将Fisher度量扩展到密度矩阵
Extending the Fisher metric to density matrices
摘要：
Chentsov研究了黎曼度量集的概率措施的角度来看，决策理论。他证明，直到一个常数因子的费舍尔信息是唯一的度量是单调的随机变换。本文在量子力学的基础上研究有限密度矩阵空间上的单调度量。这些度量的一个特征给出的运营商单调函数。构造并分析了几个具体的度量，特别是，在概率情形下，有一个大类的单调度量，而不是唯一性。其中一些在很久以前就出现在物理学文献中了。还讨论了一个纯态的限制过程。
英文摘要：
Chentsov studied Riemannian metrics on the set of probability measures from the point of view of decision theory. He proved that up to a constant factor the Fisher information is the only metric which is monotone under stochastic transformations. The present paper deals with monotone metrics on the space of finite density matrices on the basis motivated by quantum mechanics. A characterization of those metrics is given in terms of operator monotone functions. Several concrete metrics are constructed and analyzed, in particular, instead of the uniqueness in the probabilistic case, there is a large class of monotone metrics. Some of those appeared already in the physics literature a long time ago. A limiting procedure to pure states is discussed as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
