{"id":"https://openalex.org/W7220976994","doi":"https://doi.org/10.48550/arxiv.2610.08897","title":"Visualizing two qubits","display_name":"Visualizing two qubits","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220976994","doi":"https://doi.org/10.48550/arxiv.2610.08897"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08897","pdf_url":"https://arxiv.org/pdf/2610.08897","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08897","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157982677","display_name":"Simon Grosse-Holz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Grosse-Holz, Simon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5157982677"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.6284000277519226,"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":0.6284000277519226,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.2199999988079071,"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":0.1298999935388565,"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/two-qubit-states","display_name":"two-qubit states","score":0.9700000286102295},{"id":"https://openalex.org/keywords/bloch-ball","display_name":"Bloch ball","score":0.7170000076293945},{"id":"https://openalex.org/keywords/mixed-states","display_name":"mixed states","score":0.7900000214576721},{"id":"https://openalex.org/keywords/entanglement","display_name":"entanglement","score":0.8569999933242798},{"id":"https://openalex.org/keywords/contractions","display_name":"contractions","score":0.6389999985694885},{"id":"https://openalex.org/keywords/state-space-structure","display_name":"state space structure","score":0.6340000033378601},{"id":"https://openalex.org/keywords/conditional-states","display_name":"conditional states","score":0.9610000252723694},{"id":"https://openalex.org/keywords/single-qubit-rotations","display_name":"single-qubit rotations","score":0.9480000138282776}],"concepts":[{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.8136000037193298},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.7432000041007996},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.5622000098228455},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5209000110626221},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.48399999737739563},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.4431999921798706},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.421999990940094},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4016999900341034},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3763999938964844},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.36880001425743103},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C136277988","wikidata":"https://www.wikidata.org/wiki/Q884593","display_name":"Bloch sphere","level":4,"score":0.3433000147342682},{"id":"https://openalex.org/C158456648","wikidata":"https://www.wikidata.org/wiki/Q5136706","display_name":"Cluster state","level":4,"score":0.3386000096797943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32589998841285706},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.31610000133514404},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3068000078201294},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3046000003814697},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3001999855041504},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2702000141143799},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C19271316","wikidata":"https://www.wikidata.org/wiki/Q7092353","display_name":"One-way quantum computer","level":5,"score":0.25270000100135803},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08897","pdf_url":"https://arxiv.org/pdf/2610.08897","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.08897","doi":"https://doi.org/10.48550/arxiv.2610.08897","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08897","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08897","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08897","pdf_url":"https://arxiv.org/pdf/2610.08897","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220976994.pdf","grobid_xml":"https://content.openalex.org/works/W7220976994.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1492146696","https://openalex.org/W1584580574","https://openalex.org/W1990525265","https://openalex.org/W1997710075","https://openalex.org/W2031488679","https://openalex.org/W2037363234","https://openalex.org/W2073781628","https://openalex.org/W2074058884","https://openalex.org/W2093719822","https://openalex.org/W2593989580","https://openalex.org/W4393162847","https://openalex.org/W7134842702","https://openalex.org/W7164499987"],"related_works":["https://openalex.org/W7155392473","https://openalex.org/W7134842702","https://openalex.org/W3132839553","https://openalex.org/W2128368840","https://openalex.org/W2560401853","https://openalex.org/W4406388403","https://openalex.org/W2919219669","https://openalex.org/W1604952693","https://openalex.org/W3010351250","https://openalex.org/W7094088386"],"abstract_inverted_index":{"I":[0,41,74],"propose":[1],"a":[2,36,39,66],"simple":[3],"visualization":[4],"for":[5,16],"pure":[6],"two-qubit":[7],"states,":[8,81],"constructed":[9],"from":[10],"three":[11],"components:":[12],"two":[13],"Bloch":[14],"balls":[15],"the":[17,26,48,54,62,70,82],"marginal":[18],"qubits":[19],"(the":[20],"mixed":[21],"states":[22],"obtained":[23],"by":[24],"ignoring":[25],"other":[27],"qubit,":[28],"respectively)":[29],"and":[30,38,50,87],"an":[31],"entanglement":[32,83],"component":[33],"consisting":[34],"of":[35,53,85],"rotoreflection":[37],"contraction.":[40],"prove":[42],"that":[43],"this":[44,76],"picture":[45,77],"accurately":[46],"captures":[47],"local":[49],"global":[51,67],"structure":[52],"relevant":[55],"state":[56,71],"space":[57],"without":[58],"gaps":[59],"or":[60],"degeneracies:":[61],"underlying":[63],"parametrization":[64],"is":[65],"diffeomorphism":[68],"onto":[69],"space.":[72],"Finally,":[73],"use":[75],"to":[78],"visualize":[79],"conditional":[80],"degree(s)":[84],"freedom,":[86],"single":[88],"qubit":[89],"rotations.":[90]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}