{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T09:59:56Z","timestamp":1768730396768,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,11,16]],"date-time":"2017-11-16T00:00:00Z","timestamp":1510790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We develop priors for Bayes estimation of quantum states that provide minimax state estimation. The relative entropy from the true density operator to a predictive density operator is adopted as a loss function. The proposed prior maximizes the conditional Holevo mutual information, and it is a quantum version of the latent information prior in classical statistics. For one qubit system, we provide a class of measurements that is optimal from the viewpoint of minimax state estimation.<\/jats:p>","DOI":"10.3390\/e19110618","type":"journal-article","created":{"date-parts":[[2017,11,16]],"date-time":"2017-11-16T11:10:02Z","timestamp":1510830602000},"page":"618","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Minimax Estimation of Quantum States Based on the Latent Information Priors"],"prefix":"10.3390","volume":"19","author":[{"given":"Takayuki","family":"Koyama","sequence":"first","affiliation":[{"name":"FANUC Corporation, 3580 Furubaba Shibokusa Oshino-mura, Yamanashi 401-0597, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1572-5085","authenticated-orcid":false,"given":"Takeru","family":"Matsuda","sequence":"additional","affiliation":[{"name":"Department of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fumiyasu","family":"Komaki","sequence":"additional","affiliation":[{"name":"Department of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan"},{"name":"RIKEN Brain Science Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1111\/1467-9868.00415","article-title":"On quantum statistical inference","volume":"65","author":"Gill","year":"2003","journal-title":"J. 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Predictive Inference: An Introduction, Chapman & Hall.","DOI":"10.1007\/978-1-4899-4467-2"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"261","DOI":"10.3390\/e10030261","article-title":"Axiomatic characterizations of information measures","volume":"10","author":"Csiszar","year":"2008","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1093\/biomet\/62.3.547","article-title":"Goodness of prediction fit","volume":"62","author":"Aitchison","year":"1975","journal-title":"Biometrika"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.1016\/j.jspi.2011.06.009","article-title":"Bayesian predictive densities based on latent information priors","volume":"141","author":"Komaki","year":"2011","journal-title":"J. Stat. Plan. 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