{"id":"https://openalex.org/W2968911711","doi":"https://doi.org/10.1007/s10107-020-01537-7","title":"The sum-of-squares hierarchy on the sphere and applications in quantum information theory","display_name":"The sum-of-squares hierarchy on the sphere and applications in quantum information theory","publication_year":2020,"publication_date":"2020-07-06","ids":{"openalex":"https://openalex.org/W2968911711","doi":"https://doi.org/10.1007/s10107-020-01537-7","mag":"2968911711"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-020-01537-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01537-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01537-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01537-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088786789","display_name":"Kun Fang","orcid":"https://orcid.org/0000-0002-9232-6846"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Kun Fang","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0002-9232-6846","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017261970","display_name":"Hamza Fawzi","orcid":null},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Hamza Fawzi","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK"],"raw_orcid":"https://orcid.org/0000-0001-6026-4102","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088786789"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":7.0891,"has_fulltext":true,"cited_by_count":63,"citation_normalized_percentile":{"value":0.97802198,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"190","issue":"1-2","first_page":"331","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6563655734062195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39882892370224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3509673476219177},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34357357025146484}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6563655734062195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39882892370224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3509673476219177},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34357357025146484}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10107-020-01537-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01537-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01537-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1908.05155","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.05155","pdf_url":"https://arxiv.org/pdf/1908.05155","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":null,"raw_type":"text"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/307525","is_oa":false,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/307525","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"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":"Article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/329200","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/329200","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.17863/cam.54615","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.54615","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.17863/cam.76648","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.76648","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10107-020-01537-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-020-01537-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-020-01537-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G161411901","display_name":null,"funder_award_id":"RG74916","funder_id":"https://openalex.org/F4320322909","funder_display_name":"Isaac Newton Trust"}],"funders":[{"id":"https://openalex.org/F4320322909","display_name":"Isaac Newton Trust","ror":"https://ror.org/02gn6ta77"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2968911711.pdf","grobid_xml":"https://content.openalex.org/works/W2968911711.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W24931029","https://openalex.org/W1549638383","https://openalex.org/W1568816820","https://openalex.org/W1572246416","https://openalex.org/W1588255751","https://openalex.org/W1615037550","https://openalex.org/W1782308010","https://openalex.org/W1963693964","https://openalex.org/W1967344706","https://openalex.org/W1985474048","https://openalex.org/W1997973396","https://openalex.org/W2007264979","https://openalex.org/W2016990905","https://openalex.org/W2026298842","https://openalex.org/W2026507321","https://openalex.org/W2028932986","https://openalex.org/W2039088196","https://openalex.org/W2044630019","https://openalex.org/W2044949772","https://openalex.org/W2047642496","https://openalex.org/W2048648826","https://openalex.org/W2061269184","https://openalex.org/W2062549444","https://openalex.org/W2077242588","https://openalex.org/W2114467398","https://openalex.org/W2133404041","https://openalex.org/W2140214428","https://openalex.org/W2143215791","https://openalex.org/W2144362128","https://openalex.org/W2161267996","https://openalex.org/W2325692311","https://openalex.org/W2581091247","https://openalex.org/W2607074006","https://openalex.org/W2624804050","https://openalex.org/W2997618127","https://openalex.org/W3019183471","https://openalex.org/W3037737784","https://openalex.org/W3089116201","https://openalex.org/W3098084575","https://openalex.org/W3145564876","https://openalex.org/W4240963782","https://openalex.org/W4297804271","https://openalex.org/W6655849190","https://openalex.org/W6700049840"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"the":[3,11,21,32,46,74,99,102,106,114,134,143,150,158,174],"problem":[4,110],"of":[5,17,31,48,101,155,177],"maximizing":[6],"a":[7,28,109],"homogeneous":[8],"polynomial":[9,22],"on":[10,133],"unit":[12],"sphere":[13,135],"and":[14,38,40,104,120,157,180],"its":[15],"hierarchy":[16,103,160],"sum-of-squares":[18],"relaxations.":[19],"Exploiting":[20],"kernel":[23],"technique":[24],",":[25],"we":[26,43,165],"obtain":[27],"quadratic":[29],"improvement":[30],"known":[33],"convergence":[34,49,175],"rate":[35,47],"by":[36,117],"Reznick":[37],"Doherty":[39],"Wehner.":[41],"Specifically,":[42],"show":[44,166],"that":[45,167],"is":[50,98],"no":[51],"worse":[52],"than":[53],"$$O(d^2/\\ell":[54],"^2)$$":[55],"<mml:math":[56,80,94],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[57,81,95],"<mml:mrow>":[58,82],"<mml:mi>O</mml:mi>":[59],"<mml:mo>(</mml:mo>":[60,86],"<mml:msup>":[61,66],"<mml:mi>d</mml:mi>":[62,87],"<mml:mn>2</mml:mn>":[63,68],"</mml:msup>":[64,69],"<mml:mo>/</mml:mo>":[65],"<mml:mi>\u2113</mml:mi>":[67,83,96],"<mml:mo>)</mml:mo>":[70,88],"</mml:mrow>":[71,89],"</mml:math>":[72,90,97],"in":[73,113,139,161],"regime":[75],"$$\\ell":[76,92],"=":[77],"\\Omega":[78],"(d)$$":[79],"<mml:mo>=</mml:mo>":[84],"<mml:mi>\u03a9</mml:mi>":[85],"where":[91],"$$":[93],"level":[100],"d":[105],"dimension,":[107],"solving":[108],"left":[111],"open":[112],"recent":[115],"paper":[116],"de":[118],"Klerk":[119],"Laurent":[121],"(":[122],"arXiv:1904.08828":[123],").":[124],"Importantly,":[125],"our":[126,168],"analysis":[127],"also":[128],"works":[129],"for":[130,142],"matrix-valued":[131],"polynomials":[132,173],"which":[136],"has":[137],"applications":[138],"quantum":[140,162],"information":[141,163],"Best":[144],"Separable":[145],"State":[146],"problem.":[147],"By":[148],"exploiting":[149],"duality":[151],"relation":[152],"between":[153],"sums":[154],"squares":[156],"Doherty\u2013Parrilo\u2013Spedalieri":[159],"theory,":[164],"result":[169],"generalizes":[170],"to":[171],"nonquadratic":[172],"rates":[176],"Navascu\u00e9s,":[178],"Owari":[179],"Plenio.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
