Physics – Quantum Physics
Scientific paper
2007-05-09
IEEE Transaction on Automatic Control, 53(9):2048-2063, 2008
Physics
Quantum Physics
16 pages, no figures. Revised version with new title, corrected typos, partial rewriting of Section III.E and some other minor
Scientific paper
We characterize the dynamical behavior of continuous-time, Markovian quantum systems with respect to a subsystem of interest. Markovian dynamics describes a wide class of open quantum systems of relevance to quantum information processing, subsystem encodings offering a general pathway to faithfully represent quantum information. We provide explicit linear-algebraic characterizations of the notion of invariant and noiseless subsystem for Markovian master equations, under different robustness assumptions for model-parameter and initial-state variations. The stronger concept of an attractive quantum subsystem is introduced, and sufficient existence conditions are identified based on Lyapunov's stability techniques. As a main control application, we address the potential of output-feedback Markovian control strategies for quantum pure state-stabilization and noiseless-subspace generation. In particular, explicit results for the synthesis of stabilizing semigroups and noiseless subspaces in finite-dimensional Markovian systems are obtained.
Ticozzi Francesco
Viola Lorenza
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