  We analyze the dynamical-algebraic approach to universal quantum control
introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space
$\cal H$ encoding information decomposes into irreducible sectors and
subsystems associated to the group of available evolutions. If this group
coincides with the unitary part of the group-algebra $\CC{\cal K}$ of some
group $\cal K$ then universal control is achievable over the ${\cal
K}$-irreducible components of $\cal H$. This general strategy is applied to
different kind of bosonic systems. We first consider massive bosons in a
double-well and show how to achieve universal control over all
finite-dimensional
  Fock sectors. We then discuss a multi-mode massless case giving the
conditions for generating the whole infinite-dimensional multi-mode
Heisenberg-Weyl enveloping-algebra. Finally we show how to use an auxiliary
bosonic mode coupled to finite-dimensional systems to generate high-order
non-linearities needed for universal control.
