{"id":"https://openalex.org/W7141736128","doi":"https://doi.org/10.1109/tit.2026.3678348","title":"Geometrical Constructions of Purity Testing Protocols and Their Applications to Quantum Communication","display_name":"Geometrical Constructions of Purity Testing Protocols and Their Applications to Quantum Communication","publication_year":2026,"publication_date":"2026-03-27","ids":{"openalex":"https://openalex.org/W7141736128","doi":"https://doi.org/10.1109/tit.2026.3678348"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3678348","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2026.3678348","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tit.2026.3678348","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003833729","display_name":"R\u00f3bert Tr\u00e9nyi","orcid":"https://orcid.org/0000-0002-2839-0472"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"R\u00f3bert Tr\u00e9nyi","raw_affiliation_strings":["Department of Theoretical Physics, University of the Basque Country (UPV/EHU), Bilbao, Spain"],"raw_orcid":"https://orcid.org/0000-0002-2839-0472","affiliations":[{"raw_affiliation_string":"Department of Theoretical Physics, University of the Basque Country (UPV/EHU), Bilbao, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040387138","display_name":"Simeon Ball","orcid":"https://orcid.org/0000-0003-4845-2084"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Simeon Ball","raw_affiliation_strings":["Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4845-2084","affiliations":[{"raw_affiliation_string":"Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071001252","display_name":"David G. Glynn","orcid":"https://orcid.org/0000-0002-6399-7771"},"institutions":[{"id":"https://openalex.org/I169541294","display_name":"Flinders University","ror":"https://ror.org/01kpzv902","country_code":"AU","type":"education","lineage":["https://openalex.org/I169541294"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David G. Glynn","raw_affiliation_strings":["College of Science and Engineering, Flinders University, Adelaide, SA, Australia"],"raw_orcid":"https://orcid.org/0000-0002-6399-7771","affiliations":[{"raw_affiliation_string":"College of Science and Engineering, Flinders University, Adelaide, SA, Australia","institution_ids":["https://openalex.org/I169541294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003401033","display_name":"Marcos Curty","orcid":"https://orcid.org/0000-0002-0330-6828"},"institutions":[{"id":"https://openalex.org/I106437751","display_name":"Centro Tecnol\u00f3xico de Telecomunicaci\u00f3ns de Galicia","ror":"https://ror.org/045ncxc88","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I106437751"]},{"id":"https://openalex.org/I6289922","display_name":"Universidade de Vigo","ror":"https://ror.org/05rdf8595","country_code":"ES","type":"education","lineage":["https://openalex.org/I6289922"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Marcos Curty","raw_affiliation_strings":["Department of Signal Theory and Communications, and the atlanTTic Research Center, Vigo Quantum Communication Center, the Escuela de Ingeniería de Telecomunicacíon, University of Vigo, Vigo, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0330-6828","affiliations":[{"raw_affiliation_string":"Department of Signal Theory and Communications, and the atlanTTic Research Center, Vigo Quantum Communication Center, the Escuela de Ingeniería de Telecomunicacíon, University of Vigo, Vigo, Spain","institution_ids":["https://openalex.org/I6289922","https://openalex.org/I106437751"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43372231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"6","first_page":"4041","last_page":"4055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.48410001397132874,"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":0.48410001397132874,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.1662999987602234,"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":0.1420000046491623,"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/quantum","display_name":"Quantum","score":0.4244999885559082},{"id":"https://openalex.org/keywords/quantum-information-science","display_name":"Quantum information science","score":0.39980000257492065},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33219999074935913},{"id":"https://openalex.org/keywords/communication-theory","display_name":"Communication theory","score":0.3278000056743622},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.30970001220703125},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.3086000084877014},{"id":"https://openalex.org/keywords/communications-system","display_name":"Communications system","score":0.2987000048160553},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.2985999882221222}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6039999723434448},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4244999885559082},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.39980000257492065},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.3905999958515167},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3409000039100647},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3330000042915344},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.329800009727478},{"id":"https://openalex.org/C3716254","wikidata":"https://www.wikidata.org/wiki/Q83966","display_name":"Communication theory","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.30970001220703125},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C101765175","wikidata":"https://www.wikidata.org/wiki/Q577764","display_name":"Communications system","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2944999933242798},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C95466800","wikidata":"https://www.wikidata.org/wiki/Q1027298","display_name":"Quantum key distribution","level":3,"score":0.27720001339912415},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.27559998631477356},{"id":"https://openalex.org/C12269588","wikidata":"https://www.wikidata.org/wiki/Q132364","display_name":"Communications protocol","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.27160000801086426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2671000063419342},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C111996192","wikidata":"https://www.wikidata.org/wiki/Q7269075","display_name":"Quantum noise","level":3,"score":0.26170000433921814},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2508000135421753},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2026.3678348","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2026.3678348","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2503.14003","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2503.14003","pdf_url":"https://arxiv.org/pdf/2503.14003","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"doi:10.1109/tit.2026.3678348","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tit.2026.3678348","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Purity":[0],"testing":[1,9],"protocols":[2,12,55],"(PTPs),":[3],"also":[4],"known":[5],"as":[6],"Bell":[7,31],"state":[8,25],"protocols,":[10],"i.e.,":[11],"that":[13,56,69],"decide":[14],"with":[15],"high":[16],"probability":[17],"whether":[18],"or":[19],"not":[20],"a":[21,27,38,67],"distributed":[22],"bipartite":[23],"quantum":[24,43,97,107,111],"is":[26],"tensor":[28],"product":[29],"of":[30,72,81,92],"states,":[32],"have":[33],"been":[34],"proven":[35],"to":[36],"be":[37],"useful":[39],"tool":[40],"in":[41,66,85,95],"many":[42],"communication":[44,98],"applications.":[45],"In":[46],"this":[47],"paper,":[48],"we":[49],"provide":[50],"geometrical":[51],"constructions":[52],"for":[53,105],"such":[54],"originate":[57],"directly":[58],"from":[59,79],"classical":[60],"linear":[61],"error":[62,101,108],"correcting":[63],"codes":[64],"(LECCs),":[65],"way":[68],"the":[70,73,82,86,90],"properties":[71],"resulting":[74],"PTP":[75],"are":[76],"completely":[77],"determined":[78],"those":[80],"LECC":[83],"used":[84],"construction.":[87],"We":[88],"investigate":[89],"implications":[91],"our":[93],"results":[94],"various":[96],"tasks,":[99],"including":[100],"detection,":[102],"entanglement":[103],"purification":[104],"general":[106],"models":[109],"and":[110],"message":[112],"authentication.":[113]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-28T00:00:00"}