We study two related estimation problems involving phase- covariant quantum states. We first address the problem of phase estimation. We give optimal bounds for pure and mixed Gaussian states and find that for a fixed squeezing parameter a larger temperature can enhance the estimation fidelity. In addition we use state estimation concepts to give a benchmark that asses whether experimental implementations of quantum storage and teleportation protocols could be reproduced by classical means, i.e., by a measure and prepare strategy.
