Quantum Markovian Subsystems: Invariance, Attractivity, and Control

TL;DR

This paper characterizes the behavior of continuous-time Markovian quantum systems, focusing on invariant and attractive subsystems, and explores control strategies for quantum state stabilization and noiseless subspace generation.

Contribution

It provides explicit linear-algebraic characterizations of invariant and noiseless subsystems, introduces the concept of attractive quantum subsystems, and develops control methods for quantum state stabilization.

Findings

Explicit conditions for invariant and noiseless subsystems

Introduction of attractive quantum subsystems with stability criteria

Design of output-feedback control strategies for quantum state stabilization

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.