{"id":"https://openalex.org/W4405196400","doi":"https://doi.org/10.3390/e26121070","title":"Infinite-Dimensional Quantum Entropy: The Unified Entropy Case","display_name":"Infinite-Dimensional Quantum Entropy: The Unified Entropy Case","publication_year":2024,"publication_date":"2024-12-09","ids":{"openalex":"https://openalex.org/W4405196400","doi":"https://doi.org/10.3390/e26121070","pmid":"https://pubmed.ncbi.nlm.nih.gov/39766699"},"language":"en","primary_location":{"id":"doi:10.3390/e26121070","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121070","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1070/pdf?version=1733734504","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://www.mdpi.com/1099-4300/26/12/1070/pdf?version=1733734504","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012462187","display_name":"Roman Gielerak","orcid":"https://orcid.org/0000-0001-8657-0829"},"institutions":[{"id":"https://openalex.org/I46305939","display_name":"University of Zielona G\u00f3ra","ror":"https://ror.org/04fzm7v55","country_code":"PL","type":"education","lineage":["https://openalex.org/I46305939"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Roman Gielerak","raw_affiliation_strings":["Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland"],"raw_orcid":"https://orcid.org/0000-0001-8657-0829","affiliations":[{"raw_affiliation_string":"Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland","institution_ids":["https://openalex.org/I46305939"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063399140","display_name":"Joanna Wi\u015bniewska","orcid":"https://orcid.org/0000-0002-2119-3329"},"institutions":[{"id":"https://openalex.org/I2800249161","display_name":"Military University of Technology in Warsaw","ror":"https://ror.org/05fct5h31","country_code":"PL","type":"education","lineage":["https://openalex.org/I2800249161"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Joanna Wi\u015bniewska","raw_affiliation_strings":["Institute of Information Systems, Faculty of Cybernetics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warszaw, Poland"],"raw_orcid":"https://orcid.org/0000-0002-2119-3329","affiliations":[{"raw_affiliation_string":"Institute of Information Systems, Faculty of Cybernetics, Military University of Technology, Gen. S. Kaliskiego 2, 00-908 Warszaw, Poland","institution_ids":["https://openalex.org/I2800249161"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024838422","display_name":"Marek Sawerwain","orcid":"https://orcid.org/0000-0001-8468-2456"},"institutions":[{"id":"https://openalex.org/I46305939","display_name":"University of Zielona G\u00f3ra","ror":"https://ror.org/04fzm7v55","country_code":"PL","type":"education","lineage":["https://openalex.org/I46305939"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Marek Sawerwain","raw_affiliation_strings":["Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland"],"raw_orcid":"https://orcid.org/0000-0001-8468-2456","affiliations":[{"raw_affiliation_string":"Institute of Control & Computation Engineering, University of Zielona G\u00f3ra, Licealna 9, 65-417 Zielona G\u00f3ra, Poland","institution_ids":["https://openalex.org/I46305939"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024838422"],"corresponding_institution_ids":["https://openalex.org/I46305939"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.4788,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72680335,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"26","issue":"12","first_page":"1070","last_page":"1070"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","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"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","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"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9984999895095825,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9939000010490417,"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/von-neumann-entropy","display_name":"Von Neumann entropy","score":0.7840858697891235},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.6498594284057617},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6383911371231079},{"id":"https://openalex.org/keywords/generalized-relative-entropy","display_name":"Generalized relative entropy","score":0.5933356881141663},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.5849950909614563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5836917161941528},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.49797725677490234},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4464060962200165},{"id":"https://openalex.org/keywords/conditional-quantum-entropy","display_name":"Conditional quantum entropy","score":0.4100118577480316},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.37638920545578003},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.36460697650909424},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30260682106018066},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.28947824239730835},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.2861289381980896},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.2537696361541748},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21425744891166687},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1853596270084381},{"id":"https://openalex.org/keywords/open-quantum-system","display_name":"Open quantum system","score":0.15287795662879944},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12226536870002747},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.11945387721061707}],"concepts":[{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.7840858697891235},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.6498594284057617},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6383911371231079},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.5933356881141663},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.5849950909614563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5836917161941528},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.49797725677490234},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4464060962200165},{"id":"https://openalex.org/C16609844","wikidata":"https://www.wikidata.org/wiki/Q5159273","display_name":"Conditional quantum entropy","level":5,"score":0.4100118577480316},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.37638920545578003},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.36460697650909424},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30260682106018066},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.28947824239730835},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.2861289381980896},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.2537696361541748},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21425744891166687},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1853596270084381},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.15287795662879944},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12226536870002747},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.11945387721061707},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26121070","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121070","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1070/pdf?version=1733734504","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:39766699","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39766699","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:11675474","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11675474","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11675474/pdf/entropy-26-01070.pdf","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"},{"id":"pmh:oai:doaj.org/article:77eeda1ef86e4872916c8ae8ae753ec0","is_oa":true,"landing_page_url":"https://doaj.org/article/77eeda1ef86e4872916c8ae8ae753ec0","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 26, Iss 12, p 1070 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26121070","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26121070","pdf_url":"https://www.mdpi.com/1099-4300/26/12/1070/pdf?version=1733734504","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/G942980895","display_name":null,"funder_award_id":"UGB 701/2024","funder_id":"https://openalex.org/F4320323668","funder_display_name":"Wojskowa Akademia Techniczna"}],"funders":[{"id":"https://openalex.org/F4320323668","display_name":"Wojskowa Akademia Techniczna","ror":"https://ror.org/05fct5h31"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405196400.pdf"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1524267207","https://openalex.org/W1657617918","https://openalex.org/W1970948459","https://openalex.org/W1980976045","https://openalex.org/W2000430822","https://openalex.org/W2004800533","https://openalex.org/W2014704465","https://openalex.org/W2022246685","https://openalex.org/W2037163827","https://openalex.org/W2040540537","https://openalex.org/W2067709685","https://openalex.org/W2079027298","https://openalex.org/W2099744080","https://openalex.org/W2123760116","https://openalex.org/W2142739935","https://openalex.org/W2288095892","https://openalex.org/W2340110832","https://openalex.org/W2475732536","https://openalex.org/W2511750669","https://openalex.org/W2951432180","https://openalex.org/W2951868104","https://openalex.org/W3035965352","https://openalex.org/W3098914594","https://openalex.org/W3099878876","https://openalex.org/W4249726483","https://openalex.org/W4379016360","https://openalex.org/W4385857740","https://openalex.org/W6734192442","https://openalex.org/W6764898018"],"related_works":["https://openalex.org/W1980795850","https://openalex.org/W4388950697","https://openalex.org/W2949984052","https://openalex.org/W3099813660","https://openalex.org/W3126496087","https://openalex.org/W4405713915","https://openalex.org/W2083403685","https://openalex.org/W1648573185","https://openalex.org/W3103412666","https://openalex.org/W3101299541"],"abstract_inverted_index":{"Infinite-dimensional":[0],"systems":[1,72],"play":[2],"an":[3,45],"important":[4],"role":[5],"in":[6,29,50],"the":[7,32,53,59,68,75,81,84,90,105,120],"continuous-variable":[8],"quantum":[9,24,55],"computation":[10,26],"model,":[11],"which":[12,115],"can":[13],"compete":[14],"with":[15],"a":[16],"more":[17],"standard":[18,60],"approach":[19],"based":[20],"on":[21],"qubit":[22],"and":[23,108],"circuit":[25],"models.":[27],"But,":[28],"many":[30],"cases,":[31],"value":[33],"of":[34,70,80,89],"entropy":[35,56,121],"unfortunately":[36],"cannot":[37],"be":[38],"easily":[39],"computed":[40],"for":[41,103,123],"states":[42],"originating":[43],"from":[44],"infinite-dimensional":[46,71,109],"Hilbert":[47,125],"space.":[48],"Therefore,":[49],"this":[51,97],"article,":[52],"unified":[54,92],"(which":[57],"extends":[58],"von":[61],"Neumann":[62],"entropy)":[63],"notion":[64],"is":[65],"extended":[66,95],"to":[67,96,118],"case":[69,98],"by":[73],"using":[74],"Fredholm":[76],"determinant":[77],"theory.":[78],"Some":[79],"known":[82],"(in":[83],"finite-dimensional":[85],"case)":[86],"basic":[87],"properties":[88],"introduced":[91],"entropies":[93,110],"were":[94],"study.":[99],"Certain":[100],"numerical":[101],"examples":[102],"computing":[104],"proposed":[106],"finite-":[107],"are":[111],"outlined":[112],"as":[113],"well,":[114],"allowed":[116],"us":[117],"calculate":[119],"values":[122],"infinite":[124],"spaces.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}