On the quantum state estimation with imperfect observation

In this paper, we mainly investigate the problem of estimating quantum states under imperfect observation. By focusing on several specific examples, we point out that the imperfect observation can bring seriously destructive effect on the accuracy of quantum state estimation, which induces the estimate to be quickly far away from its real state. To reduce this negative influence, an averaged estimation method is adopted, which takes the observation error into account. It turns out that this method is effective to reduce the destructive influence of the observation error in some cases. However, this is not always true.