{"id":"https://openalex.org/W7222505601","doi":"https://doi.org/10.48550/arxiv.2610.22190","title":"Connectivity Bounds for GHZ Graphs","display_name":"Connectivity Bounds for GHZ Graphs","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222505601","doi":"https://doi.org/10.48550/arxiv.2610.22190"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.22190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22190","pdf_url":"https://arxiv.org/pdf/2610.22190","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/2610.22190","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024359075","display_name":"L. Sunil Chandran","orcid":"https://orcid.org/0000-0001-5451-6975","observed_orcids":["https://orcid.org/0000-0001-5451-6975"]},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Chandran, L. Sunil","raw_affiliation_strings":["Indian Institute of Science , Bengaluru , India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Science , Bengaluru , India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007094252","display_name":"Rishikesh R. Gajjala","orcid":"https://orcid.org/0000-0002-8726-3465","observed_orcids":["https://orcid.org/0000-0002-8726-3465"]},"institutions":[{"id":"https://openalex.org/I120250893","display_name":"New York University Abu Dhabi","ror":"https://ror.org/00e5k0821","country_code":"AE","type":"education","lineage":["https://openalex.org/I120250893","https://openalex.org/I57206974"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Gajjala, Rishikesh","raw_affiliation_strings":["Center for Quantum and Topological Systems , New York University Abu Dhabi , United Arab Emirates"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Quantum and Topological Systems , New York University Abu Dhabi , United Arab Emirates","institution_ids":["https://openalex.org/I120250893"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.6996999979019165,"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":0.6996999979019165,"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":0.1696999967098236,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.03449999913573265,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ghz-states","display_name":"GHZ states","score":0.7960000038146973},{"id":"https://openalex.org/keywords/multipartite-entanglement","display_name":"multipartite entanglement","score":0.8299999833106995},{"id":"https://openalex.org/keywords/graph-connectivity","display_name":"graph connectivity","score":0.38499999046325684},{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"vertex connectivity","score":0.8240000009536743},{"id":"https://openalex.org/keywords/edge-connectivity","display_name":"edge connectivity","score":0.972000002861023},{"id":"https://openalex.org/keywords/maximum-degree","display_name":"maximum degree","score":0.6140000224113464},{"id":"https://openalex.org/keywords/high-dimensional-entanglement","display_name":"high-dimensional entanglement","score":0.6940000057220459},{"id":"https://openalex.org/keywords/quantum-optics","display_name":"quantum optics","score":0.5519999861717224}],"concepts":[{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.7990999817848206},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.629800021648407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5953999757766724},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5936999917030334},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5855000019073486},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5726000070571899},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5060999989509583},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3619999885559082},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3483999967575073},{"id":"https://openalex.org/C72933692","wikidata":"https://www.wikidata.org/wiki/Q11300563","display_name":"Greenberger\u2013Horne\u2013Zeilinger state","level":5,"score":0.3400999903678894},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.28780001401901245},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.28439998626708984},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.28029999136924744},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2800999879837036},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.27469998598098755},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.2623000144958496}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.22190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22190","pdf_url":"https://arxiv.org/pdf/2610.22190","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.2610.22190","doi":"https://doi.org/10.48550/arxiv.2610.22190","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.22190","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":"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":"pmh:oai:arXiv.org:2610.22190","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.22190","pdf_url":"https://arxiv.org/pdf/2610.22190","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/W7222505601.pdf","grobid_xml":"https://content.openalex.org/works/W7222505601.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1977670750","https://openalex.org/W1986407511","https://openalex.org/W2062854284","https://openalex.org/W2154434103","https://openalex.org/W2616012638","https://openalex.org/W2890248967","https://openalex.org/W2906372686","https://openalex.org/W2915016238","https://openalex.org/W3025453511","https://openalex.org/W3109405625","https://openalex.org/W3203473787","https://openalex.org/W4221158335","https://openalex.org/W4297943426","https://openalex.org/W4385767701","https://openalex.org/W4389625446","https://openalex.org/W4400267272","https://openalex.org/W4400288542"],"related_works":["https://openalex.org/W4400267272","https://openalex.org/W2807844753","https://openalex.org/W1983316857","https://openalex.org/W2084836158","https://openalex.org/W7221836027","https://openalex.org/W2735434622","https://openalex.org/W4226224699","https://openalex.org/W4393234696","https://openalex.org/W1524958767","https://openalex.org/W2883265075"],"abstract_inverted_index":{"Greenberger-Horne-Zeilinger":[0],"(GHZ)":[1],"states":[2,7,36],"are":[3],"multipartite":[4,111],"entangled":[5,39],"quantum":[6,14,20,25,123],"that":[8,90,128,143,171],"play":[9],"a":[10,46,108,115],"central":[11],"role":[12],"in":[13,19,122,201],"information":[15],"theory,":[16],"with":[17,94,147,178],"applications":[18],"communication,":[21],"cryptography,":[22],"and":[23,43,53,66,86,142,206],"distributed":[24],"computing.":[26],"A":[27,104],"major":[28],"experimental":[29],"goal":[30],"is":[31,126,190],"to":[32,88],"create":[33],"high-dimensional":[34,110],"GHZ":[35,72,92,112,145,175],"using":[37],"multiple":[38],"parties.":[40],"Krenn,":[41],"Gu":[42,87],"Zeilinger":[44],"discovered":[45],"surprising":[47],"bridge":[48],"between":[49],"these":[50],"quantum-optical":[51],"experiments":[52,58],"graph":[54,93,176],"theory:":[55],"certain":[56],"photonic":[57],"can":[59],"be":[60],"represented":[61],"by":[62],"edge-coloured,":[63],"edge-weighted":[64],"graphs,":[65],"the":[67,70,75,129,191],"dimension":[68,100,151,184],"of":[69,77,134,194,203],"produced":[71],"state":[73],"equals":[74],"number":[76],"feasible":[78],"monochromatic":[79],"inherited":[80],"vertex":[81,135,165,192],"colourings.":[82],"This":[83],"led":[84],"Krenn":[85],"conjecture":[89,130],"every":[91,172],"more":[95],"than":[96,153],"four":[97,181],"vertices":[98,149,182],"has":[99,183],"at":[101,137,179,185],"most":[102,138,186],"$2$.":[103],"counterexample":[105],"would":[106,117],"give":[107],"new":[109,199],"construction,":[113],"while":[114],"proof":[116],"clarify":[118],"fundamental":[119],"resource":[120],"limitations":[121],"optics.":[124],"It":[125],"known":[127],"holds":[131],"for":[132],"graphs":[133,146],"connectivity":[136,166,193,205],"$2$":[139],"[MFCS":[140],"2024],":[141],"simple":[144,173],"$n>4$":[148],"have":[150],"less":[152],"$n/\\sqrt{2}$":[154],"[Quantum":[155],"2024].":[156],"However,":[157],"no":[158],"general":[159],"upper":[160],"bound":[161],"depending":[162],"only":[163],"on":[164],"was":[167],"known.":[168],"We":[169,196],"prove":[170,198],"connected":[174],"$G$":[177],"least":[180],"$2^{\u03ba(G)-1}+\\binom{\u03ba(G)}{2}$,":[187],"where":[188],"$\u03ba(G)$":[189],"$G$.":[195],"also":[197],"bounds":[200],"terms":[202],"edge":[204],"maximum":[207],"degree.":[208]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-17T00:00:00"}
