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Article

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.
Entropy 2017, 19(11), 618; https://doi.org/10.3390/e19110618
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)
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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MDPI and ACS Style

Koyama, T.; Matsuda, T.; Komaki, F. Minimax Estimation of Quantum States Based on the Latent Information Priors. Entropy 2017, 19, 618. https://doi.org/10.3390/e19110618

AMA Style

Koyama T, Matsuda T, Komaki F. Minimax Estimation of Quantum States Based on the Latent Information Priors. Entropy. 2017; 19(11):618. https://doi.org/10.3390/e19110618

Chicago/Turabian Style

Koyama, Takayuki; Matsuda, Takeru; Komaki, Fumiyasu. 2017. "Minimax Estimation of Quantum States Based on the Latent Information Priors" Entropy 19, no. 11: 618. https://doi.org/10.3390/e19110618

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