{"id":"https://openalex.org/W2145310284","doi":"https://doi.org/10.1109/tac.2011.2161792","title":"Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters","display_name":"Fidelity is a Sub-Martingale for Discrete-Time Quantum Filters","publication_year":2011,"publication_date":"2011-07-20","ids":{"openalex":"https://openalex.org/W2145310284","doi":"https://doi.org/10.1109/tac.2011.2161792","mag":"2145310284"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2011.2161792","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2161792","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1005.3119","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065752316","display_name":"Pierre Rouchon","orcid":"https://orcid.org/0000-0001-6160-5634"},"institutions":[{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Pierre Rouchon","raw_affiliation_strings":["Centre Automatique et Syst\u00e8mes, Mines Paris-Tech, Paris, France","Centre Autom. et Syst., Mines ParisTech, Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines Paris-Tech, Paris, France","institution_ids":["https://openalex.org/I70768539"]},{"raw_affiliation_string":"Centre Autom. et Syst., Mines ParisTech, Paris, France","institution_ids":["https://openalex.org/I70768539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065752316"],"corresponding_institution_ids":["https://openalex.org/I70768539"],"apc_list":null,"apc_paid":null,"fwci":3.8824,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.93869325,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"56","issue":"11","first_page":"2743","last_page":"2747"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9980000257492065,"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":0.9980000257492065,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9962000250816345,"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":0.9958000183105469,"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/fidelity","display_name":"Fidelity","score":0.7853336334228516},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6765009164810181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5562399625778198},{"id":"https://openalex.org/keywords/density-matrix","display_name":"Density matrix","score":0.5499613881111145},{"id":"https://openalex.org/keywords/martingale","display_name":"Martingale (probability theory)","score":0.49627524614334106},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.4599034786224365},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.438143253326416},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4337317645549774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3735189437866211},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3636581599712372},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.3448678255081177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2745914161205292},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19597023725509644},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16774389147758484},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1631597876548767},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08393421769142151}],"concepts":[{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.7853336334228516},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6765009164810181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5562399625778198},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.5499613881111145},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.49627524614334106},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.4599034786224365},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.438143253326416},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4337317645549774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3735189437866211},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3636581599712372},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3448678255081177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2745914161205292},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19597023725509644},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16774389147758484},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1631597876548767},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08393421769142151}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tac.2011.2161792","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2011.2161792","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1005.3119","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.3119","pdf_url":"https://arxiv.org/pdf/1005.3119","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"},{"id":"pmh:oai:HAL:hal-00654164v1","is_oa":true,"landing_page_url":"https://minesparis-psl.hal.science/hal-00654164","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2011, 56 (11), pp.2743 - 2747. ⟨10.1109/TAC.2011.2161792⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1005.3119","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.3119","pdf_url":"https://arxiv.org/pdf/1005.3119","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":14,"referenced_works":["https://openalex.org/W1530682388","https://openalex.org/W1631356911","https://openalex.org/W2014063759","https://openalex.org/W2052788241","https://openalex.org/W2081830310","https://openalex.org/W2097876164","https://openalex.org/W2106137875","https://openalex.org/W2107531798","https://openalex.org/W2124714273","https://openalex.org/W2505136320","https://openalex.org/W2764347725","https://openalex.org/W2964036780","https://openalex.org/W3100781611","https://openalex.org/W3121631129"],"related_works":["https://openalex.org/W2381850946","https://openalex.org/W4380449851","https://openalex.org/W3125091513","https://openalex.org/W4318832338","https://openalex.org/W1919390113","https://openalex.org/W4248383205","https://openalex.org/W4234745530","https://openalex.org/W2146383839","https://openalex.org/W2231829109","https://openalex.org/W2035675276"],"abstract_inverted_index":{"Fidelity":[0],"is":[1,15,34,66,71],"known":[2],"to":[3,42,74],"increase":[4],"through":[5],"any":[6],"Kraus":[7,25,45],"map:":[8,46],"the":[9,18,49,53,58,62],"fidelity":[10,19,33,47],"between":[11,20,48],"two":[12],"density":[13,50,59],"matrices":[14],"less":[16],"than":[17],"their":[21],"images":[22],"via":[23],"a":[24,67],"map.":[26],"We":[27],"prove":[28],"here":[29],"that,":[30],"in":[31],"average,":[32],"also":[35,78],"increasing":[36],"for":[37,81],"discrete-time":[38],"quantum":[39,64],"filters":[40],"attached":[41],"an":[43],"arbitrary":[44],"matrix":[51,60],"of":[52,61],"underlying":[54],"Markov":[55],"chain":[56],"and":[57],"associated":[63],"filter":[65],"sub-martingale.":[68],"This":[69],"result":[70],"not":[72],"restricted":[73],"pure":[75],"states.":[76,83],"It":[77],"holds":[79],"true":[80],"mixed":[82]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}