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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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

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spelling	doaj-8d3f6d44ee744feb826648943677809a2020-11-25T00:21:44ZengMDPI AGEntropy1099-43002017-11-01191161810.3390/e19110618e19110618Minimax Estimation of Quantum States Based on the Latent Information PriorsTakayuki Koyama0Takeru Matsuda1Fumiyasu Komaki2FANUC Corporation, 3580 Furubaba Shibokusa Oshino-mura, Yamanashi 401-0597, JapanDepartment of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, JapanDepartment of Mathematical Informatics, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, JapanWe 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.https://www.mdpi.com/1099-4300/19/11/618Bayesconditional Holevo mutual informationlatent information priorpredictive density operatorquantum estimation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Takayuki Koyama Takeru Matsuda Fumiyasu Komaki
spellingShingle	Takayuki Koyama Takeru Matsuda Fumiyasu Komaki Minimax Estimation of Quantum States Based on the Latent Information Priors Entropy Bayes conditional Holevo mutual information latent information prior predictive density operator quantum estimation
author_facet	Takayuki Koyama Takeru Matsuda Fumiyasu Komaki
author_sort	Takayuki Koyama
title	Minimax Estimation of Quantum States Based on the Latent Information Priors
title_short	Minimax Estimation of Quantum States Based on the Latent Information Priors
title_full	Minimax Estimation of Quantum States Based on the Latent Information Priors
title_fullStr	Minimax Estimation of Quantum States Based on the Latent Information Priors
title_full_unstemmed	Minimax Estimation of Quantum States Based on the Latent Information Priors
title_sort	minimax estimation of quantum states based on the latent information priors
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2017-11-01
description	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.
topic	Bayes conditional Holevo mutual information latent information prior predictive density operator quantum estimation
url	https://www.mdpi.com/1099-4300/19/11/618
work_keys_str_mv	AT takayukikoyama minimaxestimationofquantumstatesbasedonthelatentinformationpriors AT takerumatsuda minimaxestimationofquantumstatesbasedonthelatentinformationpriors AT fumiyasukomaki minimaxestimationofquantumstatesbasedonthelatentinformationpriors
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Minimax Estimation of Quantum States Based on the Latent Information Priors

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