Illustrating the Geometry of Coherently Controlled Quantum Channels
arXiv:1103.2703 · doi:10.1109/TAC.2012.2195849
Abstract
We extend standard Markovian open quantum systems (quantum channels) by allowing for Hamiltonian controls and elucidate their geometry in terms of Lie semigroups. For standard dissipative interactions with the environment and different coherent controls, we particularly specify the tangent cones (Lie wedges) of the respective Lie semigroups of quantum channels. These cones are the counterpart of the infinitesimal generator of a single one-parameter semigroup. They comprise all directions the underlying open quantum system can be steered to and thus give insight into the geometry of controlled open quantum dynamics. Such a differential characterisation is highly valuable for approximating reachable sets of given initial quantum states in a plethora of experimental implementations.
condensed and updated version; 14 pages; comments welcome
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- Isotropy and control of dissipative quantum dynamics
- Mixing of quantum states under Markovian dissipation and coherent control
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- A Lie Theoretic Framework for Controlling Open Quantum Systems