Direct state measurement (DSM) is a tomography method that allows for retrieving the wave functions of quantum states directly. However, a shortcoming of current studies on the DSM is that it does not provide access to noisy quantum systems. Here, we attempt to fulfill the gap by investigating the measurement precision in the DSM that undergoes the state-preparation-and-measurement (SPAM) errors. We manipulate a quantum controlled measurement framework with various configurations and compare the efficiency between them. Under the effect of state-preparation error, the state to be measured lightly deviates from the true state, while the measurement error affects the postselection process, and thus results in less accuracy in the tomography. Our study could provide a reliable tool for SPAM tomography and thus contribute to understanding and resolving an urgent demand for current quantum technologies.
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