In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum semiparametric estimation that can circumvent both challenges and produce simple analytic bounds for a class of problems The theory is especially relevant to the estimation of a parameter that can be expressed as a function of the density operator, such as the expectation value of an observable, the fidelity to a pure state, the purity, or the von Neumann entropy. Potential applications include quantum state characterization for many-body systems, optical imaging, and interferometry, where full tomography of the quantum state is often infeasible and only a few select properties of the system are of interest.

中文翻译：

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量子半参数估计

在参数估计的量子极限研究中，密度算子的高维和未知参数的高维一直是最困难的两个挑战。在这里，我们提出了一种量子半参数估计的理论，该理论可以规避挑战并为一类问题产生简单的解析界线。该理论尤其与参数的估计有关，该参数可以表示为密度算符的函数，例如观测值的期望值，保真度，纯净度或冯·诺依曼熵。潜在的应用包括用于多体系统的量子态表征，光学成像和干涉测量，其中对量子态进行完整的层析成像通常是不可行的，并且仅对系统的少数选定特性感兴趣。