Universal families and quantum control in infinite dimensions
Quantum Physics
2015-05-13 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0902.0561,
title = {Universal families and quantum control in infinite dimensions},
author = {R. Vilela Mendes},
journal= {arXiv preprint arXiv:0902.0561},
year = {2015}
}
Comments
9 pages Latex