{"id":"https://openalex.org/W2564079018","doi":"https://doi.org/10.1109/tit.2016.2641447","title":"Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels","display_name":"Bounds on the Distance Between a Unital Quantum Channel and the Convex Hull of Unitary Channels","publication_year":2016,"publication_date":"2016-12-19","ids":{"openalex":"https://openalex.org/W2564079018","doi":"https://doi.org/10.1109/tit.2016.2641447","mag":"2564079018"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2641447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2641447","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5088217238","display_name":"Nengkun Yu","orcid":"https://orcid.org/0000-0003-1188-3032"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["AU","CN"],"is_corresponding":true,"raw_author_name":"Nengkun Yu","raw_affiliation_strings":["Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW, Australia","State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109830244","display_name":"Runyao Duan","orcid":null},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["AU","CN"],"is_corresponding":false,"raw_author_name":"Runyao Duan","raw_affiliation_strings":["Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW, Australia","UTS-Tsinghua Joint Research Centre for Quantum Computation and Artificial Intelligence, and the UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Centre for Quantum Software and Information, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"UTS-Tsinghua Joint Research Centre for Quantum Computation and Artificial Intelligence, and the UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112434080","display_name":"Quanhua Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques Blaise Pascal","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]},{"id":"https://openalex.org/I4387152972","display_name":"Laboratoire de Math\u00e9matiques de Besan\u00e7on","ror":"https://ror.org/04nrhwg12","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4387152972","https://openalex.org/I4405256580"]}],"countries":["CN","FR"],"is_corresponding":false,"raw_author_name":"Quanhua Xu","raw_affiliation_strings":["Institut Universitaire de France, Paris, France","Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, China","Laboratoire de Math\u00e9matiques, Universit\u00e9 de Bourgogne Franche-Comt\u00e9, Besan\u00e7on, France"],"affiliations":[{"raw_affiliation_string":"Institut Universitaire de France, Paris, France","institution_ids":["https://openalex.org/I185839726"]},{"raw_affiliation_string":"Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques, Universit\u00e9 de Bourgogne Franche-Comt\u00e9, Besan\u00e7on, France","institution_ids":["https://openalex.org/I4387152972","https://openalex.org/I177064439","https://openalex.org/I4210155549"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088217238"],"corresponding_institution_ids":["https://openalex.org/I114017466","https://openalex.org/I4210096034","https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":1.7139,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.89530921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"63","issue":"2","first_page":"1299","last_page":"1310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9997000098228455,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9980999827384949,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.7628844976425171},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6444820761680603},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.6338895559310913},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6332952976226807},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5702792406082153},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5599479079246521},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.549558699131012},{"id":"https://openalex.org/keywords/quantum-capacity","display_name":"Quantum capacity","score":0.5094771981239319},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46698376536369324},{"id":"https://openalex.org/keywords/unital","display_name":"Unital","score":0.46462732553482056},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4591810405254364},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4575670063495636},{"id":"https://openalex.org/keywords/unitary-operator","display_name":"Unitary operator","score":0.4508204758167267},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4243132174015045},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.42018482089042664},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4188545346260071},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.4102644920349121},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3534526228904724},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2810545563697815},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.24046078324317932},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.16502147912979126},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14536091685295105},{"id":"https://openalex.org/keywords/quantum-network","display_name":"Quantum network","score":0.14074552059173584},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11061206459999084},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08967304229736328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7628844976425171},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6444820761680603},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.6338895559310913},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6332952976226807},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5702792406082153},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5599479079246521},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.549558699131012},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.5094771981239319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46698376536369324},{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.46462732553482056},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4591810405254364},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4575670063495636},{"id":"https://openalex.org/C188313703","wikidata":"https://www.wikidata.org/wiki/Q1972470","display_name":"Unitary operator","level":3,"score":0.4508204758167267},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4243132174015045},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.42018482089042664},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4188545346260071},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.4102644920349121},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3534526228904724},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2810545563697815},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.24046078324317932},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.16502147912979126},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14536091685295105},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.14074552059173584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11061206459999084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08967304229736328},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2016.2641447","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2641447","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03541789v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03541789","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2017, 63 (2), pp.1299-1310. ⟨10.1109/TIT.2016.2641447⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1084366706","display_name":null,"funder_award_id":"DP120103776","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G1943178281","display_name":null,"funder_award_id":"11431011","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3670282907","display_name":null,"funder_award_id":"DP110103473","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G4724055729","display_name":null,"funder_award_id":"11271292","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G510803618","display_name":null,"funder_award_id":"2011-BS01-008-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5510407270","display_name":null,"funder_award_id":"11301401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5640703879","display_name":null,"funder_award_id":"61179030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G909338052","display_name":null,"funder_award_id":"60621062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1491569431","https://openalex.org/W1523687058","https://openalex.org/W1602420091","https://openalex.org/W1621050367","https://openalex.org/W1800962207","https://openalex.org/W1968012014","https://openalex.org/W1973948469","https://openalex.org/W1981293662","https://openalex.org/W1985077192","https://openalex.org/W1988790002","https://openalex.org/W2023706405","https://openalex.org/W2032736549","https://openalex.org/W2033376433","https://openalex.org/W2051869207","https://openalex.org/W2057129626","https://openalex.org/W2061494150","https://openalex.org/W2065143310","https://openalex.org/W2116102644","https://openalex.org/W2119819325","https://openalex.org/W2124651213","https://openalex.org/W2153235257","https://openalex.org/W2159566537","https://openalex.org/W2168511581","https://openalex.org/W2476247684","https://openalex.org/W2963957678","https://openalex.org/W2990961515","https://openalex.org/W3098636779","https://openalex.org/W3098929870","https://openalex.org/W3099318861","https://openalex.org/W3102418387","https://openalex.org/W3104951025","https://openalex.org/W3105912528","https://openalex.org/W3106160368","https://openalex.org/W4206028667","https://openalex.org/W4285719527","https://openalex.org/W6629401538"],"related_works":["https://openalex.org/W2963792517","https://openalex.org/W2264989289","https://openalex.org/W2132333350","https://openalex.org/W3098756318","https://openalex.org/W3208208393","https://openalex.org/W2014135610","https://openalex.org/W2963686166","https://openalex.org/W3175244187","https://openalex.org/W1622368049","https://openalex.org/W2233795418"],"abstract_inverted_index":{"Motivated":[0],"by":[1,38],"the":[2,15,24,71],"recent":[3],"resolution":[4],"of":[5,27],"asymptotic":[6],"quantum":[7,21,42],"birkhoff":[8],"conjecture":[9],"(AQBC),":[10],"we":[11],"attempt":[12],"to":[13,52,56,61],"estimate":[14],"distance":[16,37],"between":[17,70],"a":[18],"given":[19],"unital":[20],"channel":[22],"and":[23,44,74],"convex":[25],"hull":[26],"unitary":[28],"channels.":[29],"We":[30,48,63],"provide":[31],"two":[32],"lower":[33],"bounds":[34],"on":[35],"this":[36],"employing":[39],"techniques":[40],"from":[41],"information":[43],"operator":[45],"algebras,":[46],"respectively.":[47],"then":[49],"show":[50],"how":[51],"apply":[53],"these":[54],"results":[55],"construct":[57],"some":[58],"explicit":[59],"counterexamples":[60],"AQBC.":[62,75],"also":[64],"point":[65],"out":[66],"an":[67],"interesting":[68],"connection":[69],"Grothendieck's":[72],"inequality":[73]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-01-06T00:00:00"}