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

摘要

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