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.
From Discrete to Continuous-Variable Systems via Jordan-Schwinger Tomographic Transformation
Universiteit Leiden（莱顿大学）；Applied Quantum Algorithms Leiden（莱顿应用量子算法）；Russian Quantum Center（俄罗斯量子中心）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）；Lebedev Physical Institute, Russian Academy of Sciences（俄罗斯科学院列别杰夫物理研究所）
