Template matching of mixed quantum states

We consider the problem of optimal classification of an unknown input mixed quantum state f̂ with respect to a set of predefined patterns Ci, each represented by a known mixed quantum template ĝi. The performance of the matching strategy is addressed within a Bayesian formulation where the cost function, as suggested by the theory of monotone distances between quantum states, is chosen to be the fidelity or the relative entropy between the input and the templates. We investigate various examples of quantum template matching for the case of a finite number of copies of a two-level input state f̂ and for a generic, group covariant, set of two-level template states.