  To improve the efficiency of the state tomography strategy via weak value, we
have searched the optimal coupling strength between the system and measuring
device. For an arbitrary d-dimensional quantum system, the optimal strengths
being used in measuring the real and imaginary parts of the density matrix are
obtained. The optimal efficiency of the state tomography has also been studied
by using mean square error. The minimal mean square errors in the reconstructed
density matrices have been derived. The state tomography strategy studied in
this article may be useful in the measurement of the unknown quantum states.
