{"id":"https://openalex.org/W7204811358","doi":"https://doi.org/10.48550/arxiv.2608.28235","title":"Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests","display_name":"Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests","publication_year":2026,"publication_date":"2026-08-28","ids":{"openalex":"https://openalex.org/W7204811358","doi":"https://doi.org/10.48550/arxiv.2608.28235"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.28235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28235","pdf_url":"https://arxiv.org/pdf/2608.28235","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.28235","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148828676","display_name":"Xu Kang Tan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tan, Xu Kang","raw_affiliation_strings":["School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148814694","display_name":"Jesvita Menezes","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Menezes, Jesvita","raw_affiliation_strings":["School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148819380","display_name":"Sanjan D. Murthy","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Murthy, Sanjan D.","raw_affiliation_strings":["School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063956740","display_name":"Adetunmise C. Dada","orcid":"https://orcid.org/0000-0001-9444-0127","observed_orcids":["https://orcid.org/0000-0001-9444-0127"]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dada, Adetunmise C.","raw_affiliation_strings":["School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Astronomy , University of Glasgow , Glasgow G12 8QQ , United Kingdom","institution_ids":["https://openalex.org/I7882870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I7882870"],"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":0.9121000170707703,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9121000170707703,"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":0.08129999786615372,"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":0.0006000000284984708,"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/high-dimensional-entanglement","display_name":"high-dimensional entanglement","score":0.9750000238418579},{"id":"https://openalex.org/keywords/bell-nonlocality","display_name":"Bell nonlocality","score":0.6819999814033508},{"id":"https://openalex.org/keywords/cglmp-inequality","display_name":"CGLMP inequality","score":0.8730000257492065},{"id":"https://openalex.org/keywords/qudits","display_name":"qudits","score":0.8989999890327454},{"id":"https://openalex.org/keywords/entanglement-certification","display_name":"entanglement certification","score":0.921999990940094}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.7617999911308289},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5062000155448914},{"id":"https://openalex.org/C71799126","wikidata":"https://www.wikidata.org/wiki/Q6934832","display_name":"Multipartite entanglement","level":5,"score":0.4575999975204468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4553000032901764},{"id":"https://openalex.org/C95013731","wikidata":"https://www.wikidata.org/wiki/Q7269071","display_name":"Quantum metrology","level":5,"score":0.4311999976634979},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.39890000224113464},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.396699994802475},{"id":"https://openalex.org/C159317903","wikidata":"https://www.wikidata.org/wiki/Q3198","display_name":"Photon","level":2,"score":0.3747999966144562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36719998717308044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.36160001158714294},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C123403432","wikidata":"https://www.wikidata.org/wiki/Q654068","display_name":"Visibility","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33970001339912415},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.33480000495910645},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C128108043","wikidata":"https://www.wikidata.org/wiki/Q388525","display_name":"Bell's theorem","level":4,"score":0.31769999861717224},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C138622882","wikidata":"https://www.wikidata.org/wiki/Q7269079","display_name":"Quantum nonlocality","level":4,"score":0.3086000084877014},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3018999993801117},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.29809999465942383},{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.2851000130176544},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2761000096797943},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C104434177","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Photon entanglement","level":4,"score":0.2680000066757202},{"id":"https://openalex.org/C91717678","wikidata":"https://www.wikidata.org/wiki/Q1135332","display_name":"Quantum teleportation","level":5,"score":0.26570001244544983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26489999890327454},{"id":"https://openalex.org/C5320026","wikidata":"https://www.wikidata.org/wiki/Q2122216","display_name":"Quantum information science","level":4,"score":0.2612000107765198},{"id":"https://openalex.org/C95466800","wikidata":"https://www.wikidata.org/wiki/Q1027298","display_name":"Quantum key distribution","level":3,"score":0.2603999972343445},{"id":"https://openalex.org/C206003972","wikidata":"https://www.wikidata.org/wiki/Q5380097","display_name":"Entanglement witness","level":5,"score":0.25870001316070557},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.28235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28235","pdf_url":"https://arxiv.org/pdf/2608.28235","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.2608.28235","doi":"https://doi.org/10.48550/arxiv.2608.28235","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.28235","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:2608.28235","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.28235","pdf_url":"https://arxiv.org/pdf/2608.28235","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/G4217233263","display_name":"EPSRC Centre for Doctoral Training in Applied Quantum Technologies","funder_award_id":"EP/Y035089/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204811358.pdf","grobid_xml":"https://content.openalex.org/works/W7204811358.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3106129623","https://openalex.org/W4414687603","https://openalex.org/W3210905404","https://openalex.org/W2928867891","https://openalex.org/W2760389184","https://openalex.org/W3197504729","https://openalex.org/W4413344489","https://openalex.org/W3094671459","https://openalex.org/W3015019218","https://openalex.org/W2954033858"],"abstract_inverted_index":{"Entangled":[0],"photons":[1],"play":[2],"a":[3,63,139,240],"crucial":[4],"role":[5],"in":[6,69,96,114],"quantum":[7,71,168],"applications,":[8],"and":[9,11,213],"determining":[10],"characterising":[12,175],"their":[13,28,107],"entanglement":[14,68],"is":[15,233],"vital":[16],"to":[17,38,76,244],"using":[18,81],"them":[19,35],"effectively.":[20],"High-dimensional":[21],"entangled":[22,98],"states":[23,136],"offer":[24],"richer":[25],"possibilities,":[26],"but":[27],"additional":[29],"measurement":[30,186],"degrees":[31],"of":[32,116,123,141,158,209,217,229,235,247],"freedom":[33],"make":[34],"increasingly":[36],"demanding":[37],"characterise.":[39],"However,":[40],"adaptive":[41,223],"Bell-test":[42],"methods":[43],"based":[44],"on":[45,57],"complex":[46],"simultaneous":[47],"perturbation":[48],"stochastic":[49,165],"approximation":[50],"(CSPSA)":[51],"have":[52],"so":[53],"far":[54],"focused":[55],"mainly":[56],"qubits.":[58],"Here":[59],"we":[60,126,149],"numerically":[61],"investigate":[62],"Bell-inequality-violation-based":[64],"method":[65,173,238],"for":[66,86,174],"detecting":[67],"unknown":[70,97,177],"states.":[72],"We":[73,161,203],"extend":[74],"CSPSA":[75,183,231],"high-dimensional":[77,248],"Bell":[78],"testing":[79],"by":[80],"the":[82,145,156,171,180,206,210,215,222,226,237,245],"Collins-Gisin-Linden-Massar-Popescu":[83],"(CGLMP)":[84],"inequality":[85],"bipartite":[87],"qudits.":[88],"The":[89],"resulting":[90],"protocol":[91],"can":[92],"detect":[93],"Bell-nonlocal":[94],"correlations":[95],"states,":[99],"whether":[100],"pure":[101],"or":[102],"mixed,":[103],"without":[104],"first":[105],"reconstructing":[106],"density":[108],"matrix.":[109],"Using":[110],"100":[111,117],"optimisation":[112],"iterations":[113],"each":[115,230],"independent":[118,234],"finite-shot":[119],"runs":[120],"per":[121,188,198],"number":[122],"dimensions":[124],"d,":[125],"demonstrate":[127],"certified":[128,199],"CGLMP":[129,153,211],"violations":[130,154],"throughout":[131,155],"d=2-8.":[132],"For":[133],"isotropic":[134],"mixed":[135],"tested":[137],"at":[138],"visibility":[140],"just":[142],"0.05":[143],"above":[144],"standard-Fourier":[146],"violation":[147],"threshold,":[148],"likewise":[150],"observe":[151],"confidence-certified":[152],"range":[157],"d":[159],"studied.":[160],"compare":[162],"this":[163],"direct":[164],"approach":[166],"with":[167],"state":[169],"tomography,":[170],"standard":[172],"an":[176],"state.":[178],"In":[179],"matched":[181],"benchmark,":[182],"uses":[184],"fewer":[185,195],"configurations":[187],"attempt":[189],"from":[190],"d=6,":[191],"whereas":[192],"tomography":[193],"requires":[194],"detected":[196],"pairs":[197],"result":[200],"through":[201],"d=8.":[202],"also":[204],"derive":[205],"phase":[207],"dependence":[208],"parameter":[212],"clarify":[214],"features":[216],"its":[218],"landscape":[219],"that":[220],"govern":[221],"search.":[224],"Because":[225],"measurement-setting":[227],"cost":[228],"iteration":[232],"dimension,":[236],"offers":[239],"particularly":[241],"attractive":[242],"route":[243],"certification":[246],"entanglement.":[249]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-01T00:00:00"}
