Recent Development of Quantum Statistical Decision Theory

Abstract

In modern statistics, various problems in statistical inference are formulated in statistical decision theory. Quantum analogue of the theory was first established by Holevo in 1973. After the emergence of quantum information science in 1990s, many theoretical analyses have been developed in his framework. We introduce quantum minimax theorem and quantum local asymptotic normality as recent fundamental results. We also present an attempt to modify Holevoʼs naive framework for practical application. As shown in an illustrative example, such a modification would allow us to design better experiments in quantum physics.