{"id":"https://openalex.org/W7214073290","doi":"https://doi.org/10.48550/arxiv.2609.26678","title":"Strong Selective and List-Decoding Direct Product Theorems for Quantum Query Complexity","display_name":"Strong Selective and List-Decoding Direct Product Theorems for Quantum Query Complexity","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214073290","doi":"https://doi.org/10.48550/arxiv.2609.26678"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26678","pdf_url":"https://arxiv.org/pdf/2609.26678","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/2609.26678","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042076941","display_name":"Paul W. Beame","orcid":"https://orcid.org/0000-0002-2666-3545","observed_orcids":["https://orcid.org/0000-0002-2666-3545"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Beame, Paul","raw_affiliation_strings":["Computer Science & Engineering University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science & Engineering University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066703672","display_name":"Niels Kornerup","orcid":"https://orcid.org/0000-0002-1519-726X","observed_orcids":["https://orcid.org/0000-0002-1519-726X"]},"institutions":[{"id":"https://openalex.org/I192454743","display_name":"Sandia National Laboratories California","ror":"https://ror.org/058m7ey48","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I192454743","https://openalex.org/I198811213","https://openalex.org/I4210104735"]},{"id":"https://openalex.org/I4210104735","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210104735"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kornerup, Niels","raw_affiliation_strings":["Sandia National Laboratories"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sandia National Laboratories","institution_ids":["https://openalex.org/I192454743","https://openalex.org/I4210104735"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006280608","display_name":"Michael Whitmeyer","orcid":"https://orcid.org/0000-0002-5930-4733","observed_orcids":["https://orcid.org/0000-0002-5930-4733"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Whitmeyer, Michael","raw_affiliation_strings":["Computer Science & Engineering University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science & Engineering University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9848999977111816,"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":0.9848999977111816,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.007300000172108412,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.0034000000450760126,"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-query-complexity","display_name":"quantum query complexity","score":0.9179999828338623},{"id":"https://openalex.org/keywords/space-time-tradeoff","display_name":"space-time tradeoff","score":0.8709999918937683},{"id":"https://openalex.org/keywords/partial-boolean-functions","display_name":"partial Boolean functions","score":0.7760000228881836},{"id":"https://openalex.org/keywords/query-lower-bounds","display_name":"query lower bounds","score":0.6790000200271606},{"id":"https://openalex.org/keywords/state-generation","display_name":"state generation","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6175000071525574},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5769000053405762},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5720999836921692},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.49480000138282776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4896000027656555},{"id":"https://openalex.org/C58193220","wikidata":"https://www.wikidata.org/wiki/Q1778193","display_name":"Direct product","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.35370001196861267},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3427000045776367},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3377000093460083},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.311599999666214},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3009999990463257},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C65647387","wikidata":"https://www.wikidata.org/wiki/Q1781706","display_name":"Conjunctive query","level":3,"score":0.2711000144481659},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26649999618530273},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26678","pdf_url":"https://arxiv.org/pdf/2609.26678","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.2609.26678","doi":"https://doi.org/10.48550/arxiv.2609.26678","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26678","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:2609.26678","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26678","pdf_url":"https://arxiv.org/pdf/2609.26678","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":[{"id":"https://openalex.org/G11630931","display_name":null,"funder_award_id":"DENA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1719938300","display_name":"FET: Small: Quantum Time-Space Tradeoffs and Classical Lifting","funder_award_id":"2422205","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1859920734","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G2214935549","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G413247060","display_name":null,"funder_award_id":"DE\u2010NA,0003525","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G4771968897","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4903105778","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5339743583","display_name":null,"funder_award_id":"NA0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G6338696783","display_name":null,"funder_award_id":"DE\u2010NA0003525","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G70797072","display_name":null,"funder_award_id":"DE-NA0003525","funder_id":"https://openalex.org/F4320337547","funder_display_name":"Laboratory Directed Research and Development"},{"id":"https://openalex.org/G855168022","display_name":null,"funder_award_id":"DENA-0003525","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320337547","display_name":"Laboratory Directed Research and Development","ror":"https://ror.org/01e41cf67"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214073290.pdf","grobid_xml":"https://content.openalex.org/works/W7214073290.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2167217679","https://openalex.org/W7128633611","https://openalex.org/W7097495153","https://openalex.org/W2068911609","https://openalex.org/W7095691810","https://openalex.org/W7097530749","https://openalex.org/W2148211896","https://openalex.org/W2146817307","https://openalex.org/W2149045885","https://openalex.org/W7095359773"],"abstract_inverted_index":{"Quantum":[0],"strong":[1,48,127,156,240],"direct-product":[2,49,67,129,242],"theorems":[3,50,215,243],"for":[4,10,21,119,131,167,186,217,232,266],"specific":[5],"functions":[6,133,168],"have":[7,15],"been":[8,16],"known":[9],"nearly":[11],"two":[12,86],"decades.":[13],"These":[14,190],"extended":[17,62],"to":[18,45,64,72,93,111,194],"general":[19],"results":[20,31],"function":[22],"computation":[23],"and":[24,117,145,161,184],"state":[25],"generation.":[26],"The":[27,173],"proofs":[28],"of":[29,35,138,199,206,220,229,250],"these":[30],"use":[32],"a":[33,108,125,135,155,196,226,247,257],"version":[34],"the":[36,139],"multiplicative":[37,140,251],"adversary":[38,141],"method":[39,142],"that":[40,78,95,204,213,239],"does":[41],"not":[42],"naturally":[43],"extend":[44],"relations.":[46],"Standard":[47],"apply":[51,92],"when":[52],"algorithms":[53,94],"must":[54],"correctly":[55],"answer":[56],"every":[57],"given":[58],"question.":[59],"Prior":[60],"work":[61],"them":[63,207],"equivalent":[65,152],"threshold":[66],"theorems,":[68],"which":[69,105,147,253],"require":[70,77],"answers":[71,80],"all":[73,132,221,233],"questions":[74,106],"but":[75],"only":[76],"most":[79],"are":[81,244],"correct.":[82,210],"We":[83,123,224,237],"focus":[84],"on":[85,99],"further":[87],"generalizations.":[88],"Strong":[89],"selective":[90,128,157],"direct-products":[91],"adaptively":[96],"choose,":[97],"based":[98],"what":[100],"they":[101],"learn":[102],"from":[103,107,263],"queries,":[104],"large":[109,197],"list":[110,198],"answer.":[112],"This":[113],"generalization":[114,175],"is":[115,176,208],"relational":[116,136],"useful":[118],"proving":[120],"time-space":[121],"tradeoffs.":[122],"prove":[124,225],"quantum":[126,227],"theorem":[130,231],"using":[134],"formulation":[137],"by":[143,170,182,246],"Jeffery":[144],"Zur":[146],"we":[148,254],"prove,":[149],"via":[150,256],"an":[151,192],"formulation,":[153],"satisfies":[154],"direct":[158,178],"product":[159,179],"property":[160],"captures":[162],"any":[163,267],"query":[164,188],"lower":[165],"bound":[166],"proven":[169],"negative-weights":[171,264],"adversaries.":[172],"second":[174],"list-decoding":[177,241],"problems":[180],"introduced":[181],"Ben-David":[183],"Blais":[185],"classical":[187],"complexity.":[189],"allow":[191],"algorithm":[193],"produce":[195],"possible":[200],"output":[201],"vectors":[202],"such":[203,214],"one":[205],"fully":[209],"They":[211],"proved":[212],"hold":[216],"randomized":[218],"complexity":[219],"Boolean":[222],"functions.":[223,236],"analogue":[228],"this":[230],"partial":[234],"Boolean-valued":[235,268],"show":[238],"implied":[245],"special":[248],"case":[249],"adversaries":[252,265],"show,":[255],"new":[258],"reduction,":[259],"can":[260],"be":[261],"obtained":[262],"function.":[269]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-24T00:00:00"}