量子态估计：根方法
Quantum States Estimation: Root Approach
摘要：
考虑了由观测值稳定重建参数的多参数统计模型。唯一的通用方法是根模型，它将概率密度表示为某个函数的绝对值的平方，该函数被称为与量子力学类似的psi函数。PSI函数由函数的标准正交集的展开表示。它示出的PSI函数的引入允许一个代表的Fisher信息矩阵以及统计特性的状态向量（状态估计器）的估计在简单的分析形式。引入了一个新的统计特征--置信锥来代替标准的置信区间。卡方检验被认为是检验的假设，估计向量收敛到一般人口的状态向量，两个样本是同质的。展开系数用极大似然法估计。所提出的方法可用于解决量子力学的统计逆问题（量子态的根估计）。为了提供分析的统计完整性，有必要在相互补充的实验中进行测量（根据玻尔术语）。推广了极大似然技术和似然方程，用于分析量子力学实验。它表明，要求的扩展是一个根的种类可以被认为是一个量子化条件，使它有可能选择系统所描述的量子力学从所有的统计模型一致，平均而言，与法律的经典力学。
英文摘要：
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared absolute value of a certain function, which is referred to as a psi-function in analogy with quantum mechanics. The psi-function is represented by an expansion in terms of an orthonormal set of functions. It is shown that the introduction of the psi-function allows one to represent the Fisher information matrix as well as statistical properties of the estimator of the state vector (state estimator) in simple analytical forms. A new statistical characteristic, a confidence cone, is introduced instead of a standard confidence interval. The chi-square test is considered to test the hypotheses that the estimated vector converges to the state vector of a general population and that both samples are homogeneous. The expansion coefficients are estimated by the maximum likelihood method. The method proposed may be applied to its full extent to solve the statistical inverse problem of quantum mechanics (root estimator of quantum states). In order to provide statistical completeness of the analysis, it is necessary to perform measurements in mutually complementing experiments (according to the Bohr terminology). The maximum likelihood technique and likelihood equation are generalized in order to analyze quantum mechanical experiments. It is shown that the requirement for the expansion to be of a root kind can be considered as a quantization condition making it possible to choose systems described by quantum mechanics from all statistical models consistent, on average, with the laws of classical mechanics.
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