论文标题
Bures几何形状在C* - 代数状态空间上
Bures Geometry on C*-algebraic State Spaces
论文作者
论文摘要
详细考虑了由bures距离函数诱导的内部几何形状，详细考虑了Unital c* - 代数的状态空间或部分的一部分。作为关键结果，当状态参数绑定按照通过该状态的某些参数化曲线变化时，在状态下计算局部扩张函数。所考虑的参数化曲线是那些具有可区分局部实现的曲线，相对于所涉及状态附近的某些Unital *代理。在给定状态的所有切线形式的空间与此类别曲线的通讯员相通用为标准线性空间，具有二次规范，以特征性的方式取决于状态。在分析局部扩张函数的结构时，特殊重点是描述状态空间的此类部分，并限制了线元素将是Finslerian类型的，并且在地理上是凸的子集。获得的所有结果均通过示例说明，并将获得的含义与在有限维度的Uhlmann等人的研究中所知的结果进行了比较。
The inner geometry induced by the Bures distance function on the state space of a unital C*-algebra, or on parts of it, is considered in detail. As a key result the local dilation function is calculated at a state when the state argument is bound to vary along certain parameterized curves passing through this state. The parameterized curves considered are those possessing differentiable local implementations as vector states relative to some unital *-representation in the vicinity of the state in question. The space of all tangent forms at a given state correspondent to this category of curves is specified as normed linear space with a quadratic norm which is depending from the state in a characteristic manner. In analyzing the structure of the local dilation function special emphasis is laid on describing such parts of the state space, in restriction to which the line element would be of Finslerian type, and which were geodesically convex subsets. All results obtained are illustrated by examples, and the implications obtained are compared to those known from the investigations of Uhlmann et al in the finite dimensional case.
