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This paper explores an application of quantum entanglement. The problem treated here is the quantum channel identification problem: given a parametric family {_}_ of quantum channels, find the best strategy of estimating the true value of the parameter. As a simple example, we study the estimation problem of the isotropic depolarization parameter for a two-level quantum system HC^2. In the framework of noncommutative statistics, it is shown that the optimal input state on H to the channel exhibits a transitionlike behavior according to the value of the parameter.
Akio Fujiwara (Fri,) studied this question.