Quantum channel identification problem

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