{"id":"https://openalex.org/W7197032050","doi":"https://doi.org/10.48550/arxiv.2608.04411","title":"Tightness of and counterexamples to several quantum estimates","display_name":"Tightness of and counterexamples to several quantum estimates","publication_year":2026,"publication_date":"2026-08-05","ids":{"openalex":"https://openalex.org/W7197032050","doi":"https://doi.org/10.48550/arxiv.2608.04411"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.04411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04411","pdf_url":"https://arxiv.org/pdf/2608.04411","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/2608.04411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062196623","display_name":"Joseph Slote","orcid":"https://orcid.org/0000-0002-6363-7821","observed_orcids":["https://orcid.org/0000-0002-6363-7821"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Slote, Joseph","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111868586","display_name":"Alexander L'vovich Vol'berg","orcid":"https://orcid.org/0000-0002-8127-6505","observed_orcids":["https://orcid.org/0000-0002-8127-6505"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Volberg, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100705306","display_name":"Haonan Zhang","orcid":"https://orcid.org/0000-0001-9537-9663","observed_orcids":["https://orcid.org/0000-0001-9537-9663"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Haonan","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":2,"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":0.8769999742507935,"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":0.8769999742507935,"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":0.03929999843239784,"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/T11804","display_name":"Quantum many-body systems","score":0.017000000923871994,"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/operator-norm","display_name":"operator norm","score":0.6489999890327454},{"id":"https://openalex.org/keywords/bohnenblust-hille-inequality","display_name":"Bohnenblust-Hille inequality","score":0.9890000224113464},{"id":"https://openalex.org/keywords/quantum-fourier-transform","display_name":"quantum Fourier transform","score":0.30399999022483826}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7314000129699707},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5964999794960022},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5881999731063843},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5807999968528748},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.5547999739646912},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.506600022315979},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4860999882221222},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.4406000077724457},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C180347388","wikidata":"https://www.wikidata.org/wiki/Q336233","display_name":"Pauli matrices","level":2,"score":0.4207000136375427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40380001068115234},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.3668999969959259},{"id":"https://openalex.org/C186123792","wikidata":"https://www.wikidata.org/wiki/Q7390277","display_name":"SIC-POVM","level":5,"score":0.3610999882221222},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3547999858856201},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.34060001373291016},{"id":"https://openalex.org/C59500034","wikidata":"https://www.wikidata.org/wiki/Q1464944","display_name":"Quantum Fourier transform","level":5,"score":0.326200008392334},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3255999982357025},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.32100000977516174},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C165973109","wikidata":"https://www.wikidata.org/wiki/Q894014","display_name":"Quantum probability","level":5,"score":0.29409998655319214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2921000123023987},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.2856999933719635},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.2856000065803528},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2777999937534332},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.27079999446868896},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.26930001378059387},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.2651999890804291},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2630000114440918},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C169460222","wikidata":"https://www.wikidata.org/wiki/Q1206311","display_name":"Quantum logic","level":4,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.04411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04411","pdf_url":"https://arxiv.org/pdf/2608.04411","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.2608.04411","doi":"https://doi.org/10.48550/arxiv.2608.04411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.04411","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:2608.04411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.04411","pdf_url":"https://arxiv.org/pdf/2608.04411","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7197032050.pdf","grobid_xml":"https://content.openalex.org/works/W7197032050.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2981609386","https://openalex.org/W3006823398","https://openalex.org/W3088747678","https://openalex.org/W3201120038","https://openalex.org/W4256260099","https://openalex.org/W4300900786","https://openalex.org/W4385198809","https://openalex.org/W4389377934","https://openalex.org/W4394623194","https://openalex.org/W4399930156","https://openalex.org/W4415089273","https://openalex.org/W7172410035"],"related_works":["https://openalex.org/W7213151741","https://openalex.org/W4415089273","https://openalex.org/W4399695026","https://openalex.org/W4410108046","https://openalex.org/W1528606603","https://openalex.org/W2083457727","https://openalex.org/W7140685725","https://openalex.org/W2564079018","https://openalex.org/W7095096738","https://openalex.org/W7213943934"],"abstract_inverted_index":{"We":[0,35,46],"prove":[1,39],"here":[2],"several":[3],"tightness":[4],"results":[5],"for":[6,26,30],"such":[7],"quantum":[8,31,50],"inequalities":[9],"as":[10],"1)":[11],"the":[12,41,49],"comparison":[13],"of":[14,20,40,43,57],"operator":[15],"norm":[16,19],"and":[17],"product":[18],"$d$-local":[21,27],"hamiltonians,":[22,28],"2)":[23],"Bohnenblust--Hille":[24,44],"inequality":[25],"3)":[29],"Fourier":[32],"entropy-influence":[33],"conjecture.":[34],"give":[36],"a":[37,54],"deterministic":[38],"sharpness":[42],"exponent.":[45],"also":[47],"discuss":[48],"Aaronson--Ambainis":[51],"conjecture":[52],"in":[53],"special":[55],"case":[56],"anti-commuting":[58],"Pauli":[59],"strings.":[60]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-07T00:00:00"}