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Distance to Uncontrollability is a crucial concept in classical controltheory. Here, we introduce Quantum Distance to Uncontrollability as a measurehow close a universal quantum system is to a non-universal one. This allows usto provide a quantitative version of the Quantum Speed Limit, decomposing thebound into a geometric and dynamical component. We consider several physicalexamples including globally controlled solid state qubits and a cross-Kerrsystem, showing that the Quantum Distance to Uncontrollability provides aprecise meaning to spectral crowding, weak interactions and other bottlenecksto universality. We suggest that this measure should be taken intoconsideration in the design of quantum technology.

Quantum Distance to Uncontrollability and Quantum Speed Limits