{"id":"https://openalex.org/W1542017316","doi":"https://doi.org/10.48550/arxiv.0709.3680","title":"Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation","display_name":"Inequalities that Collectively Completely Characterize the Catalytic Majorization Relation","publication_year":2007,"publication_date":"2007-09-24","ids":{"openalex":"https://openalex.org/W1542017316","doi":"https://doi.org/10.48550/arxiv.0709.3680","mag":"1542017316"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0709.3680","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0709.3680","pdf_url":"https://arxiv.org/pdf/0709.3680","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/0709.3680","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113499779","display_name":"M. Klimesh","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Klimesh, Matthew","raw_affiliation_strings":["Jet Propulsion Laboratory , California Institute of Technology , Pasadena , CA 91109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory , California Institute of Technology , Pasadena , CA 91109","institution_ids":["https://openalex.org/I122411786","https://openalex.org/I1334627681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113499779"],"corresponding_institution_ids":["https://openalex.org/I122411786","https://openalex.org/I1334627681"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":57,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.8446999788284302,"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":0.8446999788284302,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.07370000332593918,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.030500000342726707,"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/majorization","display_name":"majorization","score":0.7450000047683716},{"id":"https://openalex.org/keywords/probability-vectors","display_name":"probability vectors","score":0.7649999856948853},{"id":"https://openalex.org/keywords/quantum-state-transformation","display_name":"quantum state transformation","score":0.5799999833106995},{"id":"https://openalex.org/keywords/local-operations-and-classical-communication","display_name":"local operations and classical communication","score":0.9879999756813049},{"id":"https://openalex.org/keywords/quantum-catalysis","display_name":"quantum catalysis","score":0.5690000057220459},{"id":"https://openalex.org/keywords/inequality-mathematics","display_name":"inequality (mathematics)","score":0.37599998712539673}],"concepts":[{"id":"https://openalex.org/C2777818330","wikidata":"https://www.wikidata.org/wiki/Q1994695","display_name":"Majorization","level":2,"score":0.8346607685089111},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.6947160363197327},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6801859140396118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41475045680999756},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36283451318740845},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24106010794639587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23901855945587158},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1245843768119812},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.06154060363769531}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:0709.3680","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0709.3680","pdf_url":"https://arxiv.org/pdf/0709.3680","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.0709.3680","doi":"https://doi.org/10.48550/arxiv.0709.3680","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0709.3680","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:0709.3680","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0709.3680","pdf_url":"https://arxiv.org/pdf/0709.3680","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1542017316.pdf","grobid_xml":"https://content.openalex.org/works/W1542017316.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1520504540","https://openalex.org/W2006309149","https://openalex.org/W2798707604"],"related_works":["https://openalex.org/W2165730988","https://openalex.org/W2081131889","https://openalex.org/W6948770500","https://openalex.org/W2004853053","https://openalex.org/W2002429786","https://openalex.org/W3196661906","https://openalex.org/W3102829624","https://openalex.org/W3000376446","https://openalex.org/W3082648099","https://openalex.org/W2974887555"],"abstract_inverted_index":{"For":[0],"probability":[1,21],"vectors":[2],"x":[3,10,26,52],"and":[4,56,103],"y,":[5],"the":[6,67,117],"catalytic":[7,80],"majorization":[8,81],"relation":[9,82],"prec_T":[11,53],"y":[12,32,54],"is":[13,29,43,77,83],"defined":[14],"to":[15,48,85,115],"hold":[16],"when":[17,106],"there":[18],"exists":[19],"a":[20,72,87],"vector":[22],"z":[23,28],"such":[24,45],"that":[25],"otimes":[27,33],"majorized":[30],"by":[31],"z.":[34],"In":[35],"this":[36,75],"paper,":[37],"an":[38,107],"infinite":[39],"family":[40],"of":[41,71,74,89,92],"functions":[42,64],"given":[44],"that,":[46],"subject":[47],"some":[49],"trivial":[50],"restrictions,":[51],"if":[55,58],"only":[57],"f_r(x)":[59],"<":[60],"f_r(y)":[61],"for":[62],"all":[63],"f_r":[65],"in":[66],"family.":[68],"An":[69],"outline":[70],"proof":[73],"result":[76],"provided.":[78],"The":[79],"known":[84],"provide":[86],"determination":[88],"which":[90],"transformations":[91],"jointly":[93,109],"held":[94,110],"pure":[95],"quantum":[96],"states":[97],"are":[98],"possible":[99],"using":[100],"local":[101],"operations":[102],"classical":[104],"communication":[105],"additional":[108],"state":[111],"may":[112],"be":[113],"specified":[114],"facilitate":[116],"transformation":[118],"without":[119],"being":[120],"consumed.":[121]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}