{"id":"https://openalex.org/W7220415947","doi":"https://doi.org/10.48550/arxiv.2610.03658","title":"A note on tomography of states with low stabilizer rank","display_name":"A note on tomography of states with low stabilizer rank","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7220415947","doi":"https://doi.org/10.48550/arxiv.2610.03658"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03658","pdf_url":"https://arxiv.org/pdf/2610.03658","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/2610.03658","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074373430","display_name":"Arkopal Dutt","orcid":"https://orcid.org/0000-0001-6942-2963","observed_orcids":["https://orcid.org/0000-0001-6942-2963"]},"institutions":[{"id":"https://openalex.org/I4405286557","display_name":"IBM Research - Cambridge (United States)","ror":"https://ror.org/02gmb6f51","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4405286557"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dutt, Arkopal","raw_affiliation_strings":["IBM Research , Cambridge"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research , Cambridge","institution_ids":["https://openalex.org/I4405286557"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074373430"],"corresponding_institution_ids":["https://openalex.org/I4405286557"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9526000022888184,"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":0.9526000022888184,"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":0.04309999942779541,"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":0.0010999999940395355,"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/quantum-state-tomography","display_name":"quantum state tomography","score":0.9779999852180481},{"id":"https://openalex.org/keywords/stabilizer-states","display_name":"stabilizer states","score":0.8220000267028809},{"id":"https://openalex.org/keywords/trace-distance","display_name":"trace distance","score":0.8740000128746033}],"concepts":[{"id":"https://openalex.org/C2777502316","wikidata":"https://www.wikidata.org/wiki/Q2712515","display_name":"Stabilizer (aeronautics)","level":2,"score":0.8537999987602234},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7102000117301941},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5656999945640564},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5338000059127808},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.37630000710487366},{"id":"https://openalex.org/C163716698","wikidata":"https://www.wikidata.org/wiki/Q841267","display_name":"Tomography","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C544519230","wikidata":"https://www.wikidata.org/wiki/Q32566","display_name":"Computed tomography","level":2,"score":0.3481999933719635},{"id":"https://openalex.org/C166834278","wikidata":"https://www.wikidata.org/wiki/Q4218494","display_name":"Quantum tomography","level":4,"score":0.3084999918937683},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.301800012588501},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.03658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03658","pdf_url":"https://arxiv.org/pdf/2610.03658","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.2610.03658","doi":"https://doi.org/10.48550/arxiv.2610.03658","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03658","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:2610.03658","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03658","pdf_url":"https://arxiv.org/pdf/2610.03658","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220415947.pdf","grobid_xml":"https://content.openalex.org/works/W7220415947.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2734817276","https://openalex.org/W4416112416","https://openalex.org/W7163903604","https://openalex.org/W7167286547","https://openalex.org/W7212258339","https://openalex.org/W7213604495"],"related_works":["https://openalex.org/W7163903604","https://openalex.org/W4411319934","https://openalex.org/W7220681077","https://openalex.org/W4394591278","https://openalex.org/W4414979750","https://openalex.org/W7213359256","https://openalex.org/W3168912476","https://openalex.org/W3206309997","https://openalex.org/W7171400120","https://openalex.org/W4415316390"],"abstract_inverted_index":{"In":[0],"this":[1],"note,":[2],"we":[3],"consider":[4],"tomography":[5,40,113],"of":[6,24,83,87,103],"$n$-qubit":[7],"quantum":[8],"states":[9,44,116],"$|\u03c8\\rangle$":[10],"that":[11,68],"are":[12],"promised":[13],"to":[14,46],"have":[15],"stabilizer":[16,22,35,70,85,119],"rank":[17],"$k$":[18],"i.e.,":[19],"admit":[20],"a":[21,34,39,112],"decomposition":[23,86],"$|\u03c8\\rangle":[25],"=":[26],"\\sum_{i=1}^k":[27],"c_i":[28],"|\u03d5_i\\rangle$":[29],"where":[30],"each":[31],"$|\u03d5_i\\rangle$":[32],"is":[33,74,107],"state.":[36],"We":[37],"give":[38],"protocol":[41,106,114],"for":[42,115],"such":[43],"up":[45],"trace":[47],"distance":[48],"$\\varepsilon":[49],">":[50],"0$":[51],"running":[52],"in":[53],"$\\textsf{poly}(n,2^k,1/\\varepsilon)$":[54],"time":[55],"and":[56,96],"thus":[57],"can":[58,89],"handle":[59],"$k=O(\\log":[60],"n)$":[61],"efficiently.":[62],"This":[63],"follows":[64],"from":[65],"first":[66],"showing":[67],"the":[69,75,80,99],"extent":[71],"$\u03be(|\u03c8\\rangle)$,":[72],"which":[73],"minimal":[76],"$\\ell_1$":[77],"norm":[78],"over":[79],"coefficients":[81],"$\\{c_i\\}$":[82],"any":[84],"$|\u03c8\\rangle$,":[88],"be":[90],"bounded":[91,118],"as":[92],"$\u03be(|\u03c8\\rangle)":[93],"\\leq":[94],"2^{O(k)}$":[95],"improving":[97],"upon":[98],"previous":[100],"best":[101],"bound":[102],"$k^{O(k)}$.":[104],"The":[105],"then":[108],"obtained":[109],"by":[110],"utilizing":[111],"with":[117],"extent.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-06T00:00:00"}