中文摘要：

在古典统计，菲希尔信息在它是在概率密度的空间公制的实质上唯一的单调 Riemannian 的意义是唯一的。Inquantum 理论，这唯一垮掉，并且有菲希尔信息，二个特别版本由他们的直觉、参考的意义在之中区分自己的许多自然的量类似物：首先，它在斜信息的起源在量测量的上下文在 1963 介绍了 byWigner 和 Yanase，并且是经由密度操作员的方形的根的 deSned。第二从 Helstrom 产生“ s 在 1967 量察觉学习，并且经由对称的对数的衍生物被定义。这篇论文的目的是比较量菲希尔信息的这二个版本，并且建立联系他们的二参考不平等。

英文摘要：

In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.