{"id":"https://openalex.org/W7213228665","doi":"https://doi.org/10.48550/arxiv.2609.13870","title":"Hiai--Petz Skew Informations and Sharp Uncertainty Relations for a Single Observable","display_name":"Hiai--Petz Skew Informations and Sharp Uncertainty Relations for a Single Observable","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213228665","doi":"https://doi.org/10.48550/arxiv.2609.13870"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13870","pdf_url":"https://arxiv.org/pdf/2609.13870","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.13870","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022397838","display_name":"Gen Kimura","orcid":"https://orcid.org/0000-0003-4288-2024","observed_orcids":["https://orcid.org/0000-0003-4288-2024"]},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kimura, Gen","raw_affiliation_strings":["Graduate School of Information Sciences , Tohoku University , 6-3-09 Aoba , Aramaki-aza , Aoba-ku , Sendai 980-8579 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Information Sciences , Tohoku University , 6-3-09 Aoba , Aramaki-aza , Aoba-ku , Sendai 980-8579 , Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022397838"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.49000000953674316,"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":0.49000000953674316,"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":0.3400999903678894,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.09920000284910202,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/skew-information","display_name":"skew information","score":0.8259999752044678},{"id":"https://openalex.org/keywords/uncertainty-relations","display_name":"uncertainty relations","score":0.6019999980926514},{"id":"https://openalex.org/keywords/quantum-fisher-information","display_name":"quantum Fisher information","score":0.8790000081062317},{"id":"https://openalex.org/keywords/convexity","display_name":"convexity","score":0.6779999732971191},{"id":"https://openalex.org/keywords/quantum-indeterminacy","display_name":"quantum uncertainty","score":0.36399999260902405},{"id":"https://openalex.org/keywords/eigenvalue-bounds","display_name":"eigenvalue bounds","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.880299985408783},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7961000204086304},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6998000144958496},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5638999938964844},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5480999946594238},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5181999802589417},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4715999960899353},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.47119998931884766},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.46959999203681946},{"id":"https://openalex.org/C181543814","wikidata":"https://www.wikidata.org/wiki/Q44746","display_name":"Uncertainty principle","level":3,"score":0.46860000491142273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45159998536109924},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35409998893737793},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3456000089645386},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C2333172","wikidata":"https://www.wikidata.org/wiki/Q1425985","display_name":"Preorder","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.299699991941452},{"id":"https://openalex.org/C29406490","wikidata":"https://www.wikidata.org/wiki/Q1420659","display_name":"Fisher information","level":2,"score":0.296099990606308},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2775000035762787},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C37731324","wikidata":"https://www.wikidata.org/wiki/Q5380783","display_name":"Entropic uncertainty","level":4,"score":0.2612000107765198},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13870","pdf_url":"https://arxiv.org/pdf/2609.13870","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.13870","doi":"https://doi.org/10.48550/arxiv.2609.13870","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13870","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.13870","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13870","pdf_url":"https://arxiv.org/pdf/2609.13870","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G716777129","display_name":"\u91cf\u5b50\u8ad6\u53ca\u3073\u91cf\u5b50\u60c5\u5831\u7406\u8ad6\u306b\u304a\u3051\u308b\u666e\u904d\u5247","funder_award_id":"24K06873","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213228665.pdf","grobid_xml":"https://content.openalex.org/works/W7213228665.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2513919448","https://openalex.org/W4226253167","https://openalex.org/W3036198275","https://openalex.org/W4403086752","https://openalex.org/W3211850178","https://openalex.org/W2609088309","https://openalex.org/W2520394160","https://openalex.org/W2056654970","https://openalex.org/W4383265023","https://openalex.org/W2291301341"],"abstract_inverted_index":{"We":[0,113],"study":[1],"intrinsic":[2],"quantum":[3,106],"uncertainty":[4,25,55],"associated":[5],"with":[6],"a":[7,29,52,63],"single":[8],"observable":[9],"from":[10],"the":[11,22,43,58,66,82,87,104,110,123],"viewpoint":[12],"of":[13,31],"skew":[14,34,40,102],"information.":[15],"By":[16],"relaxing":[17],"ordinary":[18],"additivity":[19],"while":[20],"retaining":[21],"other":[23],"fundamental":[24],"requirements,":[26],"we":[27],"introduce":[28],"class":[30],"Hiai--Petz":[32,60,124],"nonadditive":[33],"informations":[35,41],"that":[36,116],"contains":[37],"Hansen's":[38],"metric-adjusted":[39,101],"as":[42,95],"boundary":[44],"case":[45],"$\u03b8=1$.":[46],"Our":[47],"main":[48],"quantitative":[49],"result":[50],"is":[51,89,120],"sharp":[53,79,98],"single-observable":[54],"relation":[56],"for":[57,100,134],"full":[59],"class.":[61],"For":[62],"fixed":[64],"state,":[65],"optimal":[67],"coefficient":[68],"depends":[69],"only":[70],"on":[71],"its":[72,132],"largest":[73],"and":[74,77,109],"smallest":[75],"eigenvalues":[76],"remains":[78],"even":[80],"after":[81],"maximal":[83],"classical":[84],"contribution":[85],"to":[86],"variance":[88],"retained.":[90],"The":[91],"general":[92],"theorem":[93],"yields,":[94],"special":[96],"cases,":[97],"bounds":[99],"informations,":[103],"SLD":[105],"Fisher":[107],"information,":[108],"power-commutator":[111],"family.":[112],"further":[114],"show":[115],"$K_s(\u03c1,A)=\\frac12\\|[\u03c1^s,A]\\|_{\\mathrm{HS}}^2$,":[117],"$1/2\\le":[118],"s<1$,":[119],"realized":[121],"within":[122],"framework":[125],"through":[126],"Stolarsky":[127],"operator":[128],"means,":[129],"thereby":[130],"establishing":[131],"convexity":[133],"$1/2":[135]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-16T00:00:00"}