{"id":"https://openalex.org/W2297929646","doi":null,"title":"Symmetric Functionals over Tensor Product Spaces in the Context of Quantum Information Theory","display_name":"Symmetric Functionals over Tensor Product Spaces in the Context of Quantum Information Theory","publication_year":2014,"publication_date":"2014-12-05","ids":{"openalex":"https://openalex.org/W2297929646","mag":"2297929646"},"language":"en","primary_location":{"id":"pmh:oai:USBKOELN.ub.uni-koeln.de:5863","doi":null,"is_oa":false,"landing_page_url":"https://kups.ub.uni-koeln.de/5863/1/PhDThesisMErnst.pdf","pdf_url":"https://kups.ub.uni-koeln.de/5863/1/PhDThesisMErnst.pdf","source":{"id":"https://openalex.org/S4306400371","display_name":"K\u00f6lner Universit\u00e4ts PublikationsServer (Universit\u00e4t zu K\u00f6ln)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210115942","host_organization_name":"Rhenish Institute for Environmental Research","host_organization_lineage":["https://openalex.org/I4210115942"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"doc-type:doctoralThesis"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018471066","display_name":"Moritz Ernst","orcid":"https://orcid.org/0000-0003-0360-913X","observed_orcids":["https://orcid.org/0000-0003-0360-913X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Moritz Ernst","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5018471066"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9564999938011169,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.9564999938011169,"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":0.013399999588727951,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.013399999588727951,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/coherent-information","display_name":"coherent information","score":0.8299999833106995},{"id":"https://openalex.org/keywords/quantum-channels","display_name":"quantum channels","score":0.722000002861023},{"id":"https://openalex.org/keywords/open-quantum-systems","display_name":"open quantum systems","score":0.7990000247955322},{"id":"https://openalex.org/keywords/uhlmann-fidelity","display_name":"Uhlmann fidelity","score":0.7950000166893005},{"id":"https://openalex.org/keywords/tensor-product-spaces","display_name":"tensor product spaces","score":0.9160000085830688},{"id":"https://openalex.org/keywords/haar-measure","display_name":"Haar measure","score":0.7099999785423279},{"id":"https://openalex.org/keywords/pauli-channels","display_name":"Pauli channels","score":0.7770000100135803},{"id":"https://openalex.org/keywords/non-additivity","display_name":"non-additive effects","score":0.5910000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5903931856155396},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.5858867168426514},{"id":"https://openalex.org/C184049767","wikidata":"https://www.wikidata.org/wiki/Q5141355","display_name":"Coherent information","level":5,"score":0.5760853290557861},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.554831326007843},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.522704005241394},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4850248694419861},{"id":"https://openalex.org/C41241483","wikidata":"https://www.wikidata.org/wiki/Q7269015","display_name":"Quantum capacity","level":5,"score":0.4711667001247406},{"id":"https://openalex.org/C168090291","wikidata":"https://www.wikidata.org/wiki/Q5128319","display_name":"Classical capacity","level":5,"score":0.44476330280303955},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.35041314363479614},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34535470604896545},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2737779915332794},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17833933234214783},{"id":"https://openalex.org/C186468114","wikidata":"https://www.wikidata.org/wiki/Q836478","display_name":"Quantum network","level":4,"score":0.1742652952671051}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:USBKOELN.ub.uni-koeln.de:5863","doi":null,"is_oa":false,"landing_page_url":"https://kups.ub.uni-koeln.de/5863/1/PhDThesisMErnst.pdf","pdf_url":"https://kups.ub.uni-koeln.de/5863/1/PhDThesisMErnst.pdf","source":{"id":"https://openalex.org/S4306400371","display_name":"K\u00f6lner Universit\u00e4ts PublikationsServer (Universit\u00e4t zu K\u00f6ln)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210115942","host_organization_name":"Rhenish Institute for Environmental Research","host_organization_lineage":["https://openalex.org/I4210115942"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"doc-type:doctoralThesis"},{"id":"mag:2297929646","doi":null,"is_oa":false,"landing_page_url":"https://kups.ub.uni-koeln.de/5863/1/PhDThesisMErnst.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W322525841","https://openalex.org/W1534413569","https://openalex.org/W1574861711","https://openalex.org/W1621050367","https://openalex.org/W1631356911","https://openalex.org/W1643301482","https://openalex.org/W1785526227","https://openalex.org/W1841201092","https://openalex.org/W1970302872","https://openalex.org/W1977821353","https://openalex.org/W1998573231","https://openalex.org/W1999462261","https://openalex.org/W2004025893","https://openalex.org/W2006369356","https://openalex.org/W2021115151","https://openalex.org/W2021889922","https://openalex.org/W2023885784","https://openalex.org/W2041905826","https://openalex.org/W2084652510","https://openalex.org/W2102008187","https://openalex.org/W2116102644","https://openalex.org/W2119819325","https://openalex.org/W2141356832","https://openalex.org/W2141412822","https://openalex.org/W2150308869","https://openalex.org/W2160212841","https://openalex.org/W2914659449","https://openalex.org/W3100059293","https://openalex.org/W7097210442"],"related_works":["https://openalex.org/W2151919909","https://openalex.org/W2112149114","https://openalex.org/W2026130436","https://openalex.org/W1993274314","https://openalex.org/W7128295231","https://openalex.org/W7154203642","https://openalex.org/W1588230544","https://openalex.org/W1963973936","https://openalex.org/W4394639763","https://openalex.org/W2185752612"],"abstract_inverted_index":{"This":[0,75,248],"thesis":[1],"consists":[2],"of":[3,23,25,53,65,83,89,94,105,117,149,216,234,236,239,254,292,301,333,389,401,419],"three":[4],"parts.":[5],"We":[6,188],"begin":[7],"our":[8,373],"investigation":[9],"with":[10,170,242,376],"a":[11,69,80,95,109,113,118,150,155,194,209,252,329,379,412,435,456],"brief":[12],"introduction":[13,211],"into":[14,140],"open":[15,54],"quantum":[16,55,66,72,84,91,97,151],"systems.":[17],"Then":[18],"we":[19,41,144,271,286,297,325,393,425],"explain":[20],"different":[21],"measures":[22],"distinguishability":[24],"density":[26],"operators,":[27],"especially":[28],"the":[29,35,38,50,62,87,90,103,106,131,146,171,181,190,197,206,213,232,245,255,263,268,290,299,302,310,336,348,365,384,390,398,417,420,441,445],"Uhlmann":[30],"Fidelity,":[31],"which":[32,121,153],"will":[33],"be":[34,128,432],"basis":[36],"for":[37,196,226,231,261,276,318,328,361,386],"model":[39,195],"function":[40,110],"investigate":[42],"in":[43,57,71,130,174,178,251,320,364,383,449],"this":[44,141,321,450],"work.":[45],"\\nWe":[46,369],"continue":[47],"by":[48,223,371,434],"explaining":[49],"time":[51],"evolution":[52],"systems":[56],"more":[58,283],"detail,":[59],"and":[60,124,200,218,228,304,313],"introducing":[61],"important":[63],"notion":[64],"channels":[67],"as":[68,133,193],"concept":[70],"information":[73,85,92,173,183,199,447],"theory.":[74],"allows":[76,355],"us":[77,356],"to":[78,127,180,212,244,281,289,309,357],"state":[79],"central":[81],"problem":[82],"theory:":[86],"characterization":[88],"capacity":[93],"given":[96],"channel.":[98],"The":[99],"major":[100],"challenge":[101],"is":[102,122,154,185,221,259,340],"maximization":[104,438,453],"coherent":[107,172,182,198,446],"information,":[108],"defined":[111,159],"on":[112,160],"n-fold":[114,161],"tensor":[115,162],"product":[116,163],"Hilbert":[119],"space,":[120],"non-additive":[123],"thus":[125,454],"has":[126],"considered":[129],"limit":[132,311,366],"n\u2192\u221e.":[134,367],"\\n":[135,204,266,368],"\\nTo":[136],"gain":[137],"an":[138,167,315],"insight":[139],"unsolved":[142],"problem,":[143],"study":[145,201,291],"channel":[147,191,264,273,337,391,399,442],"fidelity":[148,192,274,338,400,415,443],"channel,":[152],"simpler":[156],"function,":[157],"also":[158,354],"spaces.":[164],"It":[165],"shares":[166],"essential":[168],"feature":[169],"being":[175],"non-additive.":[176],"However,":[177],"contrast":[179],"it":[184],"mathematically":[186],"accessible.":[187],"establish":[189],"its":[202,452],"properties.":[203],"\\nIn":[205,267],"second":[207],"part,":[208,270],"short":[210],"representation":[214],"theory":[215],"symmetric":[217],"unitary":[219,240],"groups":[220,241],"followed":[222],"concrete":[224,284,359],"instructions":[225],"Collins'":[227],"\\\\'{S}niady's":[229],"formula":[230,257,317,350],"integration":[233],"functions":[235],"matrix":[237],"elements":[238],"respect":[243],"Haar":[246],"measure.":[247],"exposition":[249],"culminates":[250],"simplification":[253],"general":[256],"that":[258,327,396,427],"optimal":[260],"investigating":[262],"fidelity.":[265],"third":[269],"calculate":[272],"moments":[275,363],"arbitrary":[277],"n.":[278],"In":[279,323],"order":[280],"obtain":[282],"results,":[285],"restrict":[287],"ourselves":[288],"Pauli":[293,334,402],"channels.":[294],"For":[295],"these":[296,408,428],"discuss":[298],"transition":[300],"average":[303,418],"variance":[305],"from":[306,351,378],"small":[307],"n":[308,332],"n\u2192\u221e":[312],"give":[314,358],"explicit":[316],"both":[319],"limit.":[322],"particular,":[324],"find":[326],"large":[330],"number":[331],"channels,":[335,403],"distribution":[339],"peaked":[341,423],"very":[342,421,457],"strongly.":[343],"Additionally,":[344],"under":[345],"certain":[346],"restrictions,":[347],"simplified":[349],"part":[352],"two":[353],"expressions":[360],"higher":[362,414],"conclude":[370],"comparing":[372],"new":[374],"results":[375,377],"former":[380],"work,":[381],"where,":[382],"search":[385],"maximizing":[387],"states":[388,395,429],"fidelity,":[392],"found":[394,433],"maximize":[397],"at":[404],"least":[405],"locally.":[406],"Because":[407],"local":[409],"maxima":[410],"have":[411],"much":[413],"than":[416],"strongly":[422],"distribution,":[424],"infer":[426],"would":[430],"not":[431],"standard":[436],"numerical":[437],"procedure.":[439],"If":[440],"models":[444],"accurately":[448],"regard,":[451],"poses":[455],"hard":[458],"problem.":[459]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}