宇宙族和无限维的量子控制
Universal families and quantum control in infinite dimensions
摘要：
在拓扑空间中，一个连续映射族称为泛映射，如果它的作用在空间的至少一个元素中是稠密的。如果映射是酉的或保迹的完全正的，则普适性的概念与封闭或开放量子系统中的可控性的概念密切相关。在无限维量子可控性讨论在此设置和最小生成器被发现完全控制通用的家庭。在无限维中控制所需的算子的一些要求来自于无限酉群的性质。因此，还包括对这一群及其相应的数学空间的简要讨论。
英文摘要：
In a topological space, a family of continuous mappings is called universal if its action, in at least one element of the space, is dense. If the mappings are unitary or trace-preserving completely positive, the notion of universality is closely related to the notion of controllability in either closed or open quantum systems. Quantum controllability in infinite dimensions is discussed in this setting and minimal generators are found for full control universal families. Some of the requirements of the operators needed for control in infinite dimensions follow from the properties of the infinite unitary group. Hence, a brief discussed of this group and their appropriate mathematical spaces is also included.
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