{"id":"https://openalex.org/W3082443622","doi":"https://doi.org/10.3390/e26080643","title":"Revisiting Dynamics of Quantum Causal Structures\u2014When Can Causal Order Evolve?","display_name":"Revisiting Dynamics of Quantum Causal Structures\u2014When Can Causal Order Evolve?","publication_year":2024,"publication_date":"2024-07-29","ids":{"openalex":"https://openalex.org/W3082443622","doi":"https://doi.org/10.3390/e26080643","mag":"3082443622","pmid":"https://pubmed.ncbi.nlm.nih.gov/39202113"},"language":"en","primary_location":{"id":"doi:10.3390/e26080643","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26080643","pdf_url":"https://www.mdpi.com/1099-4300/26/8/643/pdf?version=1722233821","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/1099-4300/26/8/643/pdf?version=1722233821","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043209111","display_name":"John H. Selby","orcid":"https://orcid.org/0000-0002-4596-7501"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"John H. Selby","raw_affiliation_strings":["International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023433191","display_name":"Ana Bel\u00e9n Sainz","orcid":"https://orcid.org/0000-0003-3123-8436"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Ana Bel\u00e9n Sainz","raw_affiliation_strings":["International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081239197","display_name":"Pawe\u0142 Horodecki","orcid":"https://orcid.org/0000-0002-3233-1336"},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Horodecki","raw_affiliation_strings":["International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland"],"affiliations":[{"raw_affiliation_string":"International Centre for Theory of Quantum Technologies, University of Gda\u0144sk, Jana Ba\u017cy\u0144skiego 1a, 80-309 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5043209111"],"corresponding_institution_ids":["https://openalex.org/I40413290"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.705,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64681133,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"26","issue":"8","first_page":"643","last_page":"643"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9998999834060669,"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/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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.988099992275238,"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/statistical-physics","display_name":"Statistical physics","score":0.5806646347045898},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5318362712860107},{"id":"https://openalex.org/keywords/causal-structure","display_name":"Causal structure","score":0.4890778660774231},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4684968590736389},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.46714162826538086},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40930771827697754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3516271710395813},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2700667977333069},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1854410171508789},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08041331171989441}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5806646347045898},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5318362712860107},{"id":"https://openalex.org/C163504300","wikidata":"https://www.wikidata.org/wiki/Q2364925","display_name":"Causal structure","level":2,"score":0.4890778660774231},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4684968590736389},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.46714162826538086},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40930771827697754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3516271710395813},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2700667977333069},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1854410171508789},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08041331171989441},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e26080643","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26080643","pdf_url":"https://www.mdpi.com/1099-4300/26/8/643/pdf?version=1722233821","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:arXiv.org:2008.12757","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.12757","pdf_url":"https://arxiv.org/pdf/2008.12757","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmid:39202113","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39202113","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:11354062","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11354062","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11354062/pdf/entropy-26-00643.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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:c0f3585c0c014114ac9b3ba00c5ccabd","is_oa":true,"landing_page_url":"https://doaj.org/article/c0f3585c0c014114ac9b3ba00c5ccabd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 8, p 643 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/26/8/643/","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26080643","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e26080643","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e26080643","pdf_url":"https://www.mdpi.com/1099-4300/26/8/643/pdf?version=1722233821","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/G1752704862","display_name":null,"funder_award_id":"2021/41/B/ST2/03149","funder_id":"https://openalex.org/F4320322511","funder_display_name":"Narodowe Centrum Nauki"},{"id":"https://openalex.org/G7569305816","display_name":null,"funder_award_id":"2018/MAB/5","funder_id":"https://openalex.org/F4320321042","funder_display_name":"Fundacja na rzecz Nauki Polskiej"}],"funders":[{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"},{"id":"https://openalex.org/F4320322511","display_name":"Narodowe Centrum Nauki","ror":"https://ror.org/03ha2q922"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3082443622.pdf"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W7398728","https://openalex.org/W1472049032","https://openalex.org/W1501046462","https://openalex.org/W1544810690","https://openalex.org/W1615134144","https://openalex.org/W1677699058","https://openalex.org/W1968493380","https://openalex.org/W1971585707","https://openalex.org/W2008426564","https://openalex.org/W2020726398","https://openalex.org/W2044607357","https://openalex.org/W2051981547","https://openalex.org/W2068708279","https://openalex.org/W2080043022","https://openalex.org/W2094659498","https://openalex.org/W2113152322","https://openalex.org/W2113235349","https://openalex.org/W2161316267","https://openalex.org/W2241294872","https://openalex.org/W2264666866","https://openalex.org/W2291298592","https://openalex.org/W2398011416","https://openalex.org/W2480142423","https://openalex.org/W2559071265","https://openalex.org/W2571843382","https://openalex.org/W2591334902","https://openalex.org/W2649547806","https://openalex.org/W2762211079","https://openalex.org/W2790390455","https://openalex.org/W2809984647","https://openalex.org/W2944397262","https://openalex.org/W2964099448","https://openalex.org/W2964217961","https://openalex.org/W2969355317","https://openalex.org/W2993427844","https://openalex.org/W3021457633","https://openalex.org/W3023699883","https://openalex.org/W3037737784","https://openalex.org/W3082443622","https://openalex.org/W3087556218","https://openalex.org/W3098253215","https://openalex.org/W3099018298","https://openalex.org/W3100364179","https://openalex.org/W3101989525","https://openalex.org/W3102528294","https://openalex.org/W3102551045","https://openalex.org/W3103068290","https://openalex.org/W3104171426","https://openalex.org/W3123044171","https://openalex.org/W4247494971","https://openalex.org/W6829269145"],"related_works":["https://openalex.org/W3121315934","https://openalex.org/W1636325709","https://openalex.org/W2589649776","https://openalex.org/W2724817865","https://openalex.org/W2400992695","https://openalex.org/W2382944939","https://openalex.org/W2771969352","https://openalex.org/W1993066527","https://openalex.org/W4300802590","https://openalex.org/W4309734132"],"abstract_inverted_index":{"Recently,":[0],"there":[1],"has":[2],"been":[3],"substantial":[4],"interest":[5],"in":[6,17],"studying":[7],"the":[8,19,33,41,52,71,78,106,112,117,137,151,159,188,191,195],"dynamics":[9,20,43],"of":[10,15,21,40,44,54,56,60,91,105,109,119,153,166,190],"quantum":[11],"theory":[12],"beyond":[13],"that":[14,69,90,130,158],"states,":[16],"particular,":[18],"channels,":[22],"measurements,":[23],"and":[24,48,75,134,149,162,204],"higher-order":[25,167],"transformations.":[26],"Castro-Ruiz":[27,92,120],"et":[28,93,121],"al.":[29,122],"pursues":[30],"this":[31,154],"using":[32],"process-matrix":[34],"formalism,":[35,72,115],"together":[36],"with":[37],"a":[38,65,102],"definition":[39],"possible":[42],"such":[45],"process":[46],"matrices,":[47],"focusing":[49],"especially":[50],"on":[51,179,198],"question":[53],"evolution":[55,108],"causal":[57,79,138],"structures.":[58],"One":[59],"its":[61],"major":[62],"conclusions":[63,178],"is":[64,97,142,172],"strong":[66],"theorem":[67],"saying":[68],"within":[70,111],"under":[73,131],"continuous":[74,133],"reversible":[76,135],"transformations,":[77],"order":[80,139],"between":[81,140],"operations":[82,110,141,203],"must":[83],"be":[84],"preserved.":[85,145],"Our":[86],"result":[87],"here":[88],"challenges":[89],"al.:":[94],"if":[95],"one":[96],"to":[98,186],"take":[99],"into":[100],"account":[101],"full":[103],"picture":[104,193],"physical":[107,180],"standard":[113],"quantum-mechanical":[114],"then":[116],"conclusion":[118],"does":[123],"not":[124,143,173],"hold.":[125],"That":[126],"is,":[127],"we":[128,183],"show":[129,184],"certain":[132],"dynamics,":[136],"necessarily":[144],"We":[146],"moreover":[147],"identify":[148],"analyse":[150],"root":[152],"apparent":[155],"contradiction,":[156],"specifically,":[157],"commonly":[160],"accepted":[161],"widely":[163],"applied":[164],"framework":[165],"processes,":[168],"whilst":[169],"mathematically":[170],"sound,":[171],"always":[174],"appropriate":[175],"for":[176],"drawing":[177],"dynamics.":[181],"Finally,":[182],"how":[185],"reconcile":[187],"elements":[189],"whole":[192],"following":[194],"intuition":[196],"based":[197],"entanglement":[199],"processing":[200],"by":[201],"local":[202],"classical":[205],"communication.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}
