{"id":"https://openalex.org/W7213609359","doi":"https://doi.org/10.48550/arxiv.2609.20781","title":"Parallel quantum channel discrimination and numerical ranges in tensor product subspaces","display_name":"Parallel quantum channel discrimination and numerical ranges in tensor product subspaces","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7213609359","doi":"https://doi.org/10.48550/arxiv.2609.20781"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.20781","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20781","pdf_url":"https://arxiv.org/pdf/2609.20781","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/2609.20781","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140605184","display_name":"Adam B\u00edlek","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"B\u00edlek, Adam","raw_affiliation_strings":["Department of Applied Mathematics , Faculty of Electrical Engineering and Computer Science , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic","IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , Faculty of Electrical Engineering and Computer Science , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic","institution_ids":["https://openalex.org/I142208455"]},{"raw_affiliation_string":"IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073003652","display_name":"Paulina Lewandowska","orcid":"https://orcid.org/0000-0003-1564-7782","observed_orcids":["https://orcid.org/0000-0003-1564-7782"]},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Lewandowska, Paulina","raw_affiliation_strings":["IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040679414","display_name":"Ryszard Kukulski","orcid":"https://orcid.org/0000-0002-9171-1734","observed_orcids":["https://orcid.org/0000-0002-9171-1734"]},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Kukulski, Ryszard","raw_affiliation_strings":["IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IT4Innovations , VSB-Technical University of Ostrava , 17. listopadu 2172/15 , 708 33 Ostrava , Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142208455"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.9937000274658203,"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":0.9937000274658203,"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":0.004800000227987766,"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":0.000699999975040555,"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-channel-discrimination","display_name":"quantum channel discrimination","score":0.9819999933242798},{"id":"https://openalex.org/keywords/numerical-range","display_name":"numerical range","score":0.7059999704360962},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.8880000114440918}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8019000291824341},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6406000256538391},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6281999945640564},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6140000224113464},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5450999736785889},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5238999724388123},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4830000102519989},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.4537000060081482},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4481000006198883},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.44530001282691956},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.42800000309944153},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.39469999074935913},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3847000002861023},{"id":"https://openalex.org/C168090291","wikidata":"https://www.wikidata.org/wiki/Q5128319","display_name":"Classical capacity","level":5,"score":0.3714999854564667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3463999927043915},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.31619998812675476},{"id":"https://openalex.org/C191608238","wikidata":"https://www.wikidata.org/wiki/Q5249552","display_name":"Decoherence-free subspaces","level":5,"score":0.3086000084877014},{"id":"https://openalex.org/C206040425","wikidata":"https://www.wikidata.org/wiki/Q4748511","display_name":"Amplitude damping channel","level":5,"score":0.30640000104904175},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.30090001225471497},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C31599958","wikidata":"https://www.wikidata.org/wiki/Q3128632","display_name":"Bisection","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2872999906539917},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28360000252723694},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2574999928474426},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.20781","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20781","pdf_url":"https://arxiv.org/pdf/2609.20781","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.2609.20781","doi":"https://doi.org/10.48550/arxiv.2609.20781","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.20781","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:2609.20781","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.20781","pdf_url":"https://arxiv.org/pdf/2609.20781","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213609359.pdf","grobid_xml":"https://content.openalex.org/works/W7213609359.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2294902379","https://openalex.org/W7135230209","https://openalex.org/W2206545","https://openalex.org/W1726303421","https://openalex.org/W3099752100","https://openalex.org/W2894878392","https://openalex.org/W2392457299","https://openalex.org/W6944422383","https://openalex.org/W4321490811","https://openalex.org/W2015936613"],"abstract_inverted_index":{"Quantum":[0],"channel":[1,34],"discrimination":[2,35,58],"plays":[3],"a":[4,38,48,53,114,155],"crucial":[5],"role":[6],"in":[7,17,37,59,62,88],"quantum":[8,33,54,77],"information":[9],"theory.":[10],"Of":[11],"particular":[12],"interest":[13],"is":[14,145],"the":[15,19,31,63,71,89,105,126,132,137,147,151,162,165,169,173],"case":[16],"which":[18,103],"channels":[20,78],"can":[21],"be":[22],"discriminated":[23],"perfectly.":[24],"In":[25,67,135],"this":[26],"work,":[27],"we":[28,69,86,141],"focus":[29],"on":[30],"perfect":[32,57,81],"task":[36],"parallel":[39,108],"scheme.":[40],"We":[41],"develop":[42],"an":[43],"SDP":[44],"formulation":[45],"combined":[46],"with":[47],"bisection":[49],"procedure":[50],"to":[51,79,84,111],"compute":[52],"state":[55],"for":[56],"time":[60],"linear":[61],"number":[64,73,106],"of":[65,74,76,93,107,117,131,150,154,158,164,168,172],"copies.":[66],"addition,":[68],"obtain":[70],"minimal":[72,148,166],"copies":[75],"achieve":[80],"discrimination.":[82],"Thanks":[83],"that,":[85],"settle":[87],"affirmative":[90],"Conjecture":[91],"1":[92],"Duan,":[94],"Guo,":[95],"Li":[96,98],"and":[97,128,143],"[arXiv:1605.02294,":[99],"IEEE":[100],"ISIT":[101],"2016],":[102],"characterizes":[104],"uses":[109],"needed":[110],"discriminate":[112],"perfectly":[113],"distinguished":[115],"family":[116],"operator":[118],"subspaces.":[119,175],"All":[120],"our":[121],"results":[122],"are":[123],"obtained":[124],"using":[125],"notion":[127],"basic":[129],"properties":[130],"numerical":[133,152,170],"range.":[134],"particular,":[136],"key":[138],"fact":[139],"that":[140,146],"prove":[142],"use":[144],"angle":[149],"range":[153],"tensor":[156],"product":[157],"matrix":[159],"subspaces":[160],"equals":[161],"sum":[163],"angles":[167],"ranges":[171],"individual":[174]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-19T00:00:00"}