We present a general denoising algorithm for performing $\textit{simultaneous tomography}$ of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.

中文翻译：

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量子态和SPAM噪声同步断层扫描的通用框架


我们提出了一种通用的去噪算法，用于执行量子态和测量噪声的$\textit{同步断层扫描}$。该算法使我们能够全面表征任何量子系统中存在的状态准备和测量（SPAM）错误。我们的方法基于对酉运算引起的线性算子空间的属性的分析。给定任何具有噪声测量装置的量子系统，我们的方法可以输出高达单规范自由度的探测器的量子态和噪声矩阵。我们证明，这种规范自由度在一般情况下是不可避免的，但是使用状态或噪声属性的先验知识通常可以打破这种简并性，从而在不假设噪声强度的情况下固定几种类型的状态噪声组合的规范。这种组合包括具有任意相关误差的纯量子态，以及具有与块无关的误差的任意状态。该框架可以进一步使用有关设置的可用先验信息来系统地减少状态和噪声检测所需的观察和测量的数量。我们的方法有效地概括了解决该问题的现有方法，并包括文献中考虑的特殊情况常见设置，需要不相关或可逆的噪声矩阵或特定的探针状态。