Analysis on Behaviors of Controlled Quantum Systems via Quantum Entropy

In this paper, we investigate the essential properties of finite dimensional measurement-based quantum feedback control systems using a kind of quantum entropy, or socalled 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.