Analysis and synthesis of attractive quantum Markovian dynamics |
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Authors: | Francesco Ticozzi [Author Vitae] Lorenza Viola [Author Vitae] |
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Affiliation: | a Dipartimento di Ingegneria dell’Informazione, Università di Padova, via Gradenigo 6/B, 35131 Padova, Italy b Department of Physics and Astronomy, Dartmouth College, 6127 Wilder Laboratory, Hanover, NH 03755, USA |
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Abstract: | We propose a general framework for investigating a large class of stabilization problems in Markovian quantum systems. Building on the notions of invariant and attractive quantum subsystem, we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics. Our general analysis results are exploited to assess the ability of open-loop Hamiltonian and output-feedback control strategies to synthesize Markovian generators which stabilize a target subsystem, subspace, or pure state. In particular, we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite-dimensional Markovian systems, that leads to a constructive strategy for designing the relevant controllers. Implications for stabilization of entangled pure states are addressed by example. |
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Keywords: | Quantum control Quantum dynamical semigroups Quantum subsystems |
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