{"id":"https://openalex.org/W7225408906","doi":"https://doi.org/10.5281/zenodo.23996458","title":"An Exact Partial-Transpose Norm Identity at the Next-to-Next-Highest Bosonic Photon Threshold","display_name":"An Exact Partial-Transpose Norm Identity at the Next-to-Next-Highest Bosonic Photon Threshold","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225408906","doi":"https://doi.org/10.5281/zenodo.23996458"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23996458","doi":"https://doi.org/10.5281/zenodo.23996458","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23996458","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23996458","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146382536","display_name":"Kias Henry","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Henry, Kias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5146382536"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9140999913215637,"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":0.9140999913215637,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.031599998474121094,"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/T11414","display_name":"Quantum optics and atomic interactions","score":0.006899999920278788,"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/partial-transpose","display_name":"partial transposition","score":0.6830000281333923},{"id":"https://openalex.org/keywords/operator-norm","display_name":"operator norm","score":0.8619999885559082},{"id":"https://openalex.org/keywords/spectral-reduction","display_name":"spectral reduction","score":0.6610000133514404},{"id":"https://openalex.org/keywords/eigenvalue-bounds","display_name":"eigenvalue bounds","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6269999742507935},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.613099992275238},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4724000096321106},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4221000075340271},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4059000015258789},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3296000063419342},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32820001244544983},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.28630000352859497},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23996458","doi":"https://doi.org/10.5281/zenodo.23996458","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23996458","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23996459","doi":"https://doi.org/10.5281/zenodo.23996459","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23996459","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23996458","doi":"https://doi.org/10.5281/zenodo.23996458","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23996458","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225235911","https://openalex.org/W7225254255","https://openalex.org/W7225227050","https://openalex.org/W2750245396","https://openalex.org/W2796348637","https://openalex.org/W7212018099","https://openalex.org/W2086539396","https://openalex.org/W3139451309","https://openalex.org/W2066516915","https://openalex.org/W2003429723"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,14,60,90],"partial-transpose":[3],"operator-norm":[4],"equality":[5],"conjectured":[6],"by":[7],"Matthew":[8],"Barber":[9],"and":[10,34,39,63,97],"Stefano":[11],"Pirandola":[12],"for":[13,25],"entire":[15],"bosonic":[16],"photon-correlation":[17],"threshold":[18],"subfamily":[19],"h":[20],"=":[21],"min(m,k)":[22],"-":[23],"2,":[24],"every":[26],"number":[27],"of":[28],"modes":[29],"s":[30],"at":[31,41,59],"least":[32,42],"two":[33],"all":[35],"photon":[36,46],"numbers":[37],"m":[38],"k":[40],"three,":[43],"including":[44],"unequal":[45],"numbers.":[47],"The":[48,100],"argument":[49],"provides":[50],"a":[51,64,73],"three-term":[52],"spectral":[53,92],"reduction,":[54],"universal":[55],"exact":[56,84],"positivity":[57],"certificates":[58],"two-mode":[61],"boundary,":[62],"polynomial":[65],"mode-translation":[66],"argument.":[67],"Every":[68],"nonaligned":[69],"representation-sector":[70],"eigenvalue":[71],"satisfies":[72],"strict":[74],"two-sided":[75],"bound.":[76],"A":[77],"supplementary":[78],"archive":[79],"contains":[80],"Python":[81],"verification":[82,95],"programs,":[83],"integer-polynomial":[85],"checks,":[86],"regression":[87],"tests":[88],"against":[89],"original":[91],"formula,":[93],"JSON":[94],"records,":[96],"LaTeX":[98],"source.":[99],"full":[101],"arbitrary-threshold":[102],"conjecture":[103],"remains":[104],"open.":[105]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}