{"id":"https://openalex.org/W7220648536","doi":"https://doi.org/10.48550/arxiv.2610.06723","title":"Approximate cloning of structured pure states","display_name":"Approximate cloning of structured pure states","publication_year":2026,"publication_date":"2026-10-05","ids":{"openalex":"https://openalex.org/W7220648536","doi":"https://doi.org/10.48550/arxiv.2610.06723"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.06723","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06723","pdf_url":"https://arxiv.org/pdf/2610.06723","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.06723","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024530812","display_name":"Yaroslav Herasymenko","orcid":"https://orcid.org/0000-0003-0640-7429","observed_orcids":["https://orcid.org/0000-0003-0640-7429"]},"institutions":[{"id":"https://openalex.org/I183974707","display_name":"Perimeter Institute","ror":"https://ror.org/013m0ej23","country_code":"CA","type":"facility","lineage":["https://openalex.org/I183974707"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Herasymenko, Yaroslav","raw_affiliation_strings":["Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Perimeter Institute for Theoretical Physics , Waterloo , Ontario N2L 2Y5 , Canada","institution_ids":["https://openalex.org/I183974707"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014323261","display_name":"Junqiao Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]},{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Lin, Junqiao","raw_affiliation_strings":["QuSoft , CWI , Amsterdam , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuSoft , CWI , Amsterdam , The Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I4210099082"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018669779","display_name":"Philip Verduyn Lunel","orcid":"https://orcid.org/0000-0001-5419-6027","observed_orcids":["https://orcid.org/0000-0001-5419-6027"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210159731","display_name":"LIP6","ror":"https://ror.org/05krcen59","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159245","https://openalex.org/I4210159731"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lunel, Philip Verduyn","raw_affiliation_strings":["Sorbonne Universit\u00e9 , CNRS , LIP6 , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9 , CNRS , LIP6 , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210159731"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070703146","display_name":"Dmitry Grinko","orcid":"https://orcid.org/0000-0001-6438-1998","observed_orcids":["https://orcid.org/0000-0001-6438-1998"]},"institutions":[{"id":"https://openalex.org/I4210099082","display_name":"QuSoft","ror":"https://ror.org/00zq3ce72","country_code":"NL","type":"facility","lineage":["https://openalex.org/I4210099082"]},{"id":"https://openalex.org/I887064364","display_name":"University of Amsterdam","ror":"https://ror.org/04dkp9463","country_code":"NL","type":"education","lineage":["https://openalex.org/I887064364"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Grinko, Dmitry","raw_affiliation_strings":["QuSoft , University of Amsterdam , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"QuSoft , University of Amsterdam , The Netherlands","institution_ids":["https://openalex.org/I4210099082","https://openalex.org/I887064364"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.9717000126838684,"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"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9717000126838684,"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"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.019300000742077827,"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":0.00559999980032444,"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/no-cloning-theorem","display_name":"no-cloning theorem","score":0.9789999723434448},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"sample complexity","score":0.7210000157356262},{"id":"https://openalex.org/keywords/fermionic-gaussian-states","display_name":"fermionic Gaussian states","score":0.9629999995231628},{"id":"https://openalex.org/keywords/representation-theory","display_name":"representation theory","score":0.6179999709129333},{"id":"https://openalex.org/keywords/frame-potential","display_name":"frame potential","score":0.9150000214576721},{"id":"https://openalex.org/keywords/cloning-fidelity","display_name":"cloning fidelity","score":0.5019999742507935},{"id":"https://openalex.org/keywords/stabilizer-states","display_name":"stabilizer states","score":0.7049999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5982999801635742},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.512499988079071},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5060999989509583},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.4449000060558319},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4142000079154968},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C2776887110","wikidata":"https://www.wikidata.org/wiki/Q7269018","display_name":"Quantum cloning","level":5,"score":0.38659998774528503},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3790000081062317},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.34450000524520874},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.32829999923706055},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2971999943256378},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.29670000076293945},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.2930999994277954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28630000352859497},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2842000126838684},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2727000117301941},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.2678999900817871},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C199622910","wikidata":"https://www.wikidata.org/wiki/Q1128326","display_name":"Constraint satisfaction problem","level":3,"score":0.2526000142097473},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.2524999976158142},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.06723","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06723","pdf_url":"https://arxiv.org/pdf/2610.06723","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":"pmh:oai:HAL:hal-05783705v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05783705","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.06723","doi":"https://doi.org/10.48550/arxiv.2610.06723","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.06723","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:2610.06723","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.06723","pdf_url":"https://arxiv.org/pdf/2610.06723","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":[{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320331473","display_name":"Ministry of Colleges and Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220648536.pdf","grobid_xml":"https://content.openalex.org/works/W7220648536.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W2022294538","https://openalex.org/W2030969970","https://openalex.org/W2031900853","https://openalex.org/W2115693813","https://openalex.org/W2123829027","https://openalex.org/W2167117936","https://openalex.org/W2593746423","https://openalex.org/W2734817276","https://openalex.org/W2780472999","https://openalex.org/W3026234726","https://openalex.org/W4292213367","https://openalex.org/W4411319977","https://openalex.org/W4416069009","https://openalex.org/W4416544132","https://openalex.org/W4416894355","https://openalex.org/W7140424041","https://openalex.org/W7162030531","https://openalex.org/W7168303001","https://openalex.org/W7204236949","https://openalex.org/W7204564800","https://openalex.org/W7221011797"],"related_works":["https://openalex.org/W7204236949","https://openalex.org/W7204564800","https://openalex.org/W7221011797","https://openalex.org/W7223305171","https://openalex.org/W7168303001","https://openalex.org/W2150114792","https://openalex.org/W3143203722","https://openalex.org/W2059250671","https://openalex.org/W2034224857","https://openalex.org/W7214018024"],"abstract_inverted_index":{"The":[0,173,233,244],"no-cloning":[1],"theorem":[2],"is":[3,76,92,168,212],"a":[4,34,57,70,97,102,180,222,260],"cornerstone":[5],"result":[6],"in":[7,96,141,171,214],"quantum":[8,15,111],"mechanics":[9],"that":[10,152],"forbids":[11],"copying":[12],"of":[13,23,51,86,104,162,217,226,241,259],"general":[14],"information.":[16],"More":[17],"quantitatively,":[18],"even":[19],"given":[20],"$N$":[21,63],"copies":[22],"an":[24,30,149,256],"unknown":[25],"state,":[26],"any":[27,157],"channel":[28,261],"producing":[29],"$(N+1)$-copy":[31],"state":[32],"incurs":[33],"nonzero":[35],"trace-distance":[36],"error":[37,60],"on":[38,69,159,271],"some":[39],"inputs.":[40],"Turning":[41],"this":[42,165],"around,":[43],"one":[44],"can":[45],"ask":[46],"about":[47],"the":[48,74,90,135,160,163,198,209,215,218,227,238],"sample":[49],"complexity":[50,136,211],"approximate":[52],"$N\\rightarrow":[53],"N+1$":[54],"cloning:":[55],"for":[56,83,206,237,252],"desired":[58],"small":[59],"$\u03b5$,":[61],"what":[62],"suffices?":[64],"For":[65,127,143],"arbitrary":[66],"pure":[67],"states":[68],"Hilbert":[71],"space":[72],"$H$,":[73],"answer":[75],"$N\\simeq":[77],"\\dim":[78],"H/\u03b5$":[79],"-":[80],"astronomically":[81],"large":[82],"most":[84],"$H$":[85],"interest.":[87],"What":[88],"if":[89],"input":[91],"promised":[93],"to":[94,107,139],"lie":[95],"structured":[98],"family?":[99],"We":[100],"examine":[101],"range":[103],"families":[105,208],"fundamental":[106],"many-body":[108],"physics":[109],"and":[110,116,123,175,190,193],"information:":[112],"$n$-mode":[113,119],"fermionic":[114,174],"Gaussian":[115,121,145],"Slater":[117],"states,":[118,122,146],"bosonic":[120,144,176],"qudit":[124],"phase":[125,250],"states.":[126,274],"fermions,":[128],"we":[129,147,203,254],"construct":[130,148],"optimal":[131,170,263],"cloning":[132,210,264,272],"channels,":[133],"reducing":[134],"from":[137,179],"exponential":[138],"polynomial":[140,154],"$n$.":[142],"explicit":[150],"cloner":[151],"certifies":[153],"complexity,":[155],"without":[156],"constraint":[158],"energy":[161],"state;":[164],"channel,":[166],"however,":[167],"not":[169,248],"general.":[172],"results":[177,270],"follow":[178],"single":[181],"representation-theoretic":[182],"framework,":[183],"which":[184],"generalizes":[185],"previous":[186],"work":[187,267],"by":[188,191],"Werner":[189],"Chiribella":[192],"Yang;":[194],"it":[195],"also":[196],"yields":[197],"cloners'":[199],"unitary":[200],"implementation.":[201],"Furthermore,":[202],"explain":[204],"why":[205],"many":[207],"linear":[213],"dimension":[216],"family":[219],"manifold,":[220],"via":[221],"controlled":[223],"saddle-point":[224],"evaluation":[225],"frame":[228],"potential":[229],"at":[230],"high":[231],"$N$.":[232],"same":[234],"calculation":[235],"accounts":[236],"analogous":[239],"scaling":[240],"tomography":[242],"complexity.":[243],"above":[245],"framework":[246],"does":[247],"cover":[249],"states;":[251],"these":[253],"give":[255],"independent":[257],"construction":[258],"with":[262],"fidelity.":[265],"Our":[266],"complements":[268],"recent":[269],"stabilizer":[273]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
