Purity and state fidelity of quantum channels

We associate with every quantum channel T acting on a Hilbert space H a pair of Hermitian operators, referred to as Hamiltonians, over the symmetric subspace of H-x2. The expectation values of these Hamiltonians over symmetric product states give either the purity or the pure-state fidelity of T. This allows us to analytically compute these measures for a wide class of channels, and to identify states that are optimal with respect to these measures.