Robustness of Imperfect Initialization in Quantum Parameter Estimation

One of the most concerned problems in quantum metrology is exploiting quantum resources to increase the precision of quantum parameter estimation. One natural and standard way of improving the precision of estimation is letting the initial probe state being optimal. However, the optimal initial probe state on the one hand may be hard to identify, and on the other hand one cannot prepare the optimal initial state perfectly in practice. In this paper, we focus on the influence of the imperfect preparation of the optimal initial probe state to the precision limit of quantum parameter estimation. The analytical results are valid for unitary evolutions with arbitrary dimension.