One Lyapunov control for quantum systems and its application to entanglement generation

Abstract

In this Letter, we investigate the control of finite dimensional ideal quantum systems in which the quantum states are represented by the density operators. A new Lyapunov function based on the Hilbert–Schmidt distance and mechanical quantity of the quantum system is given. We present a theoretical convergence result using LaSalle invariance principle. Applying the proposed Lyapunov method, the generation of the maximally entangled quantum states of two qubits is obtained. ► A new Lyapunov function based on HS distance and mechanical quantity is given. ► This Letter investigates how to control finite dimensional ideal quantum systems. ► We present a theoretical convergence result of quantum states. ► The maximally entangled quantum states of two qubits are obtained.