{"id":"https://openalex.org/W7163928186","doi":"https://doi.org/10.48550/arxiv.2606.07110","title":"Entanglement from Expansion: High Rank-Width in Deterministic Graphs","display_name":"Entanglement from Expansion: High Rank-Width in Deterministic Graphs","publication_year":2026,"publication_date":"2026-06-05","ids":{"openalex":"https://openalex.org/W7163928186","doi":"https://doi.org/10.48550/arxiv.2606.07110"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.07110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07110","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,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.07110","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088439742","display_name":"Tristan Cam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cam, Tristan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013587418","display_name":"Cyril Gavoille","orcid":"https://orcid.org/0000-0003-3671-8607"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gavoille, Cyril","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138194387","display_name":"Yvan Le Borgne","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Borgne, Yvan Le","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5082324311","display_name":"Simon Martiel","orcid":"https://orcid.org/0000-0001-5624-2955"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martiel, Simon","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":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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.7973999977111816,"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":0.7973999977111816,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.08229999989271164,"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/T11804","display_name":"Quantum many-body systems","score":0.03240000084042549,"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-entanglement","display_name":"Quantum entanglement","score":0.4975999891757965},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.46950000524520874},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.4408999979496002},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.43290001153945923},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.40799999237060547},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3779999911785126},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.3644999861717224},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.3626999855041504}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6579999923706055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5965999960899353},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5001999735832214},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.4975999891757965},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.4408999979496002},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3779999911785126},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3644999861717224},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.3529999852180481},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.30889999866485596},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.2865000069141388},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.27709999680519104},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.26179999113082886},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.07110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07110","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,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.07110","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.07110","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,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Entanglement":[0],"in":[1,32,117,140],"quantum":[2],"graph":[3,11,30,145],"states":[4,31],"is":[5],"intrinsically":[6],"linked":[7],"to":[8,40],"rank-width,":[9],"a":[10,37,95,110,129],"complexity":[12],"measure":[13],"introduced":[14],"by":[15,35,109],"Oum":[16],"and":[17,63,85],"Seymour.":[18],"In":[19],"this":[20,88],"work,":[21],"we":[22,70,101],"enable":[23],"the":[24,45,59,76,98,103,118,137,141],"preparation":[25],"of":[26,47,78,97,120,123,147],"maximally":[27],"entangled":[28],"deterministic":[29,121,144],"constant":[33],"depth":[34],"developing":[36],"general":[38],"method":[39],"derive":[41],"lower":[42,67,73],"bounds":[43,74,104],"on":[44,125],"rank-width":[46,77,132,148],"regular":[48],"graphs":[49,124],"from":[50],"their":[51],"edge":[52],"expansion.":[53],"By":[54],"bridging":[55],"edge-isoperimetric":[56],"inequalities":[57],"with":[58,128],"strong":[60],"chromatic":[61],"index":[62],"Jel\u00ednek's":[64],"approach":[65],"for":[66,75,105,143],"bounding":[68],"cut-rank,":[69],"systematically":[71],"establish":[72],"Cartesian":[79,107],"products,":[80],"including":[81],"hypercubes,":[82],"Hamming":[83],"graphs,":[84],"grids.":[86],"Extending":[87],"framework":[89],"via":[90],"Boolean":[91],"function":[92],"analysis,":[93],"using":[94],"generalization":[96],"Kahn-Kalai-Linial's":[99],"Theorem,":[100],"strengthen":[102],"all":[106],"products":[108],"non-trivial":[111],"logarithmic":[112],"factor.":[113],"These":[114],"methods":[115],"result":[116],"discovery":[119],"families":[122,146],"$n$":[126],"vertices":[127],"provably":[130],"maximum":[131],"$\u0398(n)$.":[133],"Our":[134],"results":[135],"fill":[136],"previous":[138],"gap":[139],"literature":[142],"greater":[149],"than":[150],"$\u0398(\\sqrt{n})$.":[151]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-09T00:00:00"}
