论文标题
量子增强了哈密顿参数的计量
Quantum enhanced metrology of Hamiltonian parameters beyond the Cramèr-Rao bound
论文作者
论文摘要
这是一个教程，旨在说明量子参数估计的一些最新发展，超出了Cramèr-Rao结合，及其在量子计量学中的应用。我们的起点是观察到的是，经典和量子计量学中存在某些情况，其中未知参数（确定探针的状态）也影响了测量设备的操作，例如可能的结果范围。在这些情况下，可能会出现非规范统计模型，而Cramèr-rao定理不存在。反过来，可实现的精度可能会超过Cramèr-Rao的界限，为增强计量学开辟了新的途径。我们专注于对哈密顿参数的量子估计，并表明可以以封闭形式获得与精度达到精确度（超越cramèr-rao）的量子，以用于所谓的控制能量测量结果。在一些细节中阐明了新的量子计量问题的新限制的应用程序的示例。
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cramèr-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are situations in classical and quantum metrology where the unknown parameter of interest, besides determining the state of the probe, is also influencing the operation of the measuring devices, e.g. the range of possible outcomes. In those cases, non-regular statistical models may appear, for which the Cramèr-Rao theorem does not hold. In turn, the achievable precision may exceed the Cramèr-Rao bound, opening new avenues for enhanced metrology. We focus on quantum estimation of Hamiltonian parameters and show that an achievable bound to precision (beyond the Cramèr-Rao) may be obtained in a closed form for the class of so-called controlled energy measurements. Examples of applications of the new bound to various estimation problems in quantum metrology are worked out in some details.
