{"id":"https://openalex.org/W4389626445","doi":"https://doi.org/10.22331/q-2023-12-12-1206","title":"The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications","display_name":"The Min-Entropy of Classical-Quantum Combs for Measurement-Based Applications","publication_year":2023,"publication_date":"2023-12-12","ids":{"openalex":"https://openalex.org/W4389626445","doi":"https://doi.org/10.22331/q-2023-12-12-1206"},"language":"en","primary_location":{"id":"doi:10.22331/q-2023-12-12-1206","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2023-12-12-1206","pdf_url":"https://quantum-journal.org/papers/q-2023-12-12-1206/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2023-12-12-1206/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102591245","display_name":"Isaac D. Smith","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Isaac D. Smith","raw_affiliation_strings":["Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065187735","display_name":"Marius Krumm","orcid":null},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Marius Krumm","raw_affiliation_strings":["Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023989415","display_name":"Lukas J. Fiderer","orcid":"https://orcid.org/0000-0002-9150-1024"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Lukas J. Fiderer","raw_affiliation_strings":["Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043277691","display_name":"Hendrik Poulsen Nautrup","orcid":"https://orcid.org/0000-0001-7815-7006"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hendrik Poulsen Nautrup","raw_affiliation_strings":["Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009007803","display_name":"Hans J. Briegel","orcid":"https://orcid.org/0000-0002-9065-1565"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Hans J. Briegel","raw_affiliation_strings":["Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Theoretical Physics, UIBK, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.4895,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72352968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"1206","last_page":"1206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9997000098228455,"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":0.9979000091552734,"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/computer-science","display_name":"Computer science","score":0.6613803505897522},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.6010297536849976},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.44503793120384216},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.41404715180397034},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3244880735874176},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2010466456413269},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16541308164596558}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6613803505897522},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.6010297536849976},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.44503793120384216},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.41404715180397034},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3244880735874176},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2010466456413269},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16541308164596558}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22331/q-2023-12-12-1206","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2023-12-12-1206","pdf_url":"https://quantum-journal.org/papers/q-2023-12-12-1206/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:doaj.org/article:bfa2c36ca8a94c268c4651b58cae2b76","is_oa":true,"landing_page_url":"https://doaj.org/article/bfa2c36ca8a94c268c4651b58cae2b76","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 7, p 1206 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2023-12-12-1206","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2023-12-12-1206","pdf_url":"https://quantum-journal.org/papers/q-2023-12-12-1206/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/G1275353404","display_name":"Atoms, Light, and Molecules","funder_award_id":"W1259","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3642307514","display_name":null,"funder_award_id":"W1259-N27","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4861696250","display_name":null,"funder_award_id":"F7102","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5814117976","display_name":null,"funder_award_id":"101055129","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7853507824","display_name":null,"funder_award_id":"W1259","funder_id":"https://openalex.org/F4320327491","funder_display_name":"Universit\u00e4t Innsbruck"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320327491","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389626445.pdf"},"referenced_works_count":113,"referenced_works":["https://openalex.org/W1490034338","https://openalex.org/W1490394993","https://openalex.org/W1522547328","https://openalex.org/W1578322733","https://openalex.org/W1601313063","https://openalex.org/W1773465796","https://openalex.org/W1787342803","https://openalex.org/W1946741112","https://openalex.org/W1968493380","https://openalex.org/W1968671063","https://openalex.org/W1975408841","https://openalex.org/W1986556555","https://openalex.org/W1988844614","https://openalex.org/W1990406357","https://openalex.org/W1990843498","https://openalex.org/W1993661095","https://openalex.org/W1997837296","https://openalex.org/W2006717328","https://openalex.org/W2007542733","https://openalex.org/W2013793864","https://openalex.org/W2015179126","https://openalex.org/W2015775929","https://openalex.org/W2016236587","https://openalex.org/W2024857769","https://openalex.org/W2035993353","https://openalex.org/W2041922678","https://openalex.org/W2042723520","https://openalex.org/W2045702468","https://openalex.org/W2049844449","https://openalex.org/W2051051926","https://openalex.org/W2066072386","https://openalex.org/W2092105345","https://openalex.org/W2092857006","https://openalex.org/W2098474960","https://openalex.org/W2099382096","https://openalex.org/W2103368228","https://openalex.org/W2112813087","https://openalex.org/W2113152322","https://openalex.org/W2114805880","https://openalex.org/W2116102644","https://openalex.org/W2117593045","https://openalex.org/W2119388976","https://openalex.org/W2130674235","https://openalex.org/W2143677375","https://openalex.org/W2143891888","https://openalex.org/W2144277460","https://openalex.org/W2145304048","https://openalex.org/W2148115906","https://openalex.org/W2164253138","https://openalex.org/W2165148883","https://openalex.org/W2190871789","https://openalex.org/W2268589176","https://openalex.org/W2288174618","https://openalex.org/W2418959496","https://openalex.org/W2473976255","https://openalex.org/W2479152214","https://openalex.org/W2517979549","https://openalex.org/W2526522103","https://openalex.org/W2537390275","https://openalex.org/W2558717661","https://openalex.org/W2594899115","https://openalex.org/W2739806694","https://openalex.org/W2775516909","https://openalex.org/W2776229398","https://openalex.org/W2781738013","https://openalex.org/W2783159008","https://openalex.org/W2786366947","https://openalex.org/W2790590803","https://openalex.org/W2791875598","https://openalex.org/W2798773976","https://openalex.org/W2804172638","https://openalex.org/W2810596836","https://openalex.org/W2896792097","https://openalex.org/W2901389979","https://openalex.org/W2925491997","https://openalex.org/W2962398523","https://openalex.org/W2963245216","https://openalex.org/W2963701006","https://openalex.org/W2963966702","https://openalex.org/W2965395041","https://openalex.org/W2990961515","https://openalex.org/W2995235436","https://openalex.org/W3002228079","https://openalex.org/W3007025617","https://openalex.org/W3098193030","https://openalex.org/W3098825863","https://openalex.org/W3099834476","https://openalex.org/W3100177206","https://openalex.org/W3100657319","https://openalex.org/W3100931082","https://openalex.org/W3101663526","https://openalex.org/W3101851511","https://openalex.org/W3110848545","https://openalex.org/W3127373044","https://openalex.org/W3128474234","https://openalex.org/W3135081642","https://openalex.org/W3143400115","https://openalex.org/W3185682535","https://openalex.org/W4213004663","https://openalex.org/W4256232470","https://openalex.org/W4293578150","https://openalex.org/W4297944615","https://openalex.org/W4301019227","https://openalex.org/W4302423442","https://openalex.org/W4312354169","https://openalex.org/W4379054025","https://openalex.org/W4384389713","https://openalex.org/W4388444291","https://openalex.org/W4394645922","https://openalex.org/W4394651567","https://openalex.org/W4394658803","https://openalex.org/W4394672652","https://openalex.org/W6967373611"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Learning":[0],"a":[1,5,10,24,36,110,128,149,160,191],"hidden":[2,41,65],"property":[3,42,66],"of":[4,12,26,56,87,96,130,136,151,159,171],"quantum":[6,51,101,113,197],"system":[7],"typically":[8],"requires":[9],"series":[11],"interactions.":[13],"In":[14],"this":[15,88,203],"work,":[16],"we":[17,90,108,147],"formalise":[18],"such":[19],"multi-round":[20],"learning":[21,63,168,180],"processes":[22],"using":[23,117],"generalisation":[25],"classical-quantum":[27,30,81],"states,":[28],"called":[29],"combs.":[31,82],"Here,":[32],"\"classical\"":[33],"refers":[34,48],"to":[35,43,49,80,126,156],"random":[37],"variable":[38],"encoding":[39],"the":[40,50,54,57,64,72,85,118,124,137,140,144,157,169,172],"be":[44,68],"learnt,":[45],"and":[46,76,104,121,196],"\"quantum\"":[47],"comb":[52,73],"describing":[53],"behaviour":[55],"system.":[58],"The":[59],"optimal":[60],"strategy":[61],"for":[62,133,175,185],"can":[67],"quantified":[69],"by":[70],"applying":[71],"min-entropy":[74,125],"(Chiribella":[75],"Ebler,":[77],"NJP,":[78],"2016)":[79],"To":[83],"demonstrate":[84],"power":[86],"approach,":[89],"focus":[91],"attention":[92],"on":[93],"an":[94],"array":[95],"problems":[97],"derived":[98],"from":[99],"measurement-based":[100],"computation":[102,114],"(MBQC)":[103],"related":[105,155],"applications.":[106],"Specifically,":[107],"describe":[109],"known":[111],"blind":[112],"(BQC)":[115],"protocol":[116],"combs":[119],"formalism":[120],"thereby":[122],"leverage":[123],"provide":[127],"proof":[129],"single-shot":[131],"security":[132],"multiple":[134],"rounds":[135],"protocol,":[138],"extending":[139],"existing":[141],"result":[142],"in":[143,202],"literature.":[145],"Furthermore,":[146],"consider":[148],"range":[150],"operationally":[152],"motivated":[153],"examples":[154,166],"verification":[158],"partially":[161],"unknown":[162],"MBQC":[163,195],"device.":[164],"These":[165],"involve":[167],"features":[170],"device":[173],"necessary":[174],"its":[176,181],"correct":[177],"use,":[178],"including":[179],"internal":[182],"reference":[183],"frame":[184],"measurement":[186],"calibration.":[187],"We":[188],"also":[189],"introduce":[190],"novel":[192],"connection":[193],"between":[194],"causal":[198],"models":[199],"that":[200],"arises":[201],"context.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}