Analysis on Behaviors of Controlled Quantum Systems via Quantum Entropy

Abstract

In this paper, we investigate the essential properties of finite dimensional measurement-based quantum feedback control systems using a kind of quantum entropy, or so-called linear entropy. We show how the terms appear in the stochastic master equation affect the purity of the conditional density matrix of the system, and clarify a limitation of control action via Hamiltonian. Moreover, applying the stochastic version of LaSalle's invariance theorem, we derive a sufficient condition under which the conditional density matrix converges in probability to the set of all pure states for any control input. The result shows a class of measurement which assures preparation of a pure state.