統計学輪講（第４回）

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.