Fidelities for transformations of unknown quantum states

We present a general theoretical formalism to compute the fidelity of transformations of unknown quantum states, and we apply our theory to Gaussian transformations of continuous variable quantum systems. For the case of a Gaussian distribution of displaced coherent states, the theory is readily tractable by a covariance matrix formalism, and a wider class of states, exemplified by Fock states, can be treated efficiently by the Wigner function formalism. Given the distribution of input states, the optimum feedback gain is identified, and analytical results for the fidelities are presented for recently implemented teleportation and memory storage protocols for continuous variables.