{"id":"https://openalex.org/W2649051464","doi":"https://doi.org/10.1109/tit.2017.2719044","title":"Sample-optimal tomography of quantum states","display_name":"Sample-optimal tomography of quantum states","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2649051464","doi":"https://doi.org/10.1109/tit.2017.2719044","mag":"2649051464"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2719044","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2719044","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1508.01797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036464616","display_name":"Jeongwan Haah","orcid":"https://orcid.org/0000-0002-1087-6853"},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeongwan Haah","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA","Station Q Quantum Architectures and Computation, Microsoft Research, Redmond, WA, USA"],"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Station Q Quantum Architectures and Computation, Microsoft Research, Redmond, WA, USA","institution_ids":["https://openalex.org/I1290206253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008766821","display_name":"Aram W. Harrow","orcid":"https://orcid.org/0000-0003-3220-7682"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aram W. Harrow","raw_affiliation_strings":["Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043930796","display_name":"Zhengfeng Ji","orcid":"https://orcid.org/0000-0002-7659-3178"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I4210128818","display_name":"Institute of Software","ror":"https://ror.org/033dfsn42","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210128818"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU","CA","CN"],"is_corresponding":false,"raw_author_name":"Zhengfeng Ji","raw_affiliation_strings":["Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia","Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada","State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210128818","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044901410","display_name":"Xiaodi Wu","orcid":"https://orcid.org/0000-0001-8877-9802"},"institutions":[{"id":"https://openalex.org/I4210108409","display_name":"Joint Center for Quantum Information and Computer Science","ror":"https://ror.org/02048n894","country_code":"US","type":"facility","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065","https://openalex.org/I4210108409","https://openalex.org/I66946132"]},{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaodi Wu","raw_affiliation_strings":["Joint Center for Quantum Information and Computer Science, University of Maryland at College Park, College Park, MD, USA"],"affiliations":[{"raw_affiliation_string":"Joint Center for Quantum Information and Computer Science, University of Maryland at College Park, College Park, MD, USA","institution_ids":["https://openalex.org/I4210108409","https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088217238","display_name":"Nengkun Yu","orcid":"https://orcid.org/0000-0003-1188-3032"},"institutions":[{"id":"https://openalex.org/I4210096034","display_name":"Centre for Quantum Computation and Communication Technology","ror":"https://ror.org/00rnbty21","country_code":"AU","type":"facility","lineage":["https://openalex.org/I1337719021","https://openalex.org/I165143802","https://openalex.org/I2801453606","https://openalex.org/I4210096034","https://openalex.org/I4210132349"]},{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]},{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]},{"id":"https://openalex.org/I79817857","display_name":"University of Guelph","ror":"https://ror.org/01r7awg59","country_code":"CA","type":"education","lineage":["https://openalex.org/I79817857"]}],"countries":["AU","CA"],"is_corresponding":false,"raw_author_name":"Nengkun Yu","raw_affiliation_strings":["Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia","Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada","Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada"],"affiliations":[{"raw_affiliation_string":"Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia","institution_ids":["https://openalex.org/I4210096034","https://openalex.org/I114017466"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada","institution_ids":["https://openalex.org/I79817857"]},{"raw_affiliation_string":"Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036464616"],"corresponding_institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":7.8989,"has_fulltext":false,"cited_by_count":169,"citation_normalized_percentile":{"value":0.97826146,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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":0.9966999888420105,"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/trace-distance","display_name":"Trace distance","score":0.7248345017433167},{"id":"https://openalex.org/keywords/povm","display_name":"POVM","score":0.6203815340995789},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.6151596307754517},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5785879492759705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5778106451034546},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5188835263252258},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.4863198697566986},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.47448280453681946},{"id":"https://openalex.org/keywords/density-matrix","display_name":"Density matrix","score":0.46526575088500977},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4619806706905365},{"id":"https://openalex.org/keywords/quantum-tomography","display_name":"Quantum tomography","score":0.4579336941242218},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4525543451309204},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.44904035329818726},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.44717806577682495},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4429186284542084},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4403047561645508},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43769770860671997},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.417011559009552},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4095136523246765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30717289447784424},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30254805088043213},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.254844605922699},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22577747702598572},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.19726800918579102},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1906607449054718},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14439162611961365}],"concepts":[{"id":"https://openalex.org/C105063144","wikidata":"https://www.wikidata.org/wiki/Q7831154","display_name":"Trace distance","level":4,"score":0.7248345017433167},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.6203815340995789},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.6151596307754517},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5785879492759705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5778106451034546},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5188835263252258},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.4863198697566986},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.47448280453681946},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.46526575088500977},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4619806706905365},{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.4579336941242218},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4525543451309204},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.44904035329818726},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.44717806577682495},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4429186284542084},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4403047561645508},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43769770860671997},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.417011559009552},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4095136523246765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30717289447784424},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30254805088043213},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.254844605922699},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22577747702598572},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.19726800918579102},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1906607449054718},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14439162611961365},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2017.2719044","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2719044","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.01797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.01797","pdf_url":"https://arxiv.org/pdf/1508.01797","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1508.01797","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.01797","pdf_url":"https://arxiv.org/pdf/1508.01797","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1815357327","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320309949","funder_display_name":"Canadian Institute for Advanced Research"},{"id":"https://openalex.org/G2356925628","display_name":"CAREER: Applications of Quantum Information Theory","funder_award_id":"1452616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4952545190","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G5539695041","display_name":null,"funder_award_id":"W911NF-12-1-0486","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5614971186","display_name":null,"funder_award_id":"Fellow","funder_id":"https://openalex.org/F4320309949","funder_display_name":"Canadian Institute for Advanced Research"},{"id":"https://openalex.org/G5851453055","display_name":null,"funder_award_id":"Scott","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7489425848","display_name":null,"funder_award_id":"CCF-1452616","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7929468754","display_name":null,"funder_award_id":"CCF-1111382","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309949","display_name":"Canadian Institute for Advanced Research","ror":"https://ror.org/01sdtdd95"},{"id":"https://openalex.org/F4320322676","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W639433093","https://openalex.org/W1482020040","https://openalex.org/W1529624360","https://openalex.org/W1534413569","https://openalex.org/W1538746183","https://openalex.org/W1545094706","https://openalex.org/W1551092272","https://openalex.org/W1556924800","https://openalex.org/W1589193224","https://openalex.org/W1601059808","https://openalex.org/W1605974080","https://openalex.org/W1800240078","https://openalex.org/W1892898072","https://openalex.org/W1944079109","https://openalex.org/W1964348979","https://openalex.org/W1975049815","https://openalex.org/W1976841091","https://openalex.org/W1976865215","https://openalex.org/W1980744208","https://openalex.org/W1988369744","https://openalex.org/W1991379572","https://openalex.org/W1993000102","https://openalex.org/W1995838546","https://openalex.org/W1995989441","https://openalex.org/W1999198560","https://openalex.org/W2005097526","https://openalex.org/W2017282821","https://openalex.org/W2026059047","https://openalex.org/W2032830293","https://openalex.org/W2033879010","https://openalex.org/W2033934891","https://openalex.org/W2034274945","https://openalex.org/W2039072244","https://openalex.org/W2051869207","https://openalex.org/W2064743924","https://openalex.org/W2074626019","https://openalex.org/W2082528946","https://openalex.org/W2084157340","https://openalex.org/W2089410862","https://openalex.org/W2090368878","https://openalex.org/W2090928031","https://openalex.org/W2096150384","https://openalex.org/W2098572895","https://openalex.org/W2105886659","https://openalex.org/W2114252499","https://openalex.org/W2122401230","https://openalex.org/W2134348739","https://openalex.org/W2140336578","https://openalex.org/W2145623531","https://openalex.org/W2163261931","https://openalex.org/W2167346196","https://openalex.org/W2264297261","https://openalex.org/W2752870707","https://openalex.org/W2951499400","https://openalex.org/W2963583445","https://openalex.org/W3013565890","https://openalex.org/W3103248090","https://openalex.org/W3103665391","https://openalex.org/W3104490977","https://openalex.org/W3106202170","https://openalex.org/W3106300156","https://openalex.org/W3143400115","https://openalex.org/W4285719527","https://openalex.org/W4295163619","https://openalex.org/W6633508768","https://openalex.org/W6775454162"],"related_works":["https://openalex.org/W2950844595","https://openalex.org/W3099169560","https://openalex.org/W1964028587","https://openalex.org/W2263092286","https://openalex.org/W3100430039","https://openalex.org/W3157044737","https://openalex.org/W4309534894","https://openalex.org/W2965462801","https://openalex.org/W3204602721","https://openalex.org/W2904945257"],"abstract_inverted_index":{"It":[0],"is":[1],"a":[2,50,60,79,142],"fundamental":[3],"problem":[4],"to":[5,20,32,70,73,84,97,127],"decide":[6],"how":[7],"many":[8],"copies":[9,48,69,95,122],"of":[10,54],"an":[11],"unknown":[12],"mixed":[13],"quantum":[14,143],"state":[15],"are":[16,123],"necessary":[17,124],"and":[18,78],"sufficient":[19],"determine":[21],"the":[22],"state.":[23],"Previously,":[24],"it":[25],"was":[26],"known":[27],"only":[28],"that":[29,65,107],"estimating":[30],"states":[31],"error":[33,74,99,129],"\u03b5":[34,100],"in":[35,76,101,125,131,145,148],"trace":[36,102],"distance":[37],"required":[38],"O(dr":[39],"<sup":[40,44,90,113,117],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,45,91,114,118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[42,46,92,115,119],"/\u03b5":[43],")":[47],"for":[49,108],"d-dimensional":[51],"density":[52],"matrix":[53],"rank":[55],"r.":[56],"Here,":[57],"we":[58],"give":[59],"theoretical":[61],"measurement":[62,137],"scheme":[63],"(POVM)":[64],"requires":[66],"O(dr/\u03b4)ln":[67],"(d/\u03b4)":[68],"estimate":[71],"\u03c1":[72],"\u03b4":[75,130],"infidelity,":[77],"matching":[80],"lower":[81],"bound":[82],"up":[83],"logarithmic":[85],"factors.":[86],"This":[87],"implies":[88],"O((dr/\u03b5":[89],")ln":[93],"(d/\u03b5))":[94],"suffice":[96],"achieve":[98,128],"distance.":[103],"We":[104],"also":[105],"prove":[106],"independent":[109],"(product)":[110],"measurements,":[111],"\u03a9(dr":[112],"/\u03b4":[116],")/":[120],"ln(1/\u03b4)":[121],"order":[126],"infidelity.":[132],"For":[133],"fixed":[134],"d,":[135],"our":[136],"can":[138],"be":[139],"implemented":[140],"on":[141],"computer":[144],"time":[146],"polynomial":[147],"n.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":22},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":24},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
