Characterization of systematic errors in direct quantum state measurements

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We investigated the systematic operational errors in the direct state measurements (DSM) with a quantum controlled interaction framework. In this scheme, a target system is controlled by a qubit probe and postselected onto a conjugate basis; the outcomes of the control qubit probe can be measured and taken out of the estimated state. We have considered two types of operational interaction: (i) invert quantum controlled interaction (type-I) and (ii) arbitrary strong interaction (type-II), which is equivalent to a von Neumann interaction.We found that type-I gives lower systematic error than type-II, which means more accuracy. For the same confidence level, type-I has a higher ratio into percentage in the confidence region. The systematic error in type-I is also well against the noise as its fidelity is protected under the noise.Our study gives a better solution for quantum state tomography using the quantum controlled measurement scheme (better than conventional strong measurements and weak measurements.) Furthermore, its measurement is simple and applicable to high-dimension systems. This method, thus, could be a potential candidate for further characterizing the properties of large systems.