{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T10:47:58Z","timestamp":1781952478995,"version":"3.54.5"},"reference-count":89,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12005049"],"award-info":[{"award-number":["12005049"]}]},{"name":"National Natural Science Foundation of China","award":["11935012"],"award-info":[{"award-number":["11935012"]}]},{"name":"National Natural Science Foundation of China","award":["61871162"],"award-info":[{"award-number":["61871162"]}]},{"name":"National Natural Science Foundation of China","award":["12275062"],"award-info":[{"award-number":["12275062"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>State variable and parameter estimations are important for signal sensing and feedback control in both traditional engineering systems and quantum systems. The Kalman filter, which is one of the most popular signal recovery techniques in classical systems for decades, has now been connected to the stochastic master equations of linear quantum mechanical systems. Various studies have invested effort on mapping the state evolution of a quantum system into a set of classical filtering equations. However, establishing proper evolution models with symmetry to classical filter equation for quantum systems is not easy. Here, we review works that have successfully built a Kalman filter model for quantum systems and provide an improved method for optimal estimations. We also discuss a practical scenario involving magnetic field estimations in quantum systems, where non-linear Kalman filters could be considered an estimation solution.<\/jats:p>","DOI":"10.3390\/sym14122478","type":"journal-article","created":{"date-parts":[[2022,11,23]],"date-time":"2022-11-23T02:55:51Z","timestamp":1669172151000},"page":"2478","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Review of the Applications of Kalman Filtering in Quantum Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4623-2061","authenticated-orcid":false,"given":"Kezhao","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6518-8636","authenticated-orcid":false,"given":"Jia","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yihan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9822-5387","authenticated-orcid":false,"given":"Xiao-Ming","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1514","DOI":"10.1126\/science.1225258","article-title":"Quantum-Enhanced Optical-Phase Tracking","volume":"337","author":"Yonezawa","year":"2012","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5993","DOI":"10.1109\/TITS.2021.3074457","article-title":"A Review on Vehicle-Trailer State and Parameter Estimation","volume":"23","author":"Korayem","year":"2021","journal-title":"IEEE Trans. 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