Optimal quantum-state tomography via weak value

Abstract

To improve the efficiency of the state-tomography strategy via weak value, we have searched for the optimal measurement strength between the quantum system being measured and the measuring device. For an arbitrary $d$-dimensional quantum system, the optimal measurement strengths 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 the mean-square error. The minimum mean-square error of the reconstructed density matrix has been derived. The state-tomography strategy studied in this article may be useful in the measurement of the unknown quantum state.