论文标题
量子状态的多种指数弧
Exponential arcs in manifolds of quantum states
论文作者
论文摘要
所考虑的歧管由标准形式的Sigma-Finite von Neumann代数上的忠实正常状态组成。讨论了切线和近似切线的平面。假定给出相对的熵/发散函数。它用于概括将一个状态连接到另一种状态的指数弧的概念。指数弧的发电机被证明是唯一到添加剂常数的。对于Araki的相对熵，von Neumann代数的每个自助元件都会产生指数弧。组成的指数弧的发电机被证明加起来。显示出源自Araki的相对熵的度量标准，可复制库博 - 莫里度量。后者是线性响应理论中使用的度量。 E和M连接描述了一对几何形状。任何有限数量的线性独立发电机都会确定连接到给定参考状态的状态的子序列。这样的子手机是对双重平坦统计歧管的量子概括。
The manifold under consideration consists of the faithful normal states on a sigma-finite von Neumann algebra in standard form. Tangent planes and approximate tangent planes are discussed. A relative entropy/divergence function is assumed to be given. It is used to generalize the notion of an exponential arc connecting one state to another. The generator of the exponential arc is shown to be unique up to an additive constant. In the case of Araki's relative entropy every selfadjoint element of the von Neumann algebra generates an exponential arc. The generators of composed exponential arcs are shown to add up. The metric derived from Araki's relative entropy is shown to reproduce the Kubo-Mori metric. The latter is the metric used in Linear Response Theory. The e- and m-connections describe a dual pair of geometries. Any finite number of linearly independent generators determines a submanifold of states connected to a given reference state. Such a submanifold is a quantum generalization of a dually flat statistical manifold.
