{"id":"https://openalex.org/W4200050915","doi":"https://doi.org/10.1145/3464693","title":"Completeness of Graphical Languages for Mixed\u00a0State Quantum Mechanics","display_name":"Completeness of Graphical Languages for Mixed\u00a0State Quantum Mechanics","publication_year":2021,"publication_date":"2021-12-21","ids":{"openalex":"https://openalex.org/W4200050915","doi":"https://doi.org/10.1145/3464693"},"language":"en","primary_location":{"id":"doi:10.1145/3464693","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3464693","pdf_url":null,"source":{"id":"https://openalex.org/S4210170170","display_name":"ACM Transactions on Quantum Computing","issn_l":"2643-6809","issn":["2643-6809","2643-6817"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Quantum Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/7871393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019417035","display_name":"Titouan Carette","orcid":"https://orcid.org/0000-0002-1618-4081"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Titouan Carette","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-1618-4081","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020089810","display_name":"Emmanuel Jeandel","orcid":"https://orcid.org/0000-0001-7236-2906"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emmanuel Jeandel","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France"],"raw_orcid":"https://orcid.org/0000-0001-7236-2906","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029014455","display_name":"Simon Perdrix","orcid":"https://orcid.org/0000-0002-1808-2409"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210121838","display_name":"Laboratoire Lorrain de Recherche en Informatique et ses Applications","ror":"https://ror.org/02vnf0c38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I277688954","https://openalex.org/I4210107720","https://openalex.org/I4210121838","https://openalex.org/I4210159245","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Simon Perdrix","raw_affiliation_strings":["Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France"],"raw_orcid":"https://orcid.org/0000-0002-1808-2409","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Lorraine, CNRS, Inria, LORIA, F 54000 Nancy, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210121838","https://openalex.org/I90183372"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060401218","display_name":"Renaud Vilmart","orcid":"https://orcid.org/0000-0002-8828-4671"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Renaud Vilmart","raw_affiliation_strings":["Universit\u00e9 Paris-Saclay, CNRS, LRI, 91405, Orsay, France"],"raw_orcid":"https://orcid.org/0000-0002-8828-4671","affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Saclay, CNRS, LRI, 91405, Orsay, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210144804"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3027,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84208028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"2","issue":"4","first_page":"1","last_page":"28"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.9973000288009644,"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/categorical-quantum-mechanics","display_name":"Categorical quantum mechanics","score":0.7525533437728882},{"id":"https://openalex.org/keywords/monoidal-category","display_name":"Monoidal category","score":0.6740270256996155},{"id":"https://openalex.org/keywords/symmetric-monoidal-category","display_name":"Symmetric monoidal category","score":0.6615484356880188},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.4877934753894806},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47355571389198303},{"id":"https://openalex.org/keywords/closed-monoidal-category","display_name":"Closed monoidal category","score":0.45982125401496887},{"id":"https://openalex.org/keywords/quantum-state","display_name":"Quantum state","score":0.43046391010284424},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4225690960884094},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.41859617829322815},{"id":"https://openalex.org/keywords/enriched-category","display_name":"Enriched category","score":0.4166172444820404},{"id":"https://openalex.org/keywords/open-quantum-system","display_name":"Open quantum system","score":0.3973492980003357},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3624383807182312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3618248701095581},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.3305020332336426},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.29947900772094727},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.27623251080513},{"id":"https://openalex.org/keywords/quantum-dynamics","display_name":"Quantum dynamics","score":0.19713273644447327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13881084322929382}],"concepts":[{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.7525533437728882},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.6740270256996155},{"id":"https://openalex.org/C98912367","wikidata":"https://www.wikidata.org/wiki/Q17103860","display_name":"Symmetric monoidal category","level":3,"score":0.6615484356880188},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4877934753894806},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47355571389198303},{"id":"https://openalex.org/C56208153","wikidata":"https://www.wikidata.org/wiki/Q5135347","display_name":"Closed monoidal category","level":4,"score":0.45982125401496887},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.43046391010284424},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4225690960884094},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.41859617829322815},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.4166172444820404},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.3973492980003357},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3624383807182312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3618248701095581},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.3305020332336426},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.29947900772094727},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.27623251080513},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.19713273644447327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13881084322929382}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3464693","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3464693","pdf_url":null,"source":{"id":"https://openalex.org/S4210170170","display_name":"ACM Transactions on Quantum Computing","issn_l":"2643-6809","issn":["2643-6809","2643-6817"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Quantum Computing","raw_type":"journal-article"},{"id":"pmh:oai:zenodo.org:7871393","is_oa":true,"landing_page_url":"https://zenodo.org/record/7871393","pdf_url":"https://zenodo.org/record/7871393","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"ACM Transactions on Quantum Computing 2(4) Art. 17 pp 1-28","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-04082921v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-04082921","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM Transactions on Quantum Computing, 2021, ACM Transactions on Quantum Computing, 2 (4), pp.1-28. ⟨10.1145/3464693⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:7871393","is_oa":true,"landing_page_url":"https://zenodo.org/record/7871393","pdf_url":"https://zenodo.org/record/7871393","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"ACM Transactions on Quantum Computing 2(4) Art. 17 pp 1-28","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G2287768106","display_name":"NExt ApplicationS of Quantum Computing","funder_award_id":"951821","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2471692569","display_name":null,"funder_award_id":"ANR-17-CE24","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4324594499","display_name":"Software-based quantum program and resource optimisation","funder_award_id":"ANR-17-CE25-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G434337789","display_name":null,"funder_award_id":"HORIZON2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7107445882","display_name":null,"funder_award_id":"ANR-17-CE25","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7859344965","display_name":"Validation of near-future quantum technologies","funder_award_id":"ANR-17-CE24-0035","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200050915.pdf","grobid_xml":"https://content.openalex.org/works/W4200050915.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W583126019","https://openalex.org/W1486765721","https://openalex.org/W1617295181","https://openalex.org/W1644475622","https://openalex.org/W1761683182","https://openalex.org/W1819959283","https://openalex.org/W1925988739","https://openalex.org/W1970994416","https://openalex.org/W1982928587","https://openalex.org/W1998549791","https://openalex.org/W1999626800","https://openalex.org/W2027998831","https://openalex.org/W2081444194","https://openalex.org/W2084269802","https://openalex.org/W2096331363","https://openalex.org/W2097264545","https://openalex.org/W2104582269","https://openalex.org/W2123531794","https://openalex.org/W2144309163","https://openalex.org/W2154828304","https://openalex.org/W2263606956","https://openalex.org/W2288446724","https://openalex.org/W2331235646","https://openalex.org/W2570901353","https://openalex.org/W2598985404","https://openalex.org/W2623710274","https://openalex.org/W2758270599","https://openalex.org/W2798910219","https://openalex.org/W2802560682","https://openalex.org/W2905947940","https://openalex.org/W2918135161","https://openalex.org/W2950262429","https://openalex.org/W2950677588","https://openalex.org/W2963618180","https://openalex.org/W2963932109","https://openalex.org/W2964217961","https://openalex.org/W2964268018","https://openalex.org/W2990961515","https://openalex.org/W3015280770","https://openalex.org/W3021054643","https://openalex.org/W3029808119","https://openalex.org/W3099533840","https://openalex.org/W3100693329","https://openalex.org/W3103164351","https://openalex.org/W3103730115","https://openalex.org/W3104500086","https://openalex.org/W3104840159","https://openalex.org/W3105021321","https://openalex.org/W4254610494","https://openalex.org/W4283759833","https://openalex.org/W4289105161","https://openalex.org/W6678566718","https://openalex.org/W6693258424","https://openalex.org/W6785827599"],"related_works":["https://openalex.org/W4221164648","https://openalex.org/W2150762370","https://openalex.org/W2288880934","https://openalex.org/W2156541639","https://openalex.org/W2410174142","https://openalex.org/W1926828240","https://openalex.org/W2126973105","https://openalex.org/W4387799810","https://openalex.org/W2998447709","https://openalex.org/W1823271149"],"abstract_inverted_index":{"There":[0],"exist":[1],"several":[2,59,180],"graphical":[3,66,181],"languages":[4,20,87,182],"for":[5,62,71,179,189,197],"quantum":[6,10,53,76,90,99,125,135,191,203],"information":[7],"processing,":[8],"like":[9,201],"circuits,":[11],"ZX-calculus,":[12],"ZW-calculus,":[13],"and":[14,27,97],"so":[15],"on.":[16],"Each":[17],"of":[18,36,44,48,64,74,82,113,123],"these":[19,65,86],"forms":[21],"a":[22,114,124,139,153,159],"\u2020-symmetric":[23,149],"monoidal":[24,150,155],"category":[25,151,156,207],"(\u2020-SMC)":[26],"comes":[28],"with":[29,158],"an":[30,107,127,177],"interpretation":[31],"functor":[32],"to":[33,52,57,84,92,120,186],"the":[34,45,49,80,111,142,206],"\u2020-SMC":[35],"finite-dimensional":[37],"Hilbert":[38],"spaces.":[39],"In":[40],"recent":[41],"years,":[42],"one":[43,119],"main":[46],"achievements":[47],"categorical":[50],"approach":[51],"mechanics":[54,91],"has":[55],"been":[56],"provide":[58,176],"equational":[60],"theories":[61],"most":[63],"languages,":[67],"making":[68,168],"them":[69],"complete":[70,188],"various":[72],"fragments":[73],"pure":[75,89,134],"mechanics.":[77,136],"We":[78,137],"address":[79],"question":[81],"how":[83],"extend":[85],"beyond":[88],"reason":[93],"about":[94],"mixed":[95],"states":[96],"general":[98,190],"operations,":[100],"i.e.,":[101],"completely":[102],"positive":[103],"maps.":[104],"Intuitively,":[105],"such":[106],"extension":[108,178],"relies":[109],"on":[110],"axiomatisation":[112],"discard":[115,143,160],"map":[116],"that":[117,129,183],"allows":[118],"get":[121],"rid":[122],"system,":[126],"operation":[128],"is":[130],"not":[131,209],"allowed":[132],"in":[133,167],"introduce":[138],"new":[140],"construction,":[141,174],"construction":[144,165,195],",":[145],"which":[146],"transforms":[147],"any":[148,169],"into":[152],"symmetric":[154],"equipped":[157],"map.":[161],"Roughly":[162],"speaking":[163],"this":[164,173,194],"consists":[166],"isometry":[170],"causal.":[171],"Using":[172],"we":[175,184],"prove":[185],"be":[187],"operations.":[192],"However,":[193],"fails":[196],"some":[198],"fringe":[199],"cases":[200],"Clifford+T":[202],"mechanics,":[204],"as":[205],"does":[208],"have":[210],"enough":[211],"isometries.":[212]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}