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Entropy 2017, 19(11), 618; doi:10.3390/e19110618

Minimax Estimation of Quantum States Based on the Latent Information Priors

1
FANUC Corporation, 3580 Furubaba Shibokusa Oshino-mura, Yamanashi 401-0597, Japan
2
Department of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan
3
RIKEN Brain Science Institute, 2-1 Hirosawa, Wako-shi, Saitama 351-0198, Japan
*
Author to whom correspondence should be addressed.
Received: 13 September 2017 / Revised: 12 November 2017 / Accepted: 13 November 2017 / Published: 16 November 2017
(This article belongs to the Special Issue Transfer Entropy II)
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Abstract

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. View Full-Text
Keywords: Bayes; conditional Holevo mutual information; latent information prior; predictive density operator; quantum estimation Bayes; conditional Holevo mutual information; latent information prior; predictive density operator; quantum estimation
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Koyama, T.; Matsuda, T.; Komaki, F. Minimax Estimation of Quantum States Based on the Latent Information Priors. Entropy 2017, 19, 618.

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