalex.org/W2027628579","https://openalex.org/W2044881936","https://openalex.org/W2050401089","https://openalex.org/W2065769502","https://openalex.org/W2070256846","https://openalex.org/W2086947442","https://openalex.org/W2132764286","https://openalex.org/W2140495925","https://openalex.org/W2151914114","https://openalex.org/W2162656865","https://openalex.org/W2890292748","https://openalex.org/W2897264299","https://openalex.org/W3037737784","https://openalex.org/W3137506272","https://openalex.org/W4246877238","https://openalex.org/W4407948771"],"related_works":[],"abstract_inverted_index":{"The":[0,95],"evolution":[1],"of":[2,23,26,79,85,144],"connectivity":[3,43],"in":[4,16,46],"quantum":[5,17,50,66,99,120,145],"networks":[6,146],"under":[7,110],"decoherence":[8],"and":[9,69,87,92,113,131,142],"link":[10,36],"degradation":[11,130],"is":[12],"a":[13],"central":[14],"problem":[15],"information,":[18],"calling":[19],"for":[20,82],"further":[21],"understanding":[22],"the":[24,52,77,133,139],"nature":[25],"its":[27],"transition":[28],"during":[29],"structural":[30,129],"network":[31],"degradation.":[32],"By":[33],"diluting":[34],"each":[35],"with":[37,72,147],"probability":[38],"1\u2212f,":[39],"we":[40,75],"focus":[41],"on":[42],"strength":[44],"transitions":[45,78],"diluted":[47],"hierarchical":[48,134],"scale-free":[49,135],"networks,":[51],"(u,v)":[53],"flowers,":[54],"which":[55],"are":[56],"analytically":[57],"tractable":[58],"through":[59],"two":[60],"adjustable":[61],"path-length":[62],"parameters,":[63],"u\u2264v.":[64],"Incorporating":[65],"concurrence":[67],"percolation":[68,100],"comparing":[70],"it":[71],"classical":[73,107],"percolation,":[74,108],"analyze":[76],"critical":[80,104],"thresholds":[81,105],"various":[83,111],"values":[84],"f":[86],"v":[88],"from":[89],"analytical,":[90],"numerical,":[91],"simulation":[93],"perspectives.":[94],"results":[96],"demonstrate":[97],"that":[98,119,132],"exhibits":[101],"consistently":[102],"lower":[103],"than":[106],"even":[109],"topologies":[112],"dilution":[114],"levels.":[115],"Our":[116],"work":[117],"implies":[118],"multipath":[121,148],"entanglement":[122],"provides":[123],"an":[124],"intrinsic":[125],"compensatory":[126],"mechanism":[127],"against":[128],"topology":[136],"contributes":[137],"to":[138],"failure":[140],"resistance":[141],"robustness":[143],"coupling.":[149]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-05-27T00:00:00"}