= Density operator controllability
{title2=$\rho_1=U\rho_0U^\dagger$}
A closed system has density operator controllability when every pair of <density operators> with the same spectrum can be connected by its controls. Under the standard finite-dimensional Hamiltonian assumptions, this holds exactly for <Dynamical Lie algebra> $\mathfrak u(N)$ or $\mathfrak{su}(N)$. This definition ranges over every spectral orbit; a particular degenerate spectrum can be controllable under a smaller group.
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