Minimax Estimation of Quantum States Based on the Latent Information Priors

Minimax Estimation of Quantum States Based on the Latent Information Priors

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 quan...

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Bibliographic Details
Main Authors: Takayuki Koyama, Takeru Matsuda, Fumiyasu Komaki
Format: Article
Language:English
Published: MDPI AG 2017-11-01
Series:Entropy
Subjects:
Bayes
conditional Holevo mutual information
latent information prior
predictive density operator
quantum estimation
Online Access:https://www.mdpi.com/1099-4300/19/11/618
Description
Summary: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.
ISSN:1099-4300

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