Universal quantum control in irreducible state-space sectors: application to bosonic and spin-boson systems

Abstract

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space $\mathcal{H}$ 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 $\mathcal{K}$ then universal control is achievable over the $\mathcal{K}$-irreducible components of $\mathcal{H}$. 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.

10 pages, LaTeX, no figures

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