{"id":"https://openalex.org/W2949295853","doi":"https://doi.org/10.1017/s0960129512000047","title":"A new description of orthogonal bases","display_name":"A new description of orthogonal bases","publication_year":2012,"publication_date":"2012-11-09","ids":{"openalex":"https://openalex.org/W2949295853","doi":"https://doi.org/10.1017/s0960129512000047","mag":"2949295853"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129512000047","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129512000047","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0810.0812","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"BOB COECKE","orcid":null},"institutions":[{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"BOB COECKE","raw_affiliation_strings":["Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:"],"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"]}]},{"author_position":"middle","author":{"id":null,"display_name":"DUSKO PAVLOVIC","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"DUSKO PAVLOVIC","raw_affiliation_strings":["Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:"],"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"]}]},{"author_position":"last","author":{"id":null,"display_name":"JAMIE VICARY","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210146410","display_name":"Science Oxford","ror":"https://ror.org/04j8yhy50","country_code":"GB","type":"nonprofit","lineage":["https://openalex.org/I4210146410"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"JAMIE VICARY","raw_affiliation_strings":["Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:"],"affiliations":[{"raw_affiliation_string":"Oxford University Computing Laboratory, Department of Computer Science, University of Oxford, Parks Road, Oxford OX 1 3QD, United Kingdom Email:","institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40120149","https://openalex.org/I4210146410"],"apc_list":null,"apc_paid":null,"fwci":5.4482,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.96086428,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"23","issue":"3","first_page":"555","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.3156000077724457,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.3156000077724457,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.19910000264644623,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.15309999883174896,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.8442000150680542},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7760999798774719},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.7422000169754028},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7059999704360962},{"id":"https://openalex.org/keywords/tensor-product-of-hilbert-spaces","display_name":"Tensor product of Hilbert spaces","score":0.6553999781608582},{"id":"https://openalex.org/keywords/categorical-quantum-mechanics","display_name":"Categorical quantum mechanics","score":0.6402000188827515},{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.6347000002861023},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.6279000043869019},{"id":"https://openalex.org/keywords/closed-monoidal-category","display_name":"Closed monoidal category","score":0.595300018787384}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.8442000150680542},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7760999798774719},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7422000169754028},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7182000279426575},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7059999704360962},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.6553999781608582},{"id":"https://openalex.org/C105295557","wikidata":"https://www.wikidata.org/wiki/Q5051814","display_name":"Categorical quantum mechanics","level":5,"score":0.6402000188827515},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6347000002861023},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.6279000043869019},{"id":"https://openalex.org/C56208153","wikidata":"https://www.wikidata.org/wiki/Q5135347","display_name":"Closed monoidal category","level":4,"score":0.595300018787384},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5835999846458435},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.5685999989509583},{"id":"https://openalex.org/C98912367","wikidata":"https://www.wikidata.org/wiki/Q17103860","display_name":"Symmetric monoidal category","level":3,"score":0.5421000123023987},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5194000005722046},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4390000104904175},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4169999957084656},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.34630000591278076},{"id":"https://openalex.org/C2779904274","wikidata":"https://www.wikidata.org/wiki/Q1945014","display_name":"Monoidal category","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C41054515","wikidata":"https://www.wikidata.org/wiki/Q2000912","display_name":"Standard basis","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32179999351501465},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.31119999289512634},{"id":"https://openalex.org/C95635736","wikidata":"https://www.wikidata.org/wiki/Q1786640","display_name":"Wreath product","level":3,"score":0.29760000109672546},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2847000062465668},{"id":"https://openalex.org/C60064506","wikidata":"https://www.wikidata.org/wiki/Q1262627","display_name":"Rigged Hilbert space","level":4,"score":0.26579999923706055}],"mesh":[],"locations_count":12,"locations":[{"id":"doi:10.1017/s0960129512000047","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129512000047","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:ris.utwente.nl:openaire_cris_publications/20cd70b1-c97d-4aa5-8248-020544df361e","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/20cd70b1-c97d-4aa5-8248-020544df361e","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Coecke, B, Pavlovic, D & Vicary, J 2012, 'A new description of orthogonal bases', Mathematical structures in computer science, vol. 23, no. 3, pp. 555-567. https://doi.org/10.1017/S0960129512000047","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:0810.0812","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0810.0812","pdf_url":"https://arxiv.org/pdf/0810.0812","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:CiteSeerX.psu:10.1.1.244.6490","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.244.6490","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0810.0812v1.pdf","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:12e7aafe-634c-40ea-a5ac-13dc4efd5e6a","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:12e7aafe-634c-40ea-a5ac-13dc4efd5e6a","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Computer Science","raw_type":"Journal article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/1","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/1/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401976","display_name":"Royal Holloway Digital Repository (University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/2","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/2/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401976","display_name":"Royal Holloway Digital Repository (University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I166337079","host_organization_name":"Queen Mary University of London","host_organization_lineage":["https://openalex.org/I166337079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/4","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/4/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401062","display_name":"Royal Holloway Digital Repository (Royal Holloway University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184558857","host_organization_name":"Royal Holloway University of London","host_organization_lineage":["https://openalex.org/I184558857"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/5","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/5/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401062","display_name":"Royal Holloway Digital Repository (Royal Holloway University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184558857","host_organization_name":"Royal Holloway University of London","host_organization_lineage":["https://openalex.org/I184558857"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/6","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/6/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401062","display_name":"Royal Holloway Digital Repository (Royal Holloway University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184558857","host_organization_name":"Royal Holloway University of London","host_organization_lineage":["https://openalex.org/I184558857"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/7","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/7/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401062","display_name":"Royal Holloway Digital Repository (Royal Holloway University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184558857","host_organization_name":"Royal Holloway University of London","host_organization_lineage":["https://openalex.org/I184558857"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repository.royalholloway.ac.uk:647f48de-0f1d-92ce-438c-d1efcca64272/8","is_oa":false,"landing_page_url":"https://repository.royalholloway.ac.uk/items/647f48de-0f1d-92ce-438c-d1efcca64272/8/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401062","display_name":"Royal Holloway Digital Repository (Royal Holloway University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184558857","host_organization_name":"Royal Holloway University of London","host_organization_lineage":["https://openalex.org/I184558857"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0810.0812","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0810.0812","pdf_url":"https://arxiv.org/pdf/0810.0812","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/G2744478709","display_name":null,"funder_award_id":"EP/D072786/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W143316254","https://openalex.org/W1036779541","https://openalex.org/W1644475622","https://openalex.org/W1973799895","https://openalex.org/W1982928587","https://openalex.org/W2049471987","https://openalex.org/W2107914128","https://openalex.org/W2119180894","https://openalex.org/W2734361589","https://openalex.org/W2950993906","https://openalex.org/W4255944736"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"an":[3],"orthogonal":[4,60],"basis":[5,46,102,109],"for":[6,41,135],"a":[7,16],"finite-dimensional":[8,27],"Hilbert":[9,28],"space":[10],"can":[11,88],"be":[12,89,117],"equivalently":[13],"characterised":[14,65],"as":[15,30,36],"commutative":[17,53],"\u2020-Frobenius":[18,54,94],"monoid":[19,55],"in":[20,71],"the":[21,42,51,74,83,93,97,108],"category":[22],"FdHilb":[23],",":[24],"which":[25],"has":[26,132],"spaces":[29],"objects":[31],"and":[32,38,61,82,99,119],"continuous":[33],"linear":[34],"maps":[35],"morphisms,":[37],"tensor":[39,80],"product":[40,81],"monoidal":[43],"structure.":[44],"The":[45],"is":[47,56],"normalised":[48],"exactly":[49],"when":[50],"corresponding":[52],"special.":[57],"Hence,":[58],"both":[59],"orthonormal":[62],"bases":[63],"are":[64],"without":[66],"mentioning":[67],"vectors,":[68],"but":[69],"just":[70],"terms":[72],"of":[73,78,101],"categorical":[75,136],"structure:":[76],"composition":[77],"operations,":[79],"\u2020-functor.":[84],"Moreover,":[85],"this":[86,122],"characterisation":[87],"interpreted":[90],"operationally,":[91],"since":[92],"structure":[95],"allows":[96],"cloning":[98],"deletion":[100],"vectors.":[103],"That":[104],"is,":[105],"we":[106],"capture":[107],"vectors":[110],"by":[111],"relying":[112],"on":[113],"their":[114],"ability":[115,123],"to":[116],"cloned":[118],"deleted.":[120],"Since":[121],"distinguishes":[124],"classical":[125],"data":[126],"from":[127],"quantum":[128,137],"data,":[129],"our":[130],"result":[131],"important":[133],"implications":[134],"mechanics.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2019-06-27T00:00:00"}
