Quantum estimation and the quantum central limit theorem

This paper gives a survey about quantum estimation. We also describes the relation between the quantum central limit theorem and the asymptotic bound of mean square error in quantum state estimation.Comment: The original Japanese version of this manuscript was published as an introductory article of quantum estimation in Bulletin of Mathematical Society of Japan, Sugaku, Vol. 55, No. 4, 368--391 (2003); Received September 2, 2002, Published October 24, 2003. It was translated to English by Michikazu Sato and Masahito Hayashi. The essential content of this manuscript is the same as that of the original version, while several descriptions and references are improved. The material in this paper was presented in English in part at Joint MaPhySto and QUANTOP Workshop on Quantum Measurements and Quantum Stochastics, Department of Mathematical Sciences, University of Aarhus, Denmark, 2003, Non-locality of Quantum Mechanics and Statistical Inference, Kyoto Sangyo Univ., Kyoto, 2003, and Special Week on Quantum Statistics, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 200