Quantum Markovian Subsystems: Invariance, Attractivity, and Control
Abstract
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.
Cite
@article{arxiv.0705.1372,
title = {Quantum Markovian Subsystems: Invariance, Attractivity, and Control},
author = {Francesco Ticozzi and Lorenza Viola},
journal= {arXiv preprint arXiv:0705.1372},
year = {2010}
}