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Acta Physica Sinica

Remote state preparation with bipartite entangled states in noisy environments

Hua-Qiu Liang, Liu Jin-Ming, (1)华东师范大学物理系精密光谱科学与技术国家重点实验室，上海 200062; (2)华东师范大学物理系精密光谱科学与技术国家重点实验室，上海 200062；台州学院物理与电子工程学院物理系，台州 318000

Published Jan 1, 2009• 3 citations
Publisher

Abstract

We investigate the influence of quantum noises on the processes of remote preparation of a qubit by using an Einstein-Podolsky-Rosen （EPR） state and a bipartite partially entangled state as the quantum channel respectively. By solving the master equation in the Lindblad form, we obtain the time evolution of the quantum channels. Then we use the trace distance to describe how close the output state and the initial state are in various noisy conditions. Our results show that the influence of the noise acting on z direction is the weakest, and the influence of the noises acting simultaneously on x, y, and z directions is the strongest.

DOI
10.7498/aps.58.3692

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We investigate the influence of quantum noises on the processes of remote preparation of a qubit by using an Einstein-Podolsky-Rosen （EPR） state and a bipartite partially entangled state as the quantum channel respectively. By solving the master equation in the Lindblad form, we obtain the time evolution of the quantum channels. Then we use the trace distance to describe how close the output state and the initial state are in various noisy conditions. Our results show that the influence of the noise acting on z direction is the weakest, and the influence of the noises acting simultaneously on x, y, and z directions is the strongest.
Using a quantum channel consisting of a GHZ state exposed to noisy environment, we investigate how to remotely prepare an entangled state and a qubit state, respectively. By solving the master equation in the Lindblad form, the influence of the various types of noises on the GHZ state is first discussed. Then we use the fidelity to describe how close the remotely prepared state and the initial state are. Our results show that the fidelity is a function of the decoherence rates and the angles of the initial state. It is found that for each of the two RSP schemes, the influence of the noise acting simultaneously in x, y, and z directions on the average fidelity is the strongest while the influence of the noise acting in x or z direction on the average fidelity is relatively weaker.
A scheme is proposed for the remote preparation of a two qubit quantum state by using two nonmaximally entangled states as the quantum channel. The effects of the environment noise on the quantum channels are considered, in which the time-evolution is ruled by the master equations of the density matrices in the Lindblad form. We investi- gated the influence of environment noise on the fidelity of the remote state preparation based on three types of quantum channels. It is found that the output state of remote state preparation, as time goes on, has a higher fidelity in the case of the quantum channel consists of |01> and |10> basis than that of |00> and |11> basis. Furthermore, the results also demonstrate that the fidelity is proportional to the product of both situations above when the channel consists of the mixture basis, and its value is between of them.
Using a GHZ-class state as a quantum channel, we investigate the remote preparation of a qubit state and that of an entangled state in noisy environments. By analytically solving the master equation in Lindblad form, we first obtain the time evolution of the GHZ-class quantum channel. Then the influence of the noises on the process of remote state preparation is considered through analytical derivation of the fidelity and numerical calculations of the corresponding average fidelity. Our results show that the fidelity depends on the noise type, the state to be remotely prepared, the GHZ-class state and the decoherence rate. Moreover, it is found that no matter whether the qubit state or the entangled state is to be remotely prepared, the maximally entangled quantum channel has a relatively stronger ability to resist the influence of noises. Besides, the effect of the bit–phase flip noise on the average fidelity is relatively stronger than that of the bit flip noise or phase flip noise.
In this paper, the theoretical investigation of remote preparation of an entangled state is studied in nonideal conditions. Our studies include two parts. In the first part, we consider the remote state preparation (RSP) of an entangled state through two equally noisy quantum channel states, namely, a mixture of Bell states. Studies show there is a particular mixed-state channel for which all pure entangled states remain entangled after this inexact RSP. In the second part, we suppose that noises which quantum channels suffer from can be expressed as the Lindblad operators. The master equation of the system can be expressed in the Lindblad form. Through solving the master equation, we calculate the fidelity as a function of decoherence rates and parameters of the state to be prepared. For a given entangled state, we investigate the influence of different types of noises on the fidelity.
提出利用两对非最大纠缠态作为量子通信通道实现二比特量子态的远程态制备方案，并使用量子纠缠态密度矩阵的Lindblad主方程推导了量子纠缠态的时间演化，研究了噪声条件下三种量子纠缠通道对二比特量子态远程制备保真度的影响。结果表明，噪声条件下由|01>与|10>基构成的量子通道比由|00>与|11>基构成的量子通道更具有保护远程制备量子态保真度的能力，由这两组基构成的混合量子通道得到的保真度正比于上述两种情况保真度之积，其保真度的值介于两者之间。 A scheme is proposed for the remote preparation of a two qubit quantum state by using two nonmaximally entangled states as the quantum channel. The effects of the environment noise on the quantum channels are considered, in which the time-evolution is ruled by the master equations of the density matrices in the Lindblad form. We investigated the influence of environment noise on the fidelity of the remote state preparation based on three types of quantum channels. It is found that the output state of remote state preparation, as time goes on, has a higher fidelity in the case of the quantum channel consists of |01> and |10> basis than that of |00> and |11> basis. Furthermore, the results also demonstrate that the fidelity is proportional to the product of both situations above when the channel consists of the mixture basis, and its value is between of them.
A scheme is proposed for the remote preparation of an arbitrary two-particle quantum state by using two nonmaximally entangled states as the quantum channel. The effects of the environment noise on the quantum channels are considered, in which the time-evolution is ruled by the master equations of the density matrices in the Lindblad form. We investigated the influence of environment noise on the fidelities of the remote state preparation based on three types of quantum channels. It is found that the output state of remote state preparation, as time goes on, has a higher fidelity in the case of the quantum channel consists of |01) and |10) basis than that of |00) and |11) basis. Furthermore, the results also demonstrate that the fidelity is proportional to the product of both situations above when the quantum channel consists of the mixture basis, and its value is between of them.