{"id":"https://openalex.org/W7212325916","doi":"https://doi.org/10.48550/arxiv.2609.09663","title":"Finite Realizations and Effective Memory in Nonlinear Quantum Filtering","display_name":"Finite Realizations and Effective Memory in Nonlinear Quantum Filtering","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212325916","doi":"https://doi.org/10.48550/arxiv.2609.09663"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09663","pdf_url":"https://arxiv.org/pdf/2609.09663","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/2609.09663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144061884","display_name":"Jacob Emerson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Emerson, Jacob","raw_affiliation_strings":["Department of Electrical and Computer Engineering , Princeton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , Princeton University","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5144061884"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.6333000063896179,"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":0.6333000063896179,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.2847000062465668,"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/T11236","display_name":"Control Systems and Identification","score":0.011900000274181366,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-dimensional-filters","display_name":"finite-dimensional filters","score":0.7080000042915344},{"id":"https://openalex.org/keywords/hankel-operators","display_name":"Hankel operators","score":0.8539999723434448},{"id":"https://openalex.org/keywords/duffing-oscillator","display_name":"Duffing oscillator","score":1.0},{"id":"https://openalex.org/keywords/singular-values","display_name":"singular values","score":0.6449999809265137},{"id":"https://openalex.org/keywords/realizability","display_name":"realizability","score":0.4950000047683716},{"id":"https://openalex.org/keywords/non-gaussian-quantum-states","display_name":"non-Gaussian quantum states","score":0.6119999885559082},{"id":"https://openalex.org/keywords/moment-equations","display_name":"moment equations","score":0.40400001406669617}],"concepts":[{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.6668000221252441},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6129999756813049},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.48510000109672546},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4424999952316284},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3553999960422516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34929999709129333},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C2778926657","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum system","level":3,"score":0.3425000011920929},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3407000005245209},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2872999906539917},{"id":"https://openalex.org/C179957908","wikidata":"https://www.wikidata.org/wiki/Q907206","display_name":"POVM","level":5,"score":0.28519999980926514},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.2777000069618225},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.27250000834465027},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.26420000195503235},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.2628999948501587},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09663","pdf_url":"https://arxiv.org/pdf/2609.09663","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.2609.09663","doi":"https://doi.org/10.48550/arxiv.2609.09663","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09663","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09663","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09663","pdf_url":"https://arxiv.org/pdf/2609.09663","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212325916.pdf","grobid_xml":"https://content.openalex.org/works/W7212325916.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4414283508","https://openalex.org/W7171829914"],"related_works":["https://openalex.org/W7171829914","https://openalex.org/W7099170405","https://openalex.org/W4393027405","https://openalex.org/W2753724513","https://openalex.org/W2338179484","https://openalex.org/W2062681494","https://openalex.org/W2663845158","https://openalex.org/W2799214296","https://openalex.org/W1795870157","https://openalex.org/W2107056238"],"abstract_inverted_index":{"Nonlinear":[0],"dynamics":[1,150,162],"generate":[2],"non-Gaussian":[3],"states":[4],"and":[5,47,151,171,213],"operations,":[6],"but":[7,59],"they":[8],"also":[9],"make":[10],"continuously":[11],"monitored":[12],"quantum":[13,19,77,85,247],"systems":[14,139],"difficult":[15],"to":[16,104,117,135],"track.":[17],"A":[18],"filter":[20,114,132],"performs":[21],"this":[22,43,144],"task":[23],"by":[24],"compressing":[25],"a":[26,31,80,107,125,146,199],"noisy":[27],"measurement":[28,102],"record":[29,103],"into":[30],"set":[32],"of":[33,62,190,207],"evolving":[34],"variables":[35],"that":[36,68,128,226],"predict":[37],"future":[38,108],"observables.":[39],"For":[40,210],"Gaussian":[41,149],"dynamics,":[42],"compression":[44],"is":[45,72],"exact":[46,130,176,223,228,240],"finite.":[48],"In":[49],"nonlinear":[50,246],"systems,":[51],"conventional":[52],"moment":[53],"equations":[54],"generally":[55],"expand":[56],"without":[57],"bound,":[58],"the":[60,90,100,152,204,211],"failure":[61],"one":[63],"representation":[64],"does":[65],"not":[66,182],"prove":[67],"every":[69],"finite":[70,119,159],"description":[71],"impossible.":[73],"Here":[74],"we":[75],"formulate":[76],"filtering":[78],"as":[79],"realization":[81],"problem":[82],"for":[83],"general":[84],"input--output":[86],"maps.":[87],"We":[88],"introduce":[89],"linearized":[91],"observable":[92],"Hankel":[93],"operator":[94],"$K_O$,":[95],"which":[96],"maps":[97],"changes":[98,105],"in":[99,106,245],"past":[101],"conditional":[109],"observable.":[110,209],"Any":[111],"finite-dimensional":[112,131,174],"smooth":[113,175],"forces":[115],"$K_O$":[116,191],"have":[118],"rank,":[120,224],"so":[121],"infinite":[122,222,227],"rank":[123],"provides":[124],"coordinate-independent":[126],"proof":[127],"no":[129,173],"exists.":[133],"Applied":[134],"single-mode":[136],"polynomial":[137],"bosonic":[138],"under":[140],"continuous":[141],"quadrature":[142],"monitoring,":[143],"yields":[145],"sharp":[147],"boundary:":[148],"measurement-aligned":[153],"Conditional":[154],"Momentum":[155],"Moment":[156],"class":[157],"admit":[158,172],"realizations,":[160],"whereas":[161],"outside":[163],"these":[164,216],"classes":[165],"produce":[166],"infinitely":[167],"many":[168,194],"response":[169,195],"directions":[170,196],"filter.":[177],"Exact":[178],"impossibility,":[179],"however,":[180],"need":[181],"imply":[183],"large":[184],"practical":[185],"complexity.":[186,235],"The":[187,236],"singular":[188,217],"values":[189,218],"quantify":[192],"how":[193],"matter":[197],"at":[198],"chosen":[200],"local":[201],"accuracy,":[202],"defining":[203],"effective":[205,243],"memory":[206,229],"an":[208],"Kerr":[212],"Duffing":[214],"oscillators,":[215],"decay":[219],"rapidly":[220],"despite":[221],"showing":[225],"can":[230],"coexist":[231],"with":[232],"low":[233],"finite-accuracy":[234],"framework":[237],"therefore":[238],"separates":[239],"realizability":[241],"from":[242],"complexity":[244],"filtering.":[248]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-12T00:00:00"}
