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Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states. We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.<\/jats:p>","DOI":"10.22331\/q-2022-03-10-665","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T15:36:52Z","timestamp":1646926612000},"page":"665","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":33,"title":["Imaginarity-free quantum multiparameter estimation"],"prefix":"10.22331","volume":"6","author":[{"given":"Jisho","family":"Miyazaki","sequence":"first","affiliation":[{"name":"Shinpouin, Mikataharacho, Kita-ku, Hamamatsu, Shizuoka, 433-8105, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keiji","family":"Matsumoto","sequence":"additional","affiliation":[{"name":"Quantum Computation Group, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,3,10]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"V. 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