Estimation of quantum channels with finite resources

Abstract

We investigate the problem of determining the parameters that describe a quantum channel. It is assumed that the users of the channel have at best only partial knowledge of it and make use of a finite amount of resources to estimate it. We discuss simple protocols for the estimation of the parameters of several classes of channels that are studied in the current literature. We define two different quantitative measures of the quality of the estimation schemes, one based on the standard deviation, the other one on the fidelity. The possibility of protocols that employ entangled particles is also considered. It turns out that the use of entangled particles as a new kind of nonclassical resource enhances the estimation quality of some classes of quantum channel. Further, the investigated methods allow us to extend them to higher dimensional quantum systems.