統計学輪講（第04回） 日時 2012年05月08日(火) 14時50分～16時30分 場所 経済学部新棟３階第３教室 講演者 田中 冬彦 (情報理工) 演題 Noninformative prior in the quantum statistical model of pure states 概要 In the present talk, we consider a suitable definition of a noninformative prior on the quantum statistical model of pure states. While the full pure states model is invariant under unitary rotation and admits the Haar measure, restricted models, which we often see in quantum channel estimation and quantum process tomography, have less symmetry and no compelling rationale for any choice. We adopt a game-theoretic approach that is applicable to classical Bayesian statistics and yields a noninformative prior for a general class of probability distributions. We define the quantum detection game and show that there exist noninformative priors for a general class of pure states model. Theoretically, it gives one of the ways how we represent ignorance on the given quantum system with partial information. Practically, our method proposes a default distribution on the model in order to use the Bayesian technique in the quantum state tomography with a small sample.