{"id":"https://openalex.org/W2567518890","doi":null,"title":"Irreducible private states","display_name":"Irreducible private states","publication_year":2016,"publication_date":"2016-12-28","ids":{"openalex":"https://openalex.org/W2567518890","mag":"2567518890"},"language":"en","primary_location":{"id":"mag:2567518890","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1612.08938","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/1612.08938","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085393246","display_name":"Karol Horodecki","orcid":"https://orcid.org/0000-0001-7540-4147","observed_orcids":["https://orcid.org/0000-0001-7540-4147"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karol Horodecki","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7540-4147","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030429168","display_name":"Piotr \u0106wikli\u0144ski","orcid":"https://orcid.org/0000-0002-9315-2876","observed_orcids":["https://orcid.org/0000-0002-9315-2876"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Piotr \u0106wikli\u0144ski","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-9315-2876","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039340594","display_name":"A. Rutkowski","orcid":"https://orcid.org/0000-0002-8393-8170","observed_orcids":["https://orcid.org/0000-0002-8393-8170"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Rutkowski","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-8393-8170","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075335801","display_name":"Micha\u0142 Studzi\u0144ski","orcid":"https://orcid.org/0000-0002-5946-9845","observed_orcids":["https://orcid.org/0000-0002-5946-9845"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha\u0142 Studzi\u0144ski","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5946-9845","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"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":1.0,"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":1.0,"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/T10964","display_name":"Wireless Communication Security Techniques","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/private-states","display_name":"private states","score":0.765999972820282},{"id":"https://openalex.org/keywords/key-distillation","display_name":"key distillation","score":0.7760000228881836},{"id":"https://openalex.org/keywords/quantum-key-distribution","display_name":"quantum key distribution","score":0.5299999713897705},{"id":"https://openalex.org/keywords/separable-states","display_name":"separable states","score":0.7129999995231628},{"id":"https://openalex.org/keywords/entangled-states","display_name":"entangled states","score":0.4659999907016754}],"concepts":[{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6558952331542969},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5873380899429321},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5525097846984863},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5354673266410828},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5022497177124023},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4813281297683716},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.46570783853530884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4618500769138336},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2753751277923584},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23263758420944214},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.11248341202735901},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0692935585975647},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2567518890","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1612.08938","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2567518890","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1612.08938","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2887575233","https://openalex.org/W2015132296","https://openalex.org/W2129110882","https://openalex.org/W2523709487","https://openalex.org/W2171335291","https://openalex.org/W2041867592","https://openalex.org/W4281766982","https://openalex.org/W2794706464","https://openalex.org/W2963973102","https://openalex.org/W2028645676"],"abstract_inverted_index":{"Hereunder,":[0],"we":[1,121,134,156],"study":[2],"the":[3,16,28,37,43,47,66,78,90,95,108,116,126,144,162,182,191,201,207],"class":[4],"of":[5,94,125,146,184,193],"irreducible":[6,67,73,91,127],"private":[7,11,68,92,128,170,198],"states":[8,12,69,82,93,119,129,168,199],"that":[9,65,102,209],"are":[10,70,99,211],"from":[13,36,42],"which":[14,31],"all":[15,71,89],"secret":[17],"content":[18],"is":[19,49],"accessible":[20],"via":[21],"measuring":[22],"their":[23,131],"key":[24,33,38,84,109,118,148],"part.":[25],"We":[26,51],"provide":[27,157],"first":[29],"protocol":[30],"distills":[32],"not":[34,177],"only":[35,46,76],"part,":[39],"but":[40,80],"also":[41,53],"shield":[44],"if":[45,74,77],"state":[48],"reducible.":[50],"prove":[52],"a":[54,136,151,158],"tighter":[55],"upper":[56],"bound":[57,117,160,188],"on":[58,107,161],"its":[59],"performance.":[60],"This":[61],"implies":[62],"in":[63,143,172,200],"particular":[64],"strictly":[72,100,212],"and":[75,130,169],"entangled":[79],"key-undistillable":[81,167],"(bound":[83],"states)":[85],"exist.":[86],"In":[87],"turn,":[88],"dimension":[96],"$4\\otimes":[97],"4$":[98],"irreducible,":[101],"is,":[103],"after":[104],"an":[105],"attack":[106],"part":[110],"they":[111,210],"become":[112],"separable":[113],"states.":[114],"Providing":[115],"exist,":[120],"consider":[122],"different":[123],"subclasses":[124],"properties.":[132],"Finally":[133],"show":[135],"possible":[137],"way":[138],"to":[139,180,190],"apply":[140],"our":[141],"findings":[142],"context":[145],"quantum":[147],"repeaters.":[149],"As":[150],"step":[152],"towards":[153],"this":[154,187],"direction,":[155],"lower":[159],"trace":[163],"norm":[164],"distance":[165],"between":[166],"states,":[171],"sufficiently":[173],"high":[174],"dimensions,":[175],"yet":[176],"large":[178],"enough":[179],"reach":[181],"goal":[183],"application.":[185],"However":[186],"leads":[189],"proof":[192],"no-key":[194],"swapping":[195],"for":[196],"some":[197],"single":[202],"copy":[203],"case":[204],"without":[205],"using":[206],"fact":[208],"irreducible.":[213]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-10-02T10:15:12.560889","created_date":"2017-01-06T00:00:00"}