Wigner–Yanase information on quantum state space: The geometric approach
Wigner–Yanase information on quantum state space: The geometric approach
复制标题
DOI：
10.1063/1.1598279
复制
发表时间：
2003-04
影响因子：
1.3
通讯作者：
P. Gibilisco;T. Isola
中科院分区：
文献类型：
--
作者：
P. Gibilisco;T. Isola
在量子态空间上寻找合适的黎曼度量时，Chentsov提出了统计单调性的概念，或粗粒化下的收缩。具有此属性的度量已被Petz分类。这个几何家族的所有元素都可以被看作是费雪信息的量子类似物。虽然有一些一般定理揭示了这个问题，许多自然问题，也源于应用，仍然是开放的。在本文中，我们讨论了家庭的一个特殊成员，Wigner-Yanase信息。使用一个众所周知的方法，模仿经典的拉回方法费舍尔信息，我们能够给出明确的公式测地线距离，测地线路径，截面和标量曲率相关的Wigner-Yanase信息。此外，我们表明，这是唯一的单调度量，这种方法是可能的。
In the search of appropriate Riemannian metrics on quantum state space, the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by Petz. All the elements of this family of geometries can be seen as quantum analogs of Fisher information. Although there exists a number of general theorems shedding light on this subject, many natural questions, also stemming from applications, are still open. In this paper we discuss a particular member of the family, the Wigner–Yanase information. Using a well-known approach that mimics the classical pull-back approach to Fisher information, we are able to give explicit formulas for the geodesic distance, the geodesic path, the sectional and scalar curvatures associated to Wigner–Yanase information. Moreover, we show that this is the only monotone metric for which such an approach is possible.