{"id":"https://openalex.org/W1845175544","doi":"https://doi.org/10.26421/qic11.11-12-11","title":"Local extrema of entropy functions under tensor products","display_name":"Local extrema of entropy functions under tensor products","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W1845175544","doi":"https://doi.org/10.26421/qic11.11-12-11","mag":"1845175544"},"language":"en","primary_location":{"id":"doi:10.26421/qic11.11-12-11","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic11.11-12-11","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002855648","display_name":"Shmuel Friedland","orcid":"https://orcid.org/0000-0002-0423-5005"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shmuel Friedland","raw_affiliation_strings":["Dept. of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dept. of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL#TAB#","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089321215","display_name":"Gilad Gour","orcid":"https://orcid.org/0000-0002-4892-4072"},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gilad Gour","raw_affiliation_strings":["Institute for Quantum Information Science and Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Information Science and Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100815530","display_name":"Aidan Roy","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Aidan Roy","raw_affiliation_strings":["Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, CANADA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, CANADA","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5002855648"],"corresponding_institution_ids":["https://openalex.org/I39422238"],"apc_list":null,"apc_paid":null,"fwci":0.4182,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52639447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"11&12","first_page":"1028","last_page":"1044"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9901999831199646,"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":0.7662475109100342},{"id":"https://openalex.org/keywords/von-neumann-entropy","display_name":"Von Neumann entropy","score":0.7636056542396545},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.6596760749816895},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.6433144211769104},{"id":"https://openalex.org/keywords/generalized-relative-entropy","display_name":"Generalized relative entropy","score":0.6206429600715637},{"id":"https://openalex.org/keywords/joint-quantum-entropy","display_name":"Joint quantum entropy","score":0.597759485244751},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.5916094183921814},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.49648672342300415},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4917583763599396},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4848964810371399},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"Conditional entropy","score":0.4255436956882477},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3856159448623657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33937549591064453},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.17460277676582336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15257275104522705},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.1487179398536682},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.141606867313385},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1303432285785675}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7662475109100342},{"id":"https://openalex.org/C101973423","wikidata":"https://www.wikidata.org/wiki/Q6961323","display_name":"Von Neumann entropy","level":4,"score":0.7636056542396545},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.6596760749816895},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.6433144211769104},{"id":"https://openalex.org/C5084201","wikidata":"https://www.wikidata.org/wiki/Q17090689","display_name":"Generalized relative entropy","level":5,"score":0.6206429600715637},{"id":"https://openalex.org/C42047476","wikidata":"https://www.wikidata.org/wiki/Q6269544","display_name":"Joint quantum entropy","level":3,"score":0.597759485244751},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5916094183921814},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.49648672342300415},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4917583763599396},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4848964810371399},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.4255436956882477},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3856159448623657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33937549591064453},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.17460277676582336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15257275104522705},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.1487179398536682},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.141606867313385},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1303432285785675},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.26421/qic11.11-12-11","is_oa":false,"landing_page_url":"https://doi.org/10.26421/qic11.11-12-11","pdf_url":null,"source":{"id":"https://openalex.org/S41034432","display_name":"Quantum Information and Computation","issn_l":"1533-7146","issn":["1533-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310322612","host_organization_name":"Rinton Press","host_organization_lineage":["https://openalex.org/P4310322612"],"host_organization_lineage_names":["Rinton Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum Information and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1575147392","https://openalex.org/W1975244148","https://openalex.org/W2248300191","https://openalex.org/W2962963071"],"related_works":["https://openalex.org/W1980795850","https://openalex.org/W4283013026","https://openalex.org/W2949984052","https://openalex.org/W3099813660","https://openalex.org/W3101299541","https://openalex.org/W2050108258","https://openalex.org/W3208587035","https://openalex.org/W2558132982","https://openalex.org/W2085879623","https://openalex.org/W3098857864"],"abstract_inverted_index":{"We":[0,22],"show":[1,24],"that":[2,25],"under":[3,35],"a":[4,16],"certain":[5],"condition":[6],"of":[7,15,28,40],"local":[8,26],"commutativity":[9],"the":[10,29,41],"minimum":[11],"von-Neumann":[12],"entropy":[13,31],"output":[14],"quantum":[17],"channel":[18],"is":[19],"locally":[20],"additive.":[21],"also":[23],"minima":[27],"2-norm":[30],"functions":[32],"are":[33],"closed":[34],"tensor":[36],"products":[37],"if":[38],"one":[39],"subspaces":[42],"has":[43],"dimension":[44],"2.":[45]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
