Direct state measurement (DSM) is a tomography method that allows for retrieving quantum states’ wave functions 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 fill the gap by investigating the DSM measurement precision 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 such SPAM errors, the state to be measured lightly deviates from the true state, and the measurement error in the postselection process results in less accurate in the tomography. Our study could provide a reliable tool for SPAM errors tomography and contribute to understanding and resolving an urgent demand for current quantum technologies.

直接状态测量 (DSM) 是一种层析成像方法，可以直接检索量子态的波函数。然而，目前关于 DSM 的研究的一个缺点是它不提供对嘈杂量子系统的访问。在这里，我们试图通过研究经历状态准备和测量 (SPAM) 错误的 DSM 测量精度来填补空白。我们操纵具有各种配置的量子控制测量框架，并比较它们之间的效率。在这种SPAM误差下，要测量的状态与真实状态轻微偏离，后选择过程中的测量误差导致断层扫描的准确性降低。我们的研究可以为垃圾邮件错误断层扫描提供可靠的工具，并有助于理解和解决对当前量子技术的迫切需求。