{"id":"https://openalex.org/W4387704942","doi":"https://doi.org/10.1137/22m1500216","title":"Optimal Self-Concordant Barriers for Quantum Relative Entropies","display_name":"Optimal Self-Concordant Barriers for Quantum Relative Entropies","publication_year":2023,"publication_date":"2023-10-17","ids":{"openalex":"https://openalex.org/W4387704942","doi":"https://doi.org/10.1137/22m1500216"},"language":"en","primary_location":{"id":"doi:10.1137/22m1500216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1500216","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5017261970","display_name":"Hamza Fawzi","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hamza Fawzi","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037774037","display_name":"James Saunderson","orcid":"https://orcid.org/0000-0002-5456-0180"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"James Saunderson","raw_affiliation_strings":["Department of Electrical and Computer Systems Engineering, Monash University, Victoria 3800, Australia"],"raw_orcid":"https://orcid.org/0000-0002-5456-0180","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, Victoria 3800, Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.387,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.88322354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"33","issue":"4","first_page":"2858","last_page":"2884"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9878000020980835,"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"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9824000000953674,"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/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.7779013514518738},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.733230471611023},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.7217100858688354},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6576133966445923},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5898822546005249},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5723516941070557},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5338218212127686},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48908501863479614},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4825415015220642},{"id":"https://openalex.org/keywords/conic-optimization","display_name":"Conic optimization","score":0.4371858239173889},{"id":"https://openalex.org/keywords/quantum-relative-entropy","display_name":"Quantum relative entropy","score":0.4319700300693512},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4136379063129425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.346416711807251},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3287554383277893},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29456818103790283},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.2888336777687073},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17589899897575378},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.12492114305496216},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10599556565284729},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09168559312820435},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.09152853488922119},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08752420544624329}],"concepts":[{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.7779013514518738},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.733230471611023},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.7217100858688354},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6576133966445923},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5898822546005249},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5723516941070557},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5338218212127686},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48908501863479614},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4825415015220642},{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.4371858239173889},{"id":"https://openalex.org/C24495805","wikidata":"https://www.wikidata.org/wiki/Q7269091","display_name":"Quantum relative entropy","level":5,"score":0.4319700300693512},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4136379063129425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.346416711807251},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3287554383277893},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29456818103790283},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2888336777687073},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17589899897575378},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.12492114305496216},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10599556565284729},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09168559312820435},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.09152853488922119},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08752420544624329},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1500216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1500216","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6101260676","display_name":"Realising the potential of hyperbolic programming","funder_award_id":"DE210101056","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1584686300","https://openalex.org/W1632601927","https://openalex.org/W1973534486","https://openalex.org/W2004980778","https://openalex.org/W2023267838","https://openalex.org/W2031315527","https://openalex.org/W2061671797","https://openalex.org/W2064990832","https://openalex.org/W2077274614","https://openalex.org/W2077741783","https://openalex.org/W2094966623","https://openalex.org/W2105211531","https://openalex.org/W2105918132","https://openalex.org/W2122166994","https://openalex.org/W2144180948","https://openalex.org/W2163484647","https://openalex.org/W2168792807","https://openalex.org/W2321429733","https://openalex.org/W2471548350","https://openalex.org/W2485089179","https://openalex.org/W2607314934","https://openalex.org/W2611807022","https://openalex.org/W2767107538","https://openalex.org/W2901838001","https://openalex.org/W3005935076","https://openalex.org/W3008048690","https://openalex.org/W3045172124","https://openalex.org/W3097101327","https://openalex.org/W3100174796","https://openalex.org/W3100438626","https://openalex.org/W3101644589","https://openalex.org/W3101663526","https://openalex.org/W3103419989","https://openalex.org/W3103744872","https://openalex.org/W3105306379","https://openalex.org/W3106247388","https://openalex.org/W3122882895","https://openalex.org/W3165533811","https://openalex.org/W3181648109","https://openalex.org/W3197081982","https://openalex.org/W3210990630","https://openalex.org/W4249667877","https://openalex.org/W4255333822","https://openalex.org/W4281396973"],"related_works":["https://openalex.org/W2189660299","https://openalex.org/W2022488470","https://openalex.org/W3149261477","https://openalex.org/W83120765","https://openalex.org/W4295007075","https://openalex.org/W2021428356","https://openalex.org/W3104786485","https://openalex.org/W2117065890","https://openalex.org/W3103995399","https://openalex.org/W1980450998"],"abstract_inverted_index":{".Quantum":[0],"relative":[1,40,62,119],"entropies":[2,41,63],"are":[3,115],"jointly":[4],"convex":[5,57,97],"functions":[6,33,107],"of":[7,30,37,91,104],"two":[8],"positive":[9],"definite":[10],"matrices":[11],"that":[12,47,110],"generalize":[13],"the":[14,35,76,89,101,111],"Kullback\u2013Leibler":[15],"divergence":[16],"and":[17,42,78,108],"arise":[18],"naturally":[19],"in":[20,82],"quantum":[21,39,61],"information":[22],"theory.":[23],"In":[24],"this":[25],"paper,":[26],"we":[27,45,87],"prove":[28],"self-concordance":[29,90],"natural":[31,92],"barrier":[32,52,113],"for":[34,72,94],"epigraphs":[36],"various":[38,95],"divergences.":[43],"Furthermore":[44],"show":[46,109],"these":[48],"barriers":[49,55,93],"have":[50],"optimal":[51],"parameters.":[53],"These":[54],"allow":[56],"optimization":[58],"problems":[59],"involving":[60],"to":[64,100],"be":[65],"directly":[66],"solved":[67],"using":[68],"interior":[69],"point":[70],"methods":[71],"nonsymmetric":[73],"cones,":[74],"avoiding":[75],"approximations":[77],"lifting":[79],"techniques":[80],"used":[81],"previous":[83],"approaches.":[84],"More":[85],"generally,":[86],"establish":[88],"closed":[96],"cones":[98],"related":[99],"noncommutative":[102],"perspectives":[103],"operator":[105],"concave":[106],"resulting":[112],"parameters":[114],"optimal.Keywordsself-concordant":[116],"barrierconic":[117],"programmingquantum":[118],"entropiesinterior-point":[120],"methodsMSC":[121],"codes90C2552A2026B2581P17":[122]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
