{"id":"https://openalex.org/W2017398943","doi":"https://doi.org/10.1142/s1230161212500205","title":"Geometry of Entanglement Witnesses Parametrized by <font>SO</font>(3) Group","display_name":"Geometry of Entanglement Witnesses Parametrized by <font>SO</font>(3) Group","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2017398943","doi":"https://doi.org/10.1142/s1230161212500205","mag":"2017398943"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161212500205","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161212500205","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1204.4830","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Dariusz Chru\u015bci\u0144ski","orcid":null},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Dariusz Chru\u015bci\u0144ski","raw_affiliation_strings":["Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87\u2013100 Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87\u2013100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I4210086947","https://openalex.org/I3019271933"]}]},{"author_position":"last","author":{"id":null,"display_name":"Filip A. Wudarski","orcid":null},"institutions":[{"id":"https://openalex.org/I3019271933","display_name":"Nicolaus Copernicus University","ror":"https://ror.org/0102mm775","country_code":"PL","type":"education","lineage":["https://openalex.org/I3019271933"]},{"id":"https://openalex.org/I4210086947","display_name":"Institute of Physics","ror":"https://ror.org/000sfad56","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210086947","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Filip A. Wudarski","raw_affiliation_strings":["Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87\u2013100 Toru\u0144, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Physics, Nicolaus Copernicus University, Grudziadzka 5/7, 87\u2013100 Toru\u0144, Poland","institution_ids":["https://openalex.org/I4210086947","https://openalex.org/I3019271933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.36,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80859902,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"19","issue":"03","first_page":"1250020","last_page":"1250020"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.2628999948501587,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.2628999948501587,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.17470000684261322,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.13580000400543213,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/quantum-entanglement","display_name":"Quantum entanglement","score":0.7128999829292297},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5767999887466431},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5170000195503235},{"id":"https://openalex.org/keywords/rotation-group-so","display_name":"Rotation group SO","score":0.48840001225471497},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4431000053882599},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.4404999911785126},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41190001368522644},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.39750000834465027},{"id":"https://openalex.org/keywords/symmetry-group","display_name":"Symmetry group","score":0.3808000087738037}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.7128999829292297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6492000222206116},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5767999887466431},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5170000195503235},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.48840001225471497},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45410001277923584},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4431000053882599},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.4404999911785126},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.4334999918937683},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.39750000834465027},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.3808000087738037},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3734999895095825},{"id":"https://openalex.org/C11516046","wikidata":"https://www.wikidata.org/wiki/Q1055807","display_name":"Group representation","level":3,"score":0.31839999556541443},{"id":"https://openalex.org/C2988629283","wikidata":"https://www.wikidata.org/wiki/Q44337","display_name":"Complex matrix","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C146561895","wikidata":"https://www.wikidata.org/wiki/Q1783179","display_name":"Orthogonal group","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.28040000796318054},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C158158286","wikidata":"https://www.wikidata.org/wiki/Q9009080","display_name":"Invariants of tensors","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.26089999079704285},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C71799126","wikidata":"https://www.wikidata.org/wiki/Q6934832","display_name":"Multipartite entanglement","level":5,"score":0.2513999938964844},{"id":"https://openalex.org/C120047569","wikidata":"https://www.wikidata.org/wiki/Q92795049","display_name":"Group algebra","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1230161212500205","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161212500205","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:arXiv.org:1204.4830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.4830","pdf_url":"https://arxiv.org/pdf/1204.4830","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1204.4830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.4830","pdf_url":"https://arxiv.org/pdf/1204.4830","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1963952399","https://openalex.org/W2010553012","https://openalex.org/W2016866105","https://openalex.org/W2043052543","https://openalex.org/W2048680711","https://openalex.org/W2069471754","https://openalex.org/W2072026007","https://openalex.org/W2074112529","https://openalex.org/W2116102644","https://openalex.org/W2121359620","https://openalex.org/W2135489617","https://openalex.org/W3037737784","https://openalex.org/W3038000163"],"related_works":[],"abstract_inverted_index":{"We":[0,65],"characterize":[1],"a":[2,19],"set":[3],"of":[4,10,21,51,60,69],"positive":[5],"maps":[6],"in":[7,24,44],"matrix":[8],"algebra":[9],"4":[11,13,26,28],"\u00d7":[12],"complex":[14],"matrices.":[15],"Equivalently,":[16],"we":[17],"provide":[18],"subset":[20],"entanglement":[22],"witnesses":[23],"\u2102":[25],"\u2297\u2102":[27],"parametrized":[29],"by":[30],"the":[31,45,57,61,70],"rotation":[32],"group":[33],"SO":[34],"(3).":[35],"Interestingly,":[36],"these":[37],"maps/witnesses":[38],"define":[39],"two":[40,52],"intersecting":[41],"convex":[42],"cones":[43,53],"3-dimensional":[46],"parameter":[47],"space.":[48],"The":[49],"existence":[50],"is":[54],"related":[55],"to":[56],"topological":[58],"structure":[59],"underlying":[62],"orthogonal":[63],"group.":[64],"perform":[66],"detailed":[67],"analysis":[68],"corresponding":[71],"geometric":[72],"structure.":[73]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2016-06-24T00:00:00"}
