The impact of imperfect measurements of weak values on state tomography

We investigated the impact of imperfect measurements of weak values on state tomography due to the error of detector basis tilting, as this impact is seldom discussed before. For a given error bound, the negative influence is evaluated with two tomography performance indices-fidelity and trace distance. The simulation based on a reported experiment suggests that the tilting error would lead to a worse tomography performance. However, when the target state is in the pattern of near 50% vector elements carrying phase π, the tomography performance is relatively insensitive to such error. These results provide a choice of a suitable state type for information encoding in the task of quantum information transferring.