Quantum channel identification problem
Akio Fujiwara · Physical Review A · 2001
This paper explores an application of quantum entanglement. The problem treated here is the quantum channel identification problem: given a parametric family ${{\ensuremath{\Gamma}}_{\ensuremath{\theta}}{}}_{\ensuremath{\theta}}$ of quantum channels, find the best strategy of estimating the true value of the parameter \ensuremath{\theta}. As a simple example, we study the estimation problem of the isotropic depolarization parameter \ensuremath{\theta} for a two-level quantum system $\mathcal{H}\ensuremath{\simeq}{\mathbf{C}}^{2}.$ In the framework of noncommutative statistics, it is shown that the optimal input state on $\mathcal{H}\ensuremath{\bigotimes}\mathcal{H}$ to the channel exhibits a transitionlike behavior according to the value of the parameter \ensuremath{\theta}.