{"id":"https://openalex.org/W4403315193","doi":"https://doi.org/10.22331/q-2024-10-10-1499","title":"Quantum teleportation implies symmetry-protected topological order","display_name":"Quantum teleportation implies symmetry-protected topological order","publication_year":2024,"publication_date":"2024-10-10","ids":{"openalex":"https://openalex.org/W4403315193","doi":"https://doi.org/10.22331/q-2024-10-10-1499"},"language":"en","primary_location":{"id":"doi:10.22331/q-2024-10-10-1499","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-10-1499","pdf_url":"https://quantum-journal.org/papers/q-2024-10-10-1499/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2024-10-10-1499/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105287665","display_name":"Yifan Hong","orcid":"https://orcid.org/0000-0001-5236-8964"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yifan Hong","raw_affiliation_strings":["Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA","institution_ids":["https://openalex.org/I188538660"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075903034","display_name":"David T. Stephen","orcid":"https://orcid.org/0000-0002-3150-0169"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David T. Stephen","raw_affiliation_strings":["Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA","Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA","institution_ids":["https://openalex.org/I188538660"]},{"raw_affiliation_string":"Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052648219","display_name":"Aaron J. Friedman","orcid":"https://orcid.org/0000-0003-2159-6475"},"institutions":[{"id":"https://openalex.org/I188538660","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026","country_code":"US","type":"education","lineage":["https://openalex.org/I188538660"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aaron J. Friedman","raw_affiliation_strings":["Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA","institution_ids":["https://openalex.org/I188538660"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5105287665"],"corresponding_institution_ids":["https://openalex.org/I188538660"],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":1.3627,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.8449343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"8","issue":null,"first_page":"1499","last_page":"1499"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","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/T10020","display_name":"Quantum Information and Cryptography","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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9994000196456909,"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":0.9983999729156494,"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/teleportation","display_name":"Teleportation","score":0.7323950529098511},{"id":"https://openalex.org/keywords/quantum-teleportation","display_name":"Quantum teleportation","score":0.6590495109558105},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5650523900985718},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5153593420982361},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.48666268587112427},{"id":"https://openalex.org/keywords/symmetry-protected-topological-order","display_name":"Symmetry protected topological order","score":0.46757155656814575},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4657045006752014},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4192819595336914},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3417401611804962},{"id":"https://openalex.org/keywords/topological-order","display_name":"Topological order","score":0.33912235498428345},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.2778526842594147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.17297160625457764},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.1680983304977417},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0982612669467926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0798896849155426},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.06970241665840149}],"concepts":[{"id":"https://openalex.org/C154255573","wikidata":"https://www.wikidata.org/wiki/Q204043","display_name":"Teleportation","level":5,"score":0.7323950529098511},{"id":"https://openalex.org/C91717678","wikidata":"https://www.wikidata.org/wiki/Q1135332","display_name":"Quantum teleportation","level":5,"score":0.6590495109558105},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5650523900985718},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5153593420982361},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.48666268587112427},{"id":"https://openalex.org/C92542899","wikidata":"https://www.wikidata.org/wiki/Q7661340","display_name":"Symmetry protected topological order","level":4,"score":0.46757155656814575},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4657045006752014},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4192819595336914},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3417401611804962},{"id":"https://openalex.org/C45646460","wikidata":"https://www.wikidata.org/wiki/Q17165159","display_name":"Topological order","level":3,"score":0.33912235498428345},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2778526842594147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.17297160625457764},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.1680983304977417},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0982612669467926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0798896849155426},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.06970241665840149},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.22331/q-2024-10-10-1499","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-10-1499","pdf_url":"https://quantum-journal.org/papers/q-2024-10-10-1499/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:cuscholar:d791sh87w","is_oa":true,"landing_page_url":"https://scholar.colorado.edu/concern/articles/d791sh87w","pdf_url":"https://scholar.colorado.edu/downloads/8910jw32d","source":{"id":"https://openalex.org/S4306401957","display_name":"CU Scholar (University of Colorado Boulder)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I188538660","host_organization_name":"University of Colorado Boulder","host_organization_lineage":["https://openalex.org/I188538660"],"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:doaj.org/article:ce86e36e72b94dc7b042f03d80ca883c","is_oa":true,"landing_page_url":"https://doaj.org/article/ce86e36e72b94dc7b042f03d80ca883c","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 8, p 1499 (2024)","raw_type":"article"},{"id":"pmh:oai:osti.gov:2462836","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/2462836","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"doi:10.22331/q-2024-10-10-1499","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2024-10-10-1499","pdf_url":"https://quantum-journal.org/papers/q-2024-10-10-1499/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/G1065316766","display_name":null,"funder_award_id":"Award","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2811237814","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G4161081400","display_name":null,"funder_award_id":"FA9550-21-1-0195","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6098521345","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G651997764","display_name":null,"funder_award_id":"DE-SC0024324","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7090116110","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G8668440297","display_name":null,"funder_award_id":"N00014-23-1-2533","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8876996369","display_name":null,"funder_award_id":"N00014","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320332538","display_name":"University of Colorado Boulder","ror":"https://ror.org/02ttsq026"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403315193.pdf"},"referenced_works_count":81,"referenced_works":["https://openalex.org/W1485061101","https://openalex.org/W1490521149","https://openalex.org/W1492456063","https://openalex.org/W1576765155","https://openalex.org/W1589597714","https://openalex.org/W1600296105","https://openalex.org/W1929571218","https://openalex.org/W1942206397","https://openalex.org/W1976390224","https://openalex.org/W1978553093","https://openalex.org/W1978938446","https://openalex.org/W1983541697","https://openalex.org/W1988155384","https://openalex.org/W1997837296","https://openalex.org/W2000091162","https://openalex.org/W2003095492","https://openalex.org/W2003945081","https://openalex.org/W2005144372","https://openalex.org/W2008017776","https://openalex.org/W2011290825","https://openalex.org/W2013793864","https://openalex.org/W2014749022","https://openalex.org/W2021044075","https://openalex.org/W2024420461","https://openalex.org/W2035993353","https://openalex.org/W2037075681","https://openalex.org/W2038329709","https://openalex.org/W2040059039","https://openalex.org/W2042887371","https://openalex.org/W2044891881","https://openalex.org/W2050146474","https://openalex.org/W2055260145","https://openalex.org/W2055519393","https://openalex.org/W2073938011","https://openalex.org/W2092105345","https://openalex.org/W2093297681","https://openalex.org/W2095029021","https://openalex.org/W2097903774","https://openalex.org/W2105077826","https://openalex.org/W2116102644","https://openalex.org/W2125945272","https://openalex.org/W2154434103","https://openalex.org/W2157276712","https://openalex.org/W2342048570","https://openalex.org/W2525264660","https://openalex.org/W2557208042","https://openalex.org/W2730481230","https://openalex.org/W2738782225","https://openalex.org/W2789339600","https://openalex.org/W2802510854","https://openalex.org/W2806163378","https://openalex.org/W2962155699","https://openalex.org/W2967668138","https://openalex.org/W2982313648","https://openalex.org/W2990961515","https://openalex.org/W3003945158","https://openalex.org/W3037533686","https://openalex.org/W3097999112","https://openalex.org/W3098550047","https://openalex.org/W3099310808","https://openalex.org/W3103115834","https://openalex.org/W3216393954","https://openalex.org/W4226275796","https://openalex.org/W4241467129","https://openalex.org/W4247494971","https://openalex.org/W4283320162","https://openalex.org/W4293138302","https://openalex.org/W4306248320","https://openalex.org/W4380355680","https://openalex.org/W4386556088","https://openalex.org/W4386823127","https://openalex.org/W4387744574","https://openalex.org/W4388696645","https://openalex.org/W4390340899","https://openalex.org/W4391024116","https://openalex.org/W4392617721","https://openalex.org/W4394672652","https://openalex.org/W4394673498","https://openalex.org/W4395483892","https://openalex.org/W4399737054","https://openalex.org/W4400582788"],"related_works":["https://openalex.org/W2087498619","https://openalex.org/W1994195945","https://openalex.org/W2152930311","https://openalex.org/W4229666338","https://openalex.org/W2063073764","https://openalex.org/W2047555324","https://openalex.org/W1964216981","https://openalex.org/W2093560349","https://openalex.org/W1988988135","https://openalex.org/W4234063363"],"abstract_inverted_index":{"We":[0,33,117],"constrain":[1],"a":[2,41,131],"broad":[3],"class":[4,99],"of":[5,29,77,100,113],"teleportation":[6,15,112],"protocols":[7,16,38],"using":[8],"insights":[9],"from":[10],"locality.":[11],"In":[12],"the":[13,30,75,78,82,90,110,125],"``standard''":[14],"we":[17],"consider,":[18],"all":[19,36],"outcome-dependent":[20,94],"unitaries":[21],"are":[22,72],"Pauli":[23],"operators":[24],"conditioned":[25],"on":[26],"linear":[27],"functions":[28],"measurement":[31],"outcomes.":[32],"find":[34],"that":[35],"such":[37],"involve":[39],"preparing":[40],"``resource":[42],"state''":[43],"exhibiting":[44],"symmetry-protected":[45],"topological":[46],"(SPT)":[47],"order":[48,87],"with":[49,121],"Abelian":[50],"protecting":[51],"symmetry":[52],"<mml:math":[53,68,84,114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mrow":[54],"class=\"MJX-TeXAtom-ORD\"><mml:mi":[55,60,63],"class=\"MJX-tex-caligraphic\"":[56],"mathvariant=\"script\">G</mml:mi></mml:mrow><mml:mrow":[57],"class=\"MJX-TeXAtom-ORD\"><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mo":[58],"stretchy=\"false\">(</mml:mo><mml:msubsup><mml:mrow":[59],"mathvariant=\"double-struck\">Z</mml:mi></mml:mrow><mml:mn>2</mml:mn><mml:mrow":[61,64],"class=\"MJX-TeXAtom-ORD\"/></mml:msubsup><mml:mo>&amp;#x00D7;</mml:mo><mml:msubsup><mml:mrow":[62],"class=\"MJX-TeXAtom-ORD\"/></mml:msubsup><mml:msup><mml:mo":[65],"stretchy=\"false\">)</mml:mo><mml:mi>k</mml:mi></mml:msup></mml:math>.":[66],"The":[67],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>k</mml:mi></mml:math>":[69,115],"logical":[70],"states":[71,103],"teleported":[73],"between":[74],"edges":[76],"chain":[79],"by":[80],"measuring":[81],"corresponding":[83],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:math>":[85],"string":[86],"parameters":[88],"in":[89],"bulk":[91],"and":[92,107,130],"applying":[93],"Paulis.":[95],"Hence,":[96],"this":[97,119],"single":[98],"nontrivial":[101],"SPT":[102],"is":[104],"both":[105],"necessary":[106],"sufficient":[108],"for":[109],"standard":[111],"qubits.":[116],"illustrate":[118],"result":[120],"several":[122],"examples,":[123],"including":[124],"cluster":[126],"state,":[127],"variants":[128],"thereof,":[129],"nonstabilizer":[132],"hypergraph":[133],"state.":[134]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}