{"id":"https://openalex.org/W4400260493","doi":"https://doi.org/10.1142/s1230161224500082","title":"Multi-Unitary Complex Hadamard Matrices","display_name":"Multi-Unitary Complex Hadamard Matrices","publication_year":2024,"publication_date":"2024-06-01","ids":{"openalex":"https://openalex.org/W4400260493","doi":"https://doi.org/10.1142/s1230161224500082"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161224500082","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161224500082","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems &amp; Information Dynamics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ruj.uj.edu.pl/bitstreams/2dd47c62-e993-40e3-a7ab-6b696c29e20a/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071398167","display_name":"Wojciech Bruzda","orcid":"https://orcid.org/0000-0001-9743-7927"},"institutions":[{"id":"https://openalex.org/I3019243323","display_name":"Center for Theoretical Physics","ror":"https://ror.org/04kfyt897","country_code":"PL","type":"facility","lineage":["https://openalex.org/I3019243323","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Wojciech Bruzda","raw_affiliation_strings":["Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32/46, 02\u2013668 Warszawa, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32/46, 02\u2013668 Warszawa, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I3019243323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024042202","display_name":"Grzegorz Rajchel-Mieldzio\u0107","orcid":"https://orcid.org/0000-0003-2652-9482"},"institutions":[{"id":"https://openalex.org/I4210136276","display_name":"NASK National Research Institute","ror":"https://ror.org/03ajsaw82","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210136276"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Grzegorz Rajchel-Mieldzio\u0107","raw_affiliation_strings":["NASK National Research Institute, ul. Kolska 12, 01\u2013045 Warszawa, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NASK National Research Institute, ul. Kolska 12, 01\u2013045 Warszawa, Poland","institution_ids":["https://openalex.org/I4210136276"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072049493","display_name":"Karol \u017byczkowski","orcid":"https://orcid.org/0000-0002-0653-3639"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]},{"id":"https://openalex.org/I3019243323","display_name":"Center for Theoretical Physics","ror":"https://ror.org/04kfyt897","country_code":"PL","type":"facility","lineage":["https://openalex.org/I3019243323","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Karol \u017byczkowski","raw_affiliation_strings":["Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32/46, 02\u2013668 Warszawa, Poland","Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. \u0141ojasiewicza 11, 30-348, Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Theoretical Physics, Polish Academy of Sciences, al. Lotnik\u00f3w 32/46, 02\u2013668 Warszawa, Poland","institution_ids":["https://openalex.org/I99542240","https://openalex.org/I3019243323"]},{"raw_affiliation_string":"Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. \u0141ojasiewicza 11, 30-348, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071398167"],"corresponding_institution_ids":["https://openalex.org/I3019243323","https://openalex.org/I99542240"],"apc_list":null,"apc_paid":null,"fwci":0.6294,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72923452,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"31","issue":"02","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9995999932289124,"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":0.9995999932289124,"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/T11804","display_name":"Quantum many-body systems","score":0.9962000250816345,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9959999918937683,"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/multipartite","display_name":"Multipartite","score":0.6941548585891724},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6096791625022888},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5870370864868164},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.5500874519348145},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.5015835762023926},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4723580777645111},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44791141152381897},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4294564723968506},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.4243481755256653},{"id":"https://openalex.org/keywords/complex-hadamard-matrix","display_name":"Complex Hadamard matrix","score":0.4184810519218445},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.41176536679267883},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3876538872718811},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34617555141448975},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32668477296829224},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.2778339385986328},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2079518437385559},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20235344767570496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08355656266212463}],"concepts":[{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.6941548585891724},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6096791625022888},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5870370864868164},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.5500874519348145},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.5015835762023926},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4723580777645111},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44791141152381897},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4294564723968506},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.4243481755256653},{"id":"https://openalex.org/C6497535","wikidata":"https://www.wikidata.org/wiki/Q5156556","display_name":"Complex Hadamard matrix","level":4,"score":0.4184810519218445},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.41176536679267883},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3876538872718811},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34617555141448975},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32668477296829224},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.2778339385986328},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2079518437385559},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20235344767570496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08355656266212463},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1230161224500082","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161224500082","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems &amp; Information Dynamics","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/550679","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/handle/item/550679","pdf_url":"http://ruj.uj.edu.pl/bitstreams/2dd47c62-e993-40e3-a7ab-6b696c29e20a/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:ruj.uj.edu.pl:item/550679","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/handle/item/550679","pdf_url":"http://ruj.uj.edu.pl/bitstreams/2dd47c62-e993-40e3-a7ab-6b696c29e20a/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4400260493.pdf"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1980695100","https://openalex.org/W1986320748","https://openalex.org/W1990283121","https://openalex.org/W1994127744","https://openalex.org/W2033511209","https://openalex.org/W2034198076","https://openalex.org/W2039842791","https://openalex.org/W2044022598","https://openalex.org/W2046938896","https://openalex.org/W2075530485","https://openalex.org/W2081226011","https://openalex.org/W2093189259","https://openalex.org/W2131730048","https://openalex.org/W2132641463","https://openalex.org/W2138009125","https://openalex.org/W2144126354","https://openalex.org/W2254931868","https://openalex.org/W2313497592","https://openalex.org/W2318902967","https://openalex.org/W2334323920","https://openalex.org/W2342233014","https://openalex.org/W2493448115","https://openalex.org/W2786508440","https://openalex.org/W2791488214","https://openalex.org/W2926751802","https://openalex.org/W2963697722","https://openalex.org/W2990695459","https://openalex.org/W2997645441","https://openalex.org/W3020815329","https://openalex.org/W3037737784","https://openalex.org/W3084325236","https://openalex.org/W3101774717","https://openalex.org/W3105015276","https://openalex.org/W3106102615","https://openalex.org/W3191729695","https://openalex.org/W3207507297","https://openalex.org/W4313448102","https://openalex.org/W4321793324","https://openalex.org/W4376106346","https://openalex.org/W4377014139","https://openalex.org/W4386723245","https://openalex.org/W4390776063","https://openalex.org/W4398152574"],"related_works":["https://openalex.org/W2950874339","https://openalex.org/W1602603282","https://openalex.org/W2054788067","https://openalex.org/W2740594951","https://openalex.org/W2796326658","https://openalex.org/W4226106482","https://openalex.org/W3154819821","https://openalex.org/W2038981428","https://openalex.org/W1976224891","https://openalex.org/W2028598007"],"abstract_inverted_index":{"We":[0],"analyze":[1],"the":[2,18,39],"set":[3,40],"of":[4,20,22,27,41,45,57,92,122,131],"real":[5],"and":[6,76,102,120,126],"complex":[7,42],"Hadamard":[8,43],"matrices":[9,44,59,110],"with":[10,32],"additional":[11],"symmetry":[12],"constrains.":[13],"In":[14],"particular,":[15],"we":[16,53],"link":[17],"problem":[19],"existence":[21],"maximally":[23],"entangled":[24],"multipartite":[25,123],"states":[26],"[Formula:":[28,33,47,69,77,83,87,95,103,137],"see":[29,34,48,66,70,74,78,84,88,96,104,138],"text]":[30,35,67,75,79,89,97,105,139],"subsystems":[31],"levels":[36],"each":[37],"to":[38],"order":[46],"text].":[49],"To":[50],"this":[51],"end,":[52],"investigate":[54],"possible":[55],"subsets":[56],"such":[58],"which":[60],"are,":[61],"dual,":[62],"strongly":[63],"dual":[64],"([Formula:":[65,73],"or":[68,82],"text]),":[71],"two-unitary":[72],"are":[80],"unitary),":[81],"text]-unitary.":[85],"Here":[86],"denotes":[90],"reshuffling":[91],"a":[93,99,128],"matrix":[94],"describing":[98],"bipartite":[100],"system,":[101],"its":[106],"partial":[107],"transpose.":[108],"Such":[109],"find":[111],"several":[112],"applications":[113],"in":[114,136],"quantum":[115,124,134],"many-body":[116],"theory,":[117],"tensor":[118],"networks":[119],"classification":[121],"entanglement":[125],"imply":[127],"broad":[129],"class":[130],"analytically":[132],"solvable":[133],"models":[135],"dimensions.":[140]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
