= Unitary operator controllability
{title2=$\mathfrak g=\mathfrak u(N)$}
A finite-dimensional closed-system control model is unitarily operator controllable when its reachable propagators include every <unitary operator>. For the usual real Hamiltonian controls and freely chosen duration, this requires the <Dynamical Lie algebra> to be $\mathfrak u(N)$. If global phase is ignored, $\mathfrak{su}(N)$ also suffices; exact access to all of $U(N)$ still requires the central phase direction.
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