{"id":"https://openalex.org/W2787148027","doi":"https://doi.org/10.22331/q-2021-04-28-445","title":"Reconstructing quantum theory from diagrammatic postulates","display_name":"Reconstructing quantum theory from diagrammatic postulates","publication_year":2021,"publication_date":"2021-04-28","ids":{"openalex":"https://openalex.org/W2787148027","doi":"https://doi.org/10.22331/q-2021-04-28-445","mag":"2787148027"},"language":"en","primary_location":{"id":"doi:10.22331/q-2021-04-28-445","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-28-445","pdf_url":"https://quantum-journal.org/papers/q-2021-04-28-445/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":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2021-04-28-445/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"John H. Selby","orcid":null},"institutions":[{"id":"https://openalex.org/I40413290","display_name":"University of Gda\u0144sk","ror":"https://ror.org/011dv8m48","country_code":"PL","type":"education","lineage":["https://openalex.org/I40413290"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"John H. Selby","raw_affiliation_strings":["ICTQT, University of Gda\u0144sk, Wita Stwosza 63, 80-308 Gda\u0144sk, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ICTQT, University of Gda\u0144sk, Wita Stwosza 63, 80-308 Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I40413290"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Carlo Maria Scandolo","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Carlo Maria Scandolo","raw_affiliation_strings":["Department of Mathematics & Statistics, University of Calgary, Canada","Institute for Quantum Science and Technology, University of Calgary, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Institute for Quantum Science and Technology, University of Calgary, Canada","institution_ids":["https://openalex.org/I168635309"]}]},{"author_position":"last","author":{"id":null,"display_name":"Bob Coecke","orcid":null},"institutions":[{"id":"https://openalex.org/I4210114455","display_name":"Cambridge Quantum Computing (United Kingdom)","ror":"https://ror.org/024779x77","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210114455"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bob Coecke","raw_affiliation_strings":["Cambridge Quantum Computing Ltd"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cambridge Quantum Computing Ltd","institution_ids":["https://openalex.org/I4210114455"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":4.4892,"has_fulltext":true,"cited_by_count":41,"citation_normalized_percentile":{"value":0.951108,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"5","issue":null,"first_page":"445","last_page":"445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9383999705314636,"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"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9383999705314636,"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/T10778","display_name":"Philosophy and History of Science","score":0.01119999960064888,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.0044999998062849045,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/diagrammatic-reasoning","display_name":"Diagrammatic reasoning","score":0.928600013256073},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5713000297546387},{"id":"https://openalex.org/keywords/categorical-quantum-mechanics","display_name":"Categorical quantum mechanics","score":0.5303999781608582},{"id":"https://openalex.org/keywords/quantum-process","display_name":"Quantum process","score":0.4519999921321869},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4043999910354614},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.3917999863624573},{"id":"https://openalex.org/keywords/quantum-algorithm","display_name":"Quantum algorithm","score":0.37929999828338623},{"id":"https://openalex.org/keywords/quantum-operation","display_name":"Quantum operation","score":0.3646000027656555}],"concepts":[{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.928600013256073},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5713000297546387},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.5303999781608582},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48260000348091125},{"id":"https://openalex.org/C11255438","wikidata":"https://www.wikidata.org/wiki/Q7269085","display_name":"Quantum process","level":4,"score":0.4519999921321869},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.40799999237060547},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3917999863624573},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.37929999828338623},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.3646000027656555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36419999599456787},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.33410000801086426},{"id":"https://openalex.org/C115047598","wikidata":"https://www.wikidata.org/wiki/Q54505","display_name":"Quantum field theory","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C165973109","wikidata":"https://www.wikidata.org/wiki/Q894014","display_name":"Quantum probability","level":5,"score":0.30329999327659607},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C2778120072","wikidata":"https://www.wikidata.org/wiki/Q2858150","display_name":"Aside","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.2630000114440918},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.22331/q-2021-04-28-445","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-28-445","pdf_url":"https://quantum-journal.org/papers/q-2021-04-28-445/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:arXiv.org:1802.00367","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00367","pdf_url":"https://arxiv.org/pdf/1802.00367","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:doaj.org/article:a0fb8a7337db4c6fbf035ded2f1139cc","is_oa":true,"landing_page_url":"https://doaj.org/article/a0fb8a7337db4c6fbf035ded2f1139cc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 5, p 445 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2021-04-28-445","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2021-04-28-445","pdf_url":"https://quantum-journal.org/papers/q-2021-04-28-445/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/G7569305816","display_name":null,"funder_award_id":"2018/MAB/5","funder_id":"https://openalex.org/F4320321042","funder_display_name":"Fundacja na rzecz Nauki Polskiej"}],"funders":[{"id":"https://openalex.org/F4320306193","display_name":"John Templeton Foundation","ror":"https://ror.org/035tnyy05"},{"id":"https://openalex.org/F4320310537","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39"},{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320312716","display_name":"Innovation, Science and Economic Development Canada","ror":"https://ror.org/03zp01h17"},{"id":"https://openalex.org/F4320317153","display_name":"DeepMind","ror":"https://ror.org/00971b260"},{"id":"https://openalex.org/F4320319880","display_name":"Government of Canada","ror":"https://ror.org/010q4q527"},{"id":"https://openalex.org/F4320321042","display_name":"Fundacja na rzecz Nauki Polskiej","ror":"https://ror.org/048zd9m77"},{"id":"https://openalex.org/F4320331462","display_name":"Institut P\u00e9rim\u00e8tre de physique th\u00e9orique","ror":"https://ror.org/013m0ej23"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2787148027.pdf","grobid_xml":"https://content.openalex.org/works/W2787148027.grobid-xml"},"referenced_works_count":100,"referenced_works":["https://openalex.org/W10800830","https://openalex.org/W189607215","https://openalex.org/W209109747","https://openalex.org/W621673674","https://openalex.org/W628900295","https://openalex.org/W1589618165","https://openalex.org/W1610218046","https://openalex.org/W1617295181","https://openalex.org/W1647923837","https://openalex.org/W1656783145","https://openalex.org/W1754831402","https://openalex.org/W1824885473","https://openalex.org/W1858598740","https://openalex.org/W1937778184","https://openalex.org/W1968495841","https://openalex.org/W1982928587","https://openalex.org/W1984376813","https://openalex.org/W1998549791","https://openalex.org/W2001198704","https://openalex.org/W2008699979","https://openalex.org/W2009584590","https://openalex.org/W2009590872","https://openalex.org/W2011246386","https://openalex.org/W2017365165","https://openalex.org/W2018430837","https://openalex.org/W2040866503","https://openalex.org/W2040870895","https://openalex.org/W2046267553","https://openalex.org/W2050847409","https://openalex.org/W2058794155","https://openalex.org/W2060530067","https://openalex.org/W2060969998","https://openalex.org/W2069974662","https://openalex.org/W2076488272","https://openalex.org/W2079840239","https://openalex.org/W2080043022","https://openalex.org/W2082267666","https://openalex.org/W2097264545","https://openalex.org/W2100025838","https://openalex.org/W2113152322","https://openalex.org/W2113235349","https://openalex.org/W2114229927","https://openalex.org/W2135830616","https://openalex.org/W2142429091","https://openalex.org/W2144309163","https://openalex.org/W2145832091","https://openalex.org/W2145852050","https://openalex.org/W2145952093","https://openalex.org/W2150909030","https://openalex.org/W2161316267","https://openalex.org/W2163734234","https://openalex.org/W2189914142","https://openalex.org/W2292191240","https://openalex.org/W2313823914","https://openalex.org/W2339935580","https://openalex.org/W2402089363","https://openalex.org/W2466788633","https://openalex.org/W2522201491","https://openalex.org/W2559071265","https://openalex.org/W2561422661","https://openalex.org/W2563256558","https://openalex.org/W2580023716","https://openalex.org/W2581166775","https://openalex.org/W2585620050","https://openalex.org/W2598985404","https://openalex.org/W2609453564","https://openalex.org/W2610243179","https://openalex.org/W2623710274","https://openalex.org/W2624685823","https://openalex.org/W2625865278","https://openalex.org/W2665317427","https://openalex.org/W2760837887","https://openalex.org/W2765764239","https://openalex.org/W2767434137","https://openalex.org/W2793850372","https://openalex.org/W2911836321","https://openalex.org/W2914322689","https://openalex.org/W2914703684","https://openalex.org/W2922906818","https://openalex.org/W2950993906","https://openalex.org/W2963077944","https://openalex.org/W2963715666","https://openalex.org/W2964099448","https://openalex.org/W2969413472","https://openalex.org/W2979216389","https://openalex.org/W2990563319","https://openalex.org/W2998447709","https://openalex.org/W3003541956","https://openalex.org/W3005583570","https://openalex.org/W3009801593","https://openalex.org/W3029808119","https://openalex.org/W3037759832","https://openalex.org/W3150062340","https://openalex.org/W4205887594","https://openalex.org/W4246285206","https://openalex.org/W4246293741","https://openalex.org/W4247494971","https://openalex.org/W4254530935","https://openalex.org/W4288254508","https://openalex.org/W4297936718"],"related_works":[],"abstract_inverted_index":{"A":[0],"reconstruction":[1,59,124],"of":[2,22,28,43,60,66,101,122,128,161,165,191,203,208,241,248,257,273,295],"quantum":[3,23,44,62,102,150,162],"theory":[4,24,63,103,146,221],"refers":[5],"to":[6,17,144,175,215,304],"both":[7],"a":[8,11,26,37,46,58,129,270,296],"mathematical":[9],"and":[10,110,169,201,246,262],"conceptual":[12,99],"paradigm":[13],"that":[14,48,97,196,286],"allows":[15],"one":[16],"derive":[18],"the":[19,40,67,98,105,115,118,126,135,156,177,182,206,230,242,254,287,292,305],"usual":[20,41],"formulation":[21,42],"from":[25,114],"set":[27],"primitive":[29],"assumptions.":[30],"The":[31],"motivation":[32],"for":[33],"doing":[34,192],"so":[35],"is":[36,125,290,302],"discomfort":[38,47],"with":[39,50,222],"theory,":[45,163],"started":[49],"its":[51],"originator":[52],"John":[53],"von":[54],"Neumann.":[55],"We":[56,185],"present":[57],"finite-dimensional":[61],"where":[64],"all":[65],"postulates":[68],"are":[69,79,91],"stated":[70,80,92],"in":[71,81,93,107,218],"diagrammatic":[72,116,271],"terms,":[73,83,95],"making":[74,84],"them":[75,85],"intuitive.":[76],"Equivalently,":[77],"they":[78,90],"category-theoretic":[82],"mathematically":[86],"appealing.":[87],"Again":[88],"equivalently,":[89],"process-theoretic":[94],"establishing":[96],"backbone":[100],"concerns":[104],"manner":[106],"which":[108],"systems":[109,168,180],"processes":[111],"compose.":[112],"Aside":[113],"form,":[117],"key":[119],"novel":[120,188],"aspect":[121],"this":[123,300],"introduction":[127],"new":[130],"postulate,":[131,138],"symmetric":[132,139,243],"purification.":[133],"Unlike":[134],"ordinary":[136],"purification":[137,140,232,244],"applies":[141],"equally":[142],"well":[143,148],"classical":[145],"as":[147,149,181,237,299],"theory.":[151],"Therefore":[152],"we":[153,227,268,284],"first":[154],"reconstruct":[155],"full":[157],"process":[158,220,263,281],"theoretic":[159],"description":[160],"consisting":[164],"composite":[166],"classical-quantum":[167],"their":[170],"interactions,":[171],"before":[172],"restricting":[173],"ourselves":[174],"just":[176],"\u2018fully":[178],"quantum\u2019":[179],"final":[183],"step.":[184],"propose":[186],"two":[187],"alternative":[189],"manners":[190],"so,":[193],"\u2018no-leaking\u2019":[194],"(roughly":[195,205],"information":[197],"gain":[198],"causes":[199],"disturbance)":[200],"\u2018purity":[202],"cups\u2019":[204],"existence":[207],"entangled":[209],"states).":[210],"Interestingly,":[211],"these":[212],"turn":[213],"out":[214],"be":[216,235,278],"equivalent":[217],"any":[219],"cups":[223],"&amp;":[224],"caps.":[225],"Additionally,":[226],"show":[228],"how":[229],"standard":[231],"postulate":[233,245],"can":[234,277],"seen":[236],"an":[238],"immediate":[239],"consequence":[240],"purity":[247],"cups.":[249],"Other":[250],"tangential":[251],"results":[252],"concern":[253],"specific":[255],"frameworks":[256],"generalised":[258],"probabilistic":[259],"theories":[260,264],"(GPTs)":[261],"(a.k.a.":[265],"CQM).":[266],"Firstly,":[267],"provide":[269],"presentation":[272],"GPTs,":[274],"which,":[275],"henceforth,":[276],"subsumed":[279],"under":[280],"theories.":[282],"Secondly,":[283],"argue":[285],"\u2018sharp":[288],"dagger\u2019":[289],"indeed":[291],"right":[293],"choice":[294],"dagger":[297],"structure":[298],"sharpness":[301],"vital":[303],"reconstruction.":[306]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2018-02-23T00:00:00"}
