符合标准净化要求的连接和维护
Connections and Metrics Respecting Standard Purification
摘要：
标准净化交错厄米特和黎曼度量的空间上的密度算子的度量和连接的净化希尔伯特-施密特空间。我们讨论的连接和度量，以及采用净化，并提出了一组选定的它们之间的关系。一个连接，以及状态空间上的度量，可以从净化空间上的度量获得。我们包括一个条件，使这种对应关系成为一对一。我们的方法是借用初等 *-表示和纤维空间理论。作为一个例子，我们解除，冯诺依曼方程的解决方案，写下循环的完整不变量，并“添加噪声”到纯态曲线。
英文摘要：
Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.
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