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Entropy
Volume 19
Issue 11
10.3390/e19110618
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Article

Minimax Estimation of Quantum States Based on the Latent Information Priors

by
Takayuki Koyama
1,
Takeru Matsuda
2 and
Fumiyasu Komaki
2,3,*
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
Submission 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.
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, Takeru Matsuda, and Fumiyasu Komaki. 2017. "Minimax Estimation of Quantum States Based on the Latent Information Priors" Entropy 19, no. 11: 618. https://doi.org/10.3390/e19110618

APA Style

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

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