{"id":"https://openalex.org/W7164892791","doi":"https://doi.org/10.48550/arxiv.2606.16862","title":"The Weyl-orbit embedding and a representation-theoretic characterization of the Clifford hierarchy","display_name":"The Weyl-orbit embedding and a representation-theoretic characterization of the Clifford hierarchy","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164892791","doi":"https://doi.org/10.48550/arxiv.2606.16862"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2606.16862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.16862","pdf_url":"https://arxiv.org/pdf/2606.16862","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/2606.16862","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073749739","display_name":"Asgar Jamneshan","orcid":"https://orcid.org/0000-0002-1450-6569","observed_orcids":["https://orcid.org/0000-0002-1450-6569"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jamneshan, Asgar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5146002397","display_name":"Berke \u00dcnal","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u00dcnal, Berke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.6371999979019165,"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":0.6371999979019165,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.093299999833107,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.08959999680519104,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/clifford-hierarchy","display_name":"Clifford hierarchy","score":0.9779999852180481},{"id":"https://openalex.org/keywords/unitary-representations","display_name":"unitary representations","score":0.972000002861023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6087999939918518},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.588100016117096},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5145000219345093},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47110000252723694},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.4293999969959259},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.42809998989105225},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.40869998931884766},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.31529998779296875},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3140999972820282},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.3125},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3043999969959259},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28139999508857727},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2612999975681305},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.2606000006198883}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2606.16862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.16862","pdf_url":"https://arxiv.org/pdf/2606.16862","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2606.16862","doi":"https://doi.org/10.48550/arxiv.2606.16862","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16862","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:2606.16862","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2606.16862","pdf_url":"https://arxiv.org/pdf/2606.16862","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1521016025","display_name":"EXC 2047: Hausdorff Center for Mathematics (HCM)","funder_award_id":"390685813","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5226917192","display_name":null,"funder_award_id":"547294463","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7164892791.pdf","grobid_xml":"https://content.openalex.org/works/W7164892791.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4405635382","https://openalex.org/W4415318112","https://openalex.org/W7162515986"],"related_works":["https://openalex.org/W4416008677","https://openalex.org/W2949227982","https://openalex.org/W2920312441","https://openalex.org/W7111878760","https://openalex.org/W2554109758","https://openalex.org/W7220675423","https://openalex.org/W1981361201","https://openalex.org/W2081803222","https://openalex.org/W2482065192","https://openalex.org/W2780472999"],"abstract_inverted_index":{"Bu,":[0],"Gu,":[1],"and":[2,32,53,114],"Jaffe":[3],"introduced":[4,109],"the":[5,12,18,23,26,35,42,47,50,62,73,81,96,105,111],"quantum":[6,19,74],"uniformity":[7,20,28,65,68,75],"measures":[8,21],"to":[9],"analytically":[10],"characterize":[11],"Clifford":[13,82,97],"hierarchy.":[14],"We":[15,45],"prove":[16],"that":[17],"are":[22],"pullbacks":[24],"of":[25,30,49,61,72,95,101,104],"matrix-valued":[27,64],"functionals":[29],"Gowers":[31],"Hatami":[33],"under":[34],"map":[36],"$U\\mapsto(a\\mapsto":[37],"W_aUW_a^*)$,":[38],"which":[39],"we":[40],"call":[41],"Weyl-orbit":[43,51,78],"embedding.":[44],"study":[46],"structure":[48],"embedding,":[52],"among":[54],"other":[55],"results,":[56],"establish":[57],"a":[58,91],"canonical":[59],"decomposition":[60],"ambient":[63],"space":[66],"into":[67],"preserving":[69],"twisted":[70],"copies":[71],"space.":[76],"The":[77],"embedding":[79],"identifies":[80],"hierarchy":[83,98],"with":[84],"Leibman":[85],"polynomial":[86,107],"maps.":[87],"This":[88],"identification":[89],"yields":[90],"representation":[92],"theoretic":[93],"characterization":[94],"in":[99],"terms":[100],"unitary":[102],"representations":[103],"universal":[106],"groups":[108],"by":[110],"first":[112],"author":[113],"Thom.":[115]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-06-17T00:00:00"}
