On Quantum Channel Estimation with Minimal Resources

We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is used to develop a globally converging Newton-type algorithm that ensures a physically admissible solution to the problem. Numerical simulations are provided to support the results, and indicate that the minimal experimental setting is sufficient to guarantee good estimates.