{"id":"https://openalex.org/W3034283638","doi":"https://doi.org/10.22331/q-2021-11-25-589","title":"Entanglement marginal problems","display_name":"Entanglement marginal problems","publication_year":2021,"publication_date":"2021-11-25","ids":{"openalex":"https://openalex.org/W3034283638","doi":"https://doi.org/10.22331/q-2021-11-25-589","mag":"3034283638"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-11-25-589","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-25-589","pdf_url":"https://quantum-journal.org/papers/q-2021-11-25-589/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-11-25-589/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101453073","display_name":"Miguel Navascu\u00e9s","orcid":"https://orcid.org/0000-0003-0717-3927"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]},{"id":"https://openalex.org/I3132079568","display_name":"Institute for Quantum Optics and Quantum Information Innsbruck","ror":"https://ror.org/056hzt889","country_code":"AT","type":"facility","lineage":["https://openalex.org/I138211613","https://openalex.org/I3132079568"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Miguel Navascu\u00e9s","raw_affiliation_strings":["Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences","institution_ids":["https://openalex.org/I3132079568","https://openalex.org/I138211613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080025836","display_name":"F. Baccari","orcid":"https://orcid.org/0000-0003-3374-5968"},"institutions":[{"id":"https://openalex.org/I4210120293","display_name":"Max Planck Institute of Quantum Optics","ror":"https://ror.org/01vekys64","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210120293"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Flavio Baccari","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, 85748 Garching, Germany","Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann Stra\u00dfe 1, 85748, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann-Stra\u00dfe 1, 85748 Garching, Germany","institution_ids":["https://openalex.org/I4210120293"]},{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Quantenoptik, Hans-Kopfermann Stra\u00dfe 1, 85748, Garching, Germany","institution_ids":["https://openalex.org/I4210120293"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006366861","display_name":"Antonio Ac\u00edn","orcid":"https://orcid.org/0000-0002-1355-3435"},"institutions":[{"id":"https://openalex.org/I11932220","display_name":"Instituci\u00f3 Catalana de Recerca i Estudis Avan\u00e7ats","ror":"https://ror.org/0371hy230","country_code":"ES","type":"nonprofit","lineage":["https://openalex.org/I11932220"]},{"id":"https://openalex.org/I179630473","display_name":"Institute of Photonic Sciences","ror":"https://ror.org/03g5ew477","country_code":"ES","type":"facility","lineage":["https://openalex.org/I179630473","https://openalex.org/I4210132884","https://openalex.org/I4387153040","https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonio Ac\u00edn","raw_affiliation_strings":["ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain","ICREA-Institucio Catalana de Recerca i Estudis Avan\u00e7ats, Lluis Companys 23, 08010 Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain","institution_ids":["https://openalex.org/I179630473"]},{"raw_affiliation_string":"ICREA-Institucio Catalana de Recerca i Estudis Avan\u00e7ats, Lluis Companys 23, 08010 Barcelona, Spain","institution_ids":["https://openalex.org/I11932220"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101453073"],"corresponding_institution_ids":["https://openalex.org/I138211613","https://openalex.org/I3132079568"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.2032,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48318318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":95},"biblio":{"volume":"5","issue":null,"first_page":"589","last_page":"589"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10913","display_name":"Molecular Junctions and Nanostructures","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10913","display_name":"Molecular Junctions and Nanostructures","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10923","display_name":"Force Microscopy Techniques and Applications","score":0.9951000213623047,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9939000010490417,"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/quantum-entanglement","display_name":"Quantum entanglement","score":0.750488817691803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.662424623966217},{"id":"https://openalex.org/keywords/separable-state","display_name":"Separable state","score":0.6586962938308716},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6493239402770996},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5840663909912109},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.49340835213661194},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.47191527485847473},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.4500308036804199},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.42309463024139404},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4209047853946686},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.15221542119979858},{"id":"https://openalex.org/keywords/quantum-discord","display_name":"Quantum discord","score":0.12945914268493652},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09016337990760803}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.750488817691803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.662424623966217},{"id":"https://openalex.org/C55795843","wikidata":"https://www.wikidata.org/wiki/Q614178","display_name":"Separable state","level":5,"score":0.6586962938308716},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6493239402770996},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5840663909912109},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49340835213661194},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.47191527485847473},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4500308036804199},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.42309463024139404},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4209047853946686},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.15221542119979858},{"id":"https://openalex.org/C139356082","wikidata":"https://www.wikidata.org/wiki/Q7269038","display_name":"Quantum discord","level":4,"score":0.12945914268493652},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09016337990760803},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2021-11-25-589","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-25-589","pdf_url":"https://quantum-journal.org/papers/q-2021-11-25-589/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.09064","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.09064","pdf_url":"https://arxiv.org/pdf/2006.09064","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3034283638","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.09064.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:04860e9e1cfb4bca8f450f9f639b65a3","is_oa":true,"landing_page_url":"https://doaj.org/article/04860e9e1cfb4bca8f450f9f639b65a3","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 589 (2021)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2006.09064","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.09064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article-journal"}],"best_oa_location":{"id":"doi:10.22331/q-2021-11-25-589","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-11-25-589","pdf_url":"https://quantum-journal.org/papers/q-2021-11-25-589/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1497218953","display_name":null,"funder_award_id":"Spanish","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1874999417","display_name":null,"funder_award_id":"SEV-2015-0522","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G2718273459","display_name":null,"funder_award_id":"QuantumCAT","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G3021459029","display_name":null,"funder_award_id":"SFB F71","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G3894466083","display_name":null,"funder_award_id":"SGR 1381","funder_id":"https://openalex.org/F4320310210","funder_display_name":"Fundaci\u00f3n Cellex"},{"id":"https://openalex.org/G4276540831","display_name":null,"funder_award_id":"SEV-2015-0522","funder_id":"https://openalex.org/F4320310210","funder_display_name":"Fundaci\u00f3n Cellex"},{"id":"https://openalex.org/G4493618802","display_name":null,"funder_award_id":"30947","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4696003754","display_name":null,"funder_award_id":"414325145","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5009791170","display_name":null,"funder_award_id":"Project 414325145","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5617805276","display_name":null,"funder_award_id":"SGR 1381","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G5658388395","display_name":null,"funder_award_id":"CERCA","funder_id":"https://openalex.org/F4320321505","funder_display_name":"Generalitat de Catalunya"},{"id":"https://openalex.org/G581184630","display_name":null,"funder_award_id":"414325145","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6783783255","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7290919025","display_name":null,"funder_award_id":"P 30947","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G762232396","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7864958084","display_name":null,"funder_award_id":"Cellex","funder_id":"https://openalex.org/F4320310210","funder_display_name":"Fundaci\u00f3n Cellex"},{"id":"https://openalex.org/G8184292771","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G8687424366","display_name":null,"funder_award_id":"CERCA","funder_id":"https://openalex.org/F4320310210","funder_display_name":"Fundaci\u00f3n Cellex"}],"funders":[{"id":"https://openalex.org/F4320310210","display_name":"Fundaci\u00f3n Cellex","ror":null},{"id":"https://openalex.org/F4320315803","display_name":"Centres de Recerca de Catalunya","ror":null},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321505","display_name":"Generalitat de Catalunya","ror":"https://ror.org/01bg62x04"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3034283638.pdf","grobid_xml":"https://content.openalex.org/works/W3034283638.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W2007264979","https://openalex.org/W2016990905","https://openalex.org/W2020582629","https://openalex.org/W2022122405","https://openalex.org/W2026298842","https://openalex.org/W2027562075","https://openalex.org/W2030328439","https://openalex.org/W2034920898","https://openalex.org/W2041389295","https://openalex.org/W2043915619","https://openalex.org/W2055253753","https://openalex.org/W2059372025","https://openalex.org/W2072603413","https://openalex.org/W2072919800","https://openalex.org/W2087083200","https://openalex.org/W2092206895","https://openalex.org/W2095620539","https://openalex.org/W2120062331","https://openalex.org/W2126736947","https://openalex.org/W2139995600","https://openalex.org/W2144126354","https://openalex.org/W2283338604","https://openalex.org/W2339513643","https://openalex.org/W2485429769","https://openalex.org/W2536620281","https://openalex.org/W2593149766","https://openalex.org/W2593344530","https://openalex.org/W2604868470","https://openalex.org/W2612899195","https://openalex.org/W2763152578","https://openalex.org/W2883401671","https://openalex.org/W2912522929","https://openalex.org/W2916047539","https://openalex.org/W2982169647","https://openalex.org/W3119976028","https://openalex.org/W4292070118","https://openalex.org/W6604871844"],"related_works":["https://openalex.org/W3008523995","https://openalex.org/W3098084575","https://openalex.org/W2297316452","https://openalex.org/W2797346236","https://openalex.org/W3207076202","https://openalex.org/W2091745684","https://openalex.org/W41794807","https://openalex.org/W2580380742","https://openalex.org/W3102849376","https://openalex.org/W1674520449","https://openalex.org/W2950214556","https://openalex.org/W3159535941","https://openalex.org/W3101989717","https://openalex.org/W1899677993","https://openalex.org/W2797393359","https://openalex.org/W1502908815","https://openalex.org/W3106117938","https://openalex.org/W3213854893","https://openalex.org/W3105872779","https://openalex.org/W3128860145"],"abstract_inverted_index":{"We":[0,48],"consider":[1],"the":[2,37,50,56,71,97,113],"entanglement":[3],"marginal":[4,62],"problem,":[5,28],"which":[6],"consists":[7],"of":[8,13,32,36,39,52,58,99,102],"deciding":[9],"whether":[10],"a":[11,44,80,84,106],"number":[12],"reduced":[14],"density":[15],"matrices":[16],"are":[17,73],"compatible":[18],"with":[19,105,135],"an":[20,59,92],"overall":[21],"separable":[22,46,103],"quantum":[23,40],"state.":[24],"To":[25],"tackle":[26],"this":[27],"we":[29,86,89],"propose":[30],"hierarchies":[31,72],"semidefinite":[33],"programming":[34],"relaxations":[35],"set":[38,98],"state":[41],"marginals":[42,101],"admitting":[43],"fully":[45],"extension.":[47],"connect":[49],"completeness":[51],"each":[53],"hierarchy":[54],"to":[55,96,120],"resolution":[57],"analog":[60],"classical":[61],"problem":[63],"and":[64],"thus":[65],"identify":[66],"relevant":[67],"experimental":[68],"situations":[69],"where":[70],"complete.":[74],"For":[75],"finitely":[76],"many":[77],"parties":[78],"on":[79,112],"star":[81],"configuration":[82],"or":[83],"chain,":[85],"find":[87],"that":[88],"can":[90],"achieve":[91],"arbitrarily":[93],"good":[94],"approximation":[95],"nearest-neighbour":[100],"states":[104],"time":[107],"(space)":[108],"complexity":[109],"polynomial":[110],"(linear)":[111],"system":[114],"size.":[115],"Our":[116],"results":[117],"even":[118],"extend":[119],"infinite":[121],"systems,":[122],"such":[123],"as":[124,129,131],"translation-invariant":[125],"systems":[126],"in":[127],"1D,":[128],"well":[130],"higher":[132],"spatial":[133],"dimensions":[134],"extra":[136],"symmetries.":[137]},"counts_by_year":[{"year":2021,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}