# A universal gap for non-spin quantum control systems

## TL;DR

This paper proves a universal gap in the minimum time controllability for most finite-dimensional quantum systems, linking control theory with Lie group orbit space geometry.

## Contribution

It establishes the existence of a universal gap in quantum control time, except for certain spin group representations, connecting control properties with Lie group actions.

## Key findings

- Universal gap in quantum control time proven
- Gap exists in orbit space diameters of Lie group actions
- Results exclude some spin group representations

## Abstract

We prove the existence of a universal gap for minimum time controllability of finite dimensional quantum systems, except for some basic representations of spin groups. This is equivalent to the existence of a gap in the diameter of orbit spaces of the corresponding compact connected Lie group unitary actions on the Hermitian spheres.