{"id":"https://openalex.org/W2914771158","doi":"https://doi.org/10.22331/q-2020-04-16-253","title":"Detecting mixed-unitary quantum channels is NP-hard","display_name":"Detecting mixed-unitary quantum channels is NP-hard","publication_year":2020,"publication_date":"2020-04-16","ids":{"openalex":"https://openalex.org/W2914771158","doi":"https://doi.org/10.22331/q-2020-04-16-253","mag":"2914771158"},"language":"en","primary_location":{"id":"doi:10.22331/q-2020-04-16-253","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-04-16-253","pdf_url":"https://quantum-journal.org/papers/q-2020-04-16-253/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2020-04-16-253/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021428568","display_name":"Colin Do-Yan Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Colin Do-Yan Lee","raw_affiliation_strings":["Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022329888","display_name":"John Watrous","orcid":"https://orcid.org/0000-0002-4263-9393"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"John Watrous","raw_affiliation_strings":["Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Computing and School of Computer Science, University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021428568"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.4953,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.85950689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"4","issue":null,"first_page":"253","last_page":"253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994999766349792,"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":0.9994999766349792,"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/T10237","display_name":"Cryptography and Data Security","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/T10020","display_name":"Quantum Information and Cryptography","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4823960065841675},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.44484972953796387},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.43638959527015686},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4025714695453644},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36768901348114014}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4823960065841675},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44484972953796387},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.43638959527015686},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4025714695453644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36768901348114014},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2020-04-16-253","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-04-16-253","pdf_url":"https://quantum-journal.org/papers/q-2020-04-16-253/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1902.03164","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.03164","pdf_url":"https://arxiv.org/pdf/1902.03164","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:doaj.org/article:ad68155921174404ab19c108cc4d38f6","is_oa":true,"landing_page_url":"https://doaj.org/article/ad68155921174404ab19c108cc4d38f6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 4, p 253 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2020-04-16-253","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2020-04-16-253","pdf_url":"https://quantum-journal.org/papers/q-2020-04-16-253/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320309949","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914771158.pdf","grobid_xml":"https://content.openalex.org/works/W2914771158.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W250374846","https://openalex.org/W987035227","https://openalex.org/W1527197079","https://openalex.org/W1644115585","https://openalex.org/W1833422638","https://openalex.org/W1980744208","https://openalex.org/W2008152388","https://openalex.org/W2010699490","https://openalex.org/W2044630019","https://openalex.org/W2098611377","https://openalex.org/W2100440346","https://openalex.org/W2103122463","https://openalex.org/W2103486884","https://openalex.org/W2115297457","https://openalex.org/W2116102644","https://openalex.org/W2166716414","https://openalex.org/W2775838261","https://openalex.org/W2804172638","https://openalex.org/W2952067539","https://openalex.org/W3100792714","https://openalex.org/W3102152880","https://openalex.org/W4298227433","https://openalex.org/W4300645277"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W4304699869"],"abstract_inverted_index":{"A":[0],"quantum":[1,33],"channel":[2],"is":[3,38],"said":[4],"to":[5,42,46],"be":[6,15],"a<mml:math":[7],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow":[8],"class=\"MJX-TeXAtom-ORD\"><mml:mtext":[9],"class=\"MJX-tex-mathit\"":[10],"mathvariant=\"italic\">mixed-unitary</mml:mtext></mml:mrow></mml:math>channel":[11],"if":[12],"it":[13,37],"can":[14],"expressed":[16],"as":[17],"a":[18,32,53],"convex":[19],"combination":[20],"of":[21,31,75,82,85],"unitary":[22],"channels.":[23,88],"We":[24],"prove":[25],"that,":[26],"given":[27],"the":[28,62,73,76,83,86],"Choi":[29],"representation":[30],"channel<mml:math":[34],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi":[35,51,65,80],"mathvariant=\"normal\">\u03a6</mml:mi></mml:math>,":[36],"NP-hard":[39],"with":[40],"respect":[41],"polynomial-time":[43],"Turing":[44],"reductions":[45],"determine":[47],"whether":[48],"or":[49],"not<mml:math":[50],"mathvariant=\"normal\">\u03a6</mml:mi></mml:math>is":[52,66],"mixed-unitary":[54,87],"channel.":[55],"This":[56],"hardness":[57],"result":[58],"holds":[59],"even":[60],"under":[61],"assumption":[63],"that<mml:math":[64],"not":[67],"within":[68],"an":[69],"inverse-polynomial":[70],"distance":[71],"(in":[72],"dimension":[74],"space":[77],"upon":[78],"which<mml:math":[79],"mathvariant=\"normal\">\u03a6</mml:mi></mml:math>acts)":[81],"boundary":[84]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
