Resonant purification of mixed states for closed and open quantum systems

Abstract

Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system S have been developed in the past years. In this letter we present a new approach, based on the interaction of S with an auxiliary system P , having a wide range of applicability. Considering two-level systems S and P and assuming a particular interaction between them, we prove that complete purifications can be obtained under suitable conditions on the parameters characterizing P . Using analytical and numerical tools, we show that the purification process exhibits a resonant behavior in both the cases of system isolated from the external environment or not.

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

“…Reference [11] investigated accessibility and controllability of such a composite system in the twodimensional Hilbert spaces. Further, some results of purification of mixed states for closed and open quantum systems have been achieved in [12], in which the main result is that the purification process exhibits a resonant behavior depending on the energy difference between S and P. But this strategy suffered from the issue that the mixed state can not be purified completely for the cases of nonzero energy difference.…”

“…In order to resolve this issue, based on [12], we propose a purification strategy that purifies an arbitrary mixed state into a pure state through controlling the interaction between S and P. Generally, the pure state can be either eigenstate or superposition state. For the sake of simplicity, the eigenstate is selected as the target state in this paper.…”

“…For the sake of simplicity, the eigenstate is selected as the target state in this paper. The coupling between S and P is time-and controls-dependent function, which is the most significant difference of this paper from that of [12]. In this paper, the control is designed by Lyapunov-based control, in which the Lyapunov indirect stability theorem is used and a feedback control law is derived by means of the sufficient condition of guaranteeing the system controlled to be stable.…”

“…This paper is organized as follows. Section Ⅱ briefly introduces purification by means of a probe in [12]. In Section Ⅲ, the strategy that drives an arbitrary mixed state to a pre-determined eigenstate is proposed and analyzed.…”

“…Particularly the design of control based on the Lyapunov method is derived. In order to compare with [12], the effectiveness of control under the different parameters is compared and analyzed in Section Ⅳ by means of the numerical experiments. Finally, the conclusion is given in Sec Ⅴ.…”