{"id":"https://openalex.org/W4220652585","doi":"https://doi.org/10.3390/e24030395","title":"Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert\u2013Schmidt Speed-Based Witness","display_name":"Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert\u2013Schmidt Speed-Based Witness","publication_year":2022,"publication_date":"2022-03-12","ids":{"openalex":"https://openalex.org/W4220652585","doi":"https://doi.org/10.3390/e24030395","pmid":"https://pubmed.ncbi.nlm.nih.gov/35327906"},"language":"en","primary_location":{"id":"doi:10.3390/e24030395","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030395","pdf_url":"https://www.mdpi.com/1099-4300/24/3/395/pdf?version=1647248684","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/1099-4300/24/3/395/pdf?version=1647248684","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044339853","display_name":"Kobra Mahdavipour","orcid":"https://orcid.org/0000-0003-0922-795X"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["CA","IT"],"is_corresponding":false,"raw_author_name":"Kobra Mahdavipour","raw_affiliation_strings":["Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy","INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"],"raw_orcid":"https://orcid.org/0000-0003-0922-795X","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]},{"raw_affiliation_string":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003935010","display_name":"Mahshid Khazaei Shadfar","orcid":"https://orcid.org/0000-0002-2357-1194"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["CA","IT"],"is_corresponding":false,"raw_author_name":"Mahshid Khazaei Shadfar","raw_affiliation_strings":["Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy","INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"],"raw_orcid":"https://orcid.org/0000-0002-2357-1194","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]},{"raw_affiliation_string":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030482186","display_name":"Hossein Rangani Jahromi","orcid":"https://orcid.org/0000-0001-7208-2437"},"institutions":[{"id":"https://openalex.org/I2800262513","display_name":"Jahrom University","ror":"https://ror.org/03xp8p672","country_code":"IR","type":"education","lineage":["https://openalex.org/I2800262513"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Hossein Rangani Jahromi","raw_affiliation_strings":["Physics Department, Faculty of Sciences, Jahrom University, Jahrom P.O. Box 74135111, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7208-2437","affiliations":[{"raw_affiliation_string":"Physics Department, Faculty of Sciences, Jahrom University, Jahrom P.O. Box 74135111, Iran","institution_ids":["https://openalex.org/I2800262513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015051704","display_name":"Roberto Morandotti","orcid":"https://orcid.org/0000-0001-7717-1519"},"institutions":[{"id":"https://openalex.org/I39481719","display_name":"Institut National de la Recherche Scientifique","ror":"https://ror.org/04td37d32","country_code":"CA","type":"education","lineage":["https://openalex.org/I39481719","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Roberto Morandotti","raw_affiliation_strings":["INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada"],"raw_orcid":"https://orcid.org/0000-0001-7717-1519","affiliations":[{"raw_affiliation_string":"INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, QC J3X 1S2, Canada","institution_ids":["https://openalex.org/I39481719"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002338165","display_name":"Rosario Lo Franco","orcid":"https://orcid.org/0000-0002-3281-0935"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Rosario Lo Franco","raw_affiliation_strings":["Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy"],"raw_orcid":"https://orcid.org/0000-0002-3281-0935","affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria, Universit\u00e0 di Palermo, Viale delle Scienze, 90128 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002338165","https://openalex.org/A5030482186"],"corresponding_institution_ids":["https://openalex.org/I2800262513","https://openalex.org/I900890020"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3936,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64749339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"24","issue":"3","first_page":"395","last_page":"395"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9993000030517578,"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":0.9993000030517578,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9970999956130981,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.995199978351593,"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/witness","display_name":"Witness","score":0.5625219941139221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4351498782634735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41103309392929077},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.38383594155311584},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.329853892326355},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25008487701416016}],"concepts":[{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.5625219941139221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4351498782634735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41103309392929077},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.38383594155311584},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.329853892326355},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25008487701416016},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.3390/e24030395","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030395","pdf_url":"https://www.mdpi.com/1099-4300/24/3/395/pdf?version=1647248684","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:35327906","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35327906","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:2201.08617","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.08617","pdf_url":"https://arxiv.org/pdf/2201.08617","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:98dc3a1c2eb546a28ecf1326124385c2","is_oa":true,"landing_page_url":"https://doaj.org/article/98dc3a1c2eb546a28ecf1326124385c2","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 3, p 395 (2022)","raw_type":"article"},{"id":"pmh:oai:iris.unipa.it:10447/547871","is_oa":true,"landing_page_url":"http://hdl.handle.net/10447/547871","pdf_url":null,"source":{"id":"https://openalex.org/S4306401065","display_name":"Nova Science Publishers (Nova Science Publishers, Inc.)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/3/395/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24030395","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 3; Pages: 395","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8947421","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8947421","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/e24030395","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24030395","pdf_url":"https://www.mdpi.com/1099-4300/24/3/395/pdf?version=1647248684","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":[{"score":0.6499999761581421,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4220652585.pdf","grobid_xml":"https://content.openalex.org/works/W4220652585.grobid-xml"},"referenced_works_count":112,"referenced_works":["https://openalex.org/W375307776","https://openalex.org/W792163153","https://openalex.org/W1409569118","https://openalex.org/W1530995657","https://openalex.org/W1536865027","https://openalex.org/W1571362567","https://openalex.org/W1571385165","https://openalex.org/W1619293558","https://openalex.org/W1832011267","https://openalex.org/W1835673560","https://openalex.org/W1966396518","https://openalex.org/W1968351384","https://openalex.org/W1968661061","https://openalex.org/W1972188952","https://openalex.org/W1973657277","https://openalex.org/W1975677983","https://openalex.org/W1976340877","https://openalex.org/W1979369481","https://openalex.org/W1981105843","https://openalex.org/W1983785874","https://openalex.org/W1985618326","https://openalex.org/W1996075932","https://openalex.org/W1998723694","https://openalex.org/W1998783091","https://openalex.org/W2000386694","https://openalex.org/W2000467687","https://openalex.org/W2002430008","https://openalex.org/W2002887576","https://openalex.org/W2003403720","https://openalex.org/W2004247220","https://openalex.org/W2004976239","https://openalex.org/W2005164286","https://openalex.org/W2008925509","https://openalex.org/W2011277039","https://openalex.org/W2015263507","https://openalex.org/W2015486074","https://openalex.org/W2016384025","https://openalex.org/W2020179434","https://openalex.org/W2027529302","https://openalex.org/W2031255223","https://openalex.org/W2032234739","https://openalex.org/W2036296465","https://openalex.org/W2036414032","https://openalex.org/W2043317809","https://openalex.org/W2044133255","https://openalex.org/W2045434389","https://openalex.org/W2046788269","https://openalex.org/W2047497165","https://openalex.org/W2047969991","https://openalex.org/W2048703935","https://openalex.org/W2050257404","https://openalex.org/W2051163841","https://openalex.org/W2052495957","https://openalex.org/W2052910233","https://openalex.org/W2064206864","https://openalex.org/W2069043908","https://openalex.org/W2072055974","https://openalex.org/W2075175704","https://openalex.org/W2081768854","https://openalex.org/W2082688097","https://openalex.org/W2087654101","https://openalex.org/W2087844534","https://openalex.org/W2088991820","https://openalex.org/W2090471280","https://openalex.org/W2094648505","https://openalex.org/W2115509850","https://openalex.org/W2117897634","https://openalex.org/W2119401520","https://openalex.org/W2130117852","https://openalex.org/W2138574865","https://openalex.org/W2142904307","https://openalex.org/W2156590677","https://openalex.org/W2169844369","https://openalex.org/W2181284682","https://openalex.org/W2203720464","https://openalex.org/W2214479636","https://openalex.org/W2264137339","https://openalex.org/W2317012956","https://openalex.org/W2320666705","https://openalex.org/W2493185506","https://openalex.org/W2511481862","https://openalex.org/W2519383683","https://openalex.org/W2653200766","https://openalex.org/W2697995376","https://openalex.org/W2726838789","https://openalex.org/W2773836929","https://openalex.org/W2783223581","https://openalex.org/W2789916496","https://openalex.org/W2924903915","https://openalex.org/W2974427948","https://openalex.org/W2975127619","https://openalex.org/W2995094734","https://openalex.org/W3013810143","https://openalex.org/W3037637275","https://openalex.org/W3091044725","https://openalex.org/W3099756982","https://openalex.org/W3100140276","https://openalex.org/W3100408653","https://openalex.org/W3100741959","https://openalex.org/W3102340246","https://openalex.org/W3103222636","https://openalex.org/W3111237355","https://openalex.org/W3151432352","https://openalex.org/W3171749606","https://openalex.org/W3197168569","https://openalex.org/W3204646413","https://openalex.org/W3215390054","https://openalex.org/W3216242988","https://openalex.org/W4205538429","https://openalex.org/W4360937856","https://openalex.org/W6684722310","https://openalex.org/W6772575355"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W2890518300","https://openalex.org/W2366687089","https://openalex.org/W588843504","https://openalex.org/W2382947717","https://openalex.org/W4302574074","https://openalex.org/W2360970878","https://openalex.org/W2006894296"],"abstract_inverted_index":{"A":[0],"witness":[1,28,52,77,97],"of":[2,13,38,49,74,84,102,111],"non-Markovianity":[3,27,55],"based":[4],"on":[5],"the":[6,39,47,71,75,95,103,108],"Hilbert-Schmidt":[7],"speed":[8],"(HSS),":[9],"a":[10,26,99,112,116],"special":[11],"type":[12],"quantum":[14,23,62,85,88,109],"statistical":[15],"speed,":[16],"has":[17],"been":[18],"recently":[19],"introduced":[20],"for":[21],"low-dimensional":[22],"systems.":[24],"Such":[25],"is":[29,43,98],"particularly":[30],"useful,":[31],"being":[32],"easily":[33],"computable":[34],"since":[35],"no":[36],"diagonalization":[37],"system":[40,114],"density":[41],"matrix":[42],"required.":[44],"We":[45,68],"investigate":[46],"sensitivity":[48],"this":[50],"HSS-based":[51,76,96],"to":[53],"detect":[54],"in":[56,80,107],"various":[57],"high-dimensional":[58,113],"and":[59],"multipartite":[60],"open":[61],"systems":[63],"with":[64,82,115],"finite":[65,117],"Hilbert":[66,118],"spaces.":[67],"find":[69],"that":[70,94],"time":[72],"behaviors":[73],"are":[78],"always":[79],"agreement":[81],"those":[83],"negativity":[86],"or":[87],"correlation":[89],"measure.":[90],"These":[91],"results":[92],"show":[93],"faithful":[100],"identifier":[101],"memory":[104],"effects":[105],"appearing":[106],"evolution":[110],"space.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}