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International Conference on Intelligent System Design and Engineering Application (ISDEA)

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

Fei Yang, Shuang Cong

Published Oct 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1109/isdea.2010.163

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Pure states are fundamental for the implementation of quantum technologies, and several methods for the purification of the state of a quantum system SSS have been developed in the past years. In this work we describe a mechanism leading to purification of mixed states, based on the interaction of SSS with an auxiliary system PPP. Considering two-level systems and assuming a particular interaction between them, we study how the dynamical parameters of the system PPP affect the purification of SSS. By 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.
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One main problem of quantum control in quantum systems is the manipulation of states including state transfer and state tracking. We design control fields to realize arbitrary state transfer for open quantum system by Lyapunov stability theory, and investigate the state transfer for non-Markovian system with phase relaxation and energy dissipative relaxation. The numerical simulations illustrate that arbitrary state (eigenstate, superposition state or mixed state) transfer and maintenance for non-Markovian system can be realized under Lyapunov control function by an external steady control field of proper amplitude, with a success rate of more than 98%. When the right control field and function are implemented, not only the decoherence is compensated completely but also the purity of quantum states is maintained in the process of state transfer.
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A rapid incoherent control scheme for driving a simple qubit system from an initial mixed state to an arbitrary target pure state is proposed. This scheme consists of two main steps: rapid purification of the initial mixed state and time optimal transition from the conditional state to the target state. The first step rapidly purifies the initial mixed state into an almost-pure state of the simple qubit system through continuous measurements and feedback control by the protocol proposed in Jacobs 2003 Physical Review A 67 030301(R). The second step finds a set of suitable time optimal controls to drive the simple qubit system from the conditional state to the target state. The switching time between the first step and the second step is determined by the expected purity and the resultant state is an almost-pure state with a high fidelity with the target state. This rapid incoherent control scheme provides an alternative quantum engineering strategy for the rapid preparation of arbitrary pure states of a simple qubit system.