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arXiv:quant-ph/0308132

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

Paolo Giorda, Paolo Zanardi A, Seth Lloyd

Published Aug 25, 2003• 0 citations
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Abstract

This paper has been withdrawn by the authors because it was just an early submission of quant-ph/0308133 with the wrong title. Sorry.
DOI
10.48550/arxiv.quant-ph/0308132

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We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi and S. Lloyd, e-print quant-ph/0305013. The quantum state space H\mathcal{H}H encoding information decomposes into irreducible sectors and subsystems associated with the group of available evolutions. If this group coincides with the unitary part of the group algebra CKC\mathcal{K}CK of some group K\mathcal{K}K then universal control is achievable over the K-irreducible components of H.\mathcal{H}.H. This general strategy is applied to different kinds 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 multimode massless case giving the conditions for generating the whole infinite-dimensional multimode Heisenberg-Weyl enveloping algebra. Finally we show how to use an auxiliary bosonic mode coupled to finite-dimensional systems to generate high-order nonlinearities needed for universal control.