Purification of Mixed State for Two-Dimensional Systems via Interaction Control

Pure states are fundamental for the implementation of quantum technologies. Several methods for the purification of the state of a quantum system S have been developed in the past years. Considering two-level systems and assuming a particular interaction between the system S and probe P, we propose a control strategy that purifies an arbitrary mixed state to an eigenstate. An interaction control is designed to improve the quality of the purification of mixed state. The Lyapunov-based control method is used to design the part of interaction control. Compared numerical simulation experiments demonstrate superiority of the purification strategy proposed: the purification of an arbitrary mixed state can be realized in the energy difference between S and P being not only zero case, but also in the nonzero case.