Maximum-likelihood reconstruction of completely positive maps - art. no. 054104

We present a method for the determination of the completely positive (CP) m ap describing a physical device based on random preparation of the input st ates, random measurements at the output, and the maximum-likelihood princip le. In the numerical implementation the constraint of completely positivity can be imposed by exploiting the isomorphism between linear transformation s from Hilbert spaces H to K and linear operators in K circle timesH. The e ffectiveness of the method is shown on the basis of some examples of recons truction of CP maps related to quantum communication channels for qubits.