Universal families and quantum control in infinite dimensions

TL;DR

This paper explores the concept of universality in families of quantum mappings in infinite-dimensional spaces, linking it to controllability in quantum systems and identifying minimal generators for full control.

Contribution

It introduces the notion of universal families in infinite dimensions and finds minimal generators for control, extending quantum controllability theory.

Findings

Identified minimal generators for universal control families.

Linked universality to controllability in infinite-dimensional quantum systems.

Discussed properties of the infinite unitary group relevant to control.

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.