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 θ. As a simple example, we study the estimation problem of the isotropic depolarization parameter θ for a two-level quantum system $\mathcal{H}\simeq {\mathbf{C}}^2.$ In the framework of noncommutative statistics, it is shown that the optimal input state on $\mathcal{H}\otimes \mathcal{H}$ to the channel exhibits a transitionlike behavior according to the value of the parameter θ.