The success of quantum noise sensing methods depends on the optimal interplay between properly designed control pulses and statistically informative measurement data on a specific quantum-probe observable. To enhance the information content of the data and reduce as much as possible the number of measurements on the probe, the filter orthogonalization method has been recently introduced. The latter is able to transform the control filter functions on an orthogonal basis allowing for the optimal reconstruction of the noise power spectral density. In this paper, we formalize this method within the standard formalism of minimum mean squared error estimation and we show the equivalence between the solutions of the two approaches. Then, we introduce a nonnegative least squares formulation that ensures the nonnegativeness of the estimated noise spectral density. Moreover, we also propose a novel protocol for the design in the frequency domain of the set of filter functions. The frequency-designed filter functions and the nonnegative least squares reconstruction are numerically tested on noise spectra with multiple components and as a function of the estimation parameters.

中文翻译：

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滤波器函数在噪声光谱中的作用

量子噪声传感方法的成功取决于适当设计的控制脉冲与特定量子探针可观测的统计信息测量数据之间的最佳相互作用。为了增强数据的信息含量并尽可能减少探头上的测量次数，最近引入了滤波器正交化方法。后者能够在正交基础上变换控制滤波器函数，从而实现噪声功率谱密度的最佳重构。在本文中，我们在最小均方误差估计的标准形式中对该方法进行了形式化，并展示了两种方法的解决方案之间的等价性。然后，我们引入了一个非负最小二乘公式，以确保估计的噪声谱密度的非负性。此外，我们还提出了一种新的协议，用于在一组滤波器函数的频域中进行设计。频率设计的滤波器函数和非负最小二乘重建在具有多个分量的噪声谱上进行了数值测试，并作为估计参数的函数。