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Modern Physics

Probabilistic Remote State Preparation of an Arbitrary Two-Qubit State via Two Three-Qubit Partially Entangled States

毅琼 徐

Published Jan 1, 2017• 0 citations
Publisher

Abstract

本文提出了一种基于两个三粒子部分纠缠GHZ态的任意两粒子远程态制备方案。此制备协议并不需要引入辅助粒子，总体成功概率等于纠缠通道两个最小幅值模平方之积。结合具体幺正矩阵与测量基形式，本文给出了制备协议实现步骤。当纠缠通道取为两个最大纠缠GHZ态时，总体成功概率则等于1/4。 In this paper, we presented a novel scheme for probabilistic remote preparation of arbitrary two-qubit state via two three-qubit GHZ states. Any auxiliary particles need not to be introduced in our proposal. The total successful probability is equal to the square of the norm of the minimum amplitude coefficients of the partially entangled channel. The concrete processe of this scheme is presented via some appropriate local unitary operations and measurement basis. When quantum channel is composed of two three-qubit maximally entangled states, the successful probability is equal to 1/4.

DOI
10.12677/mp.2017.76031

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本文提出了一种基于两个三粒子部分纠缠GHZ态的任意两粒子远程态制备方案。此制备协议并不需要引入辅助粒子，总体成功概率等于纠缠通道两个最小幅值模平方之积。结合具体幺正矩阵与测量基形式，本文给出了制备协议实现步骤。当纠缠通道取为两个最大纠缠GHZ态时，总体成功概率则等于1/4。 In this paper, we presented a novel scheme for probabilistic remote preparation of arbitrary two-qubit state via two three-qubit GHZ states. Any auxiliary particles need not to be introduced in our proposal. The total successful probability is equal to the square of the norm of the minimum amplitude coefficients of the partially entangled channel. The concrete processe of this scheme is presented via some appropriate local unitary operations and measurement basis. When quantum channel is composed of two three-qubit maximally entangled states, the successful probability is equal to 1/4.
We propose a novel and efficient scheme for probabilistic controlled remote state preparation of an arbitrary two-qubit quantum state with the aid of the introduction of auxiliary particles and some appropriate local unitary operations. In this scheme, two partially three-qubit entangled states are used as quantum channel. The controlled preparation with one sender, two receivers and one controller can be realized when the information of nonmaximally entangled states are only available for the sender. Furthermore, the concrete implementation processes of this proposal are presented, and the successful probability of our scheme are calculated in the general case and special case, respectively.
An efficient proposal for probabilistic remote preparation of single-states is presented by using of four-qubit GHZ states without the introduction of auxiliary particles in this paper. It is noting that this scheme can be utilized to perform the remote state preparation when the information of the partially four-qubit GHZ state is only available for the sender. Some appropriate local unitary operations need to be introduced to improve the successful probability of the preparation, and the total probability is twice as much as the one of the previous proposals. Thus, our scheme can expand the research range of the preparation.
\n Recently Liu et al. (EPL, 87 (2009) 30006) have proposed two new schemes for probabilistically preparing arbitrary two- and three-qubit states with complex coefficients based on two- and three-qubit projective measurement, respectively. In this letter, we present a possible improvement of the successful probability for their schemes. For this purpose, we put forward two novel schemes for remote preparation of arbitrary two- and three-qubit states with complex coefficients via two and three GHZ states as the quantum channel, respectively. To complete the schemes, two novel unitary operations have been introduced. Compared with the previous schemes, the advantage of our schemes is that the total successful probability can reach 100%.\n
We present a scheme for remotely preparing an arbitrary two-qubit pure state by using two bipartite partially entangled states as the quantum channel, the scheme is then generalized to the arbitrary three-qubit case. For the two cases of remote state preparation, we construct two different efficient projective measurement bases at sender's side and calculate the corresponding success probabilities. It is shown that remote preparation of the two-qubit or three-qubit state can be probabilistically achieved with unity fidelity. Moreover, for some special ensembles of the initial states, we find that the success probability of preparation can be increased to four times for two-qubit states and eight times for three-qubit states, and is equal to one in the case of the maximal entanglement resources.
Using partial entangled states as the quantum channel, two schemes for probabilistic remote preparation of the four-particle cluster-type state with real and complex coefficients are presented. In the first scheme, the sender and the receiver share two partial Bell states and one partial three-qubit GHZ stats as the quantum channel, and the sender can help a remote receiver to prepare a four-particle entangled cluster-type state by using three-qubit projective measurements with certain probability. In the second scheme, the quantum channel is composed of two partial three-qubit GHZ states, the remote state preparation (RSP) can be successfully realized via the positive operator valued measure (POVM), and the two-particle projective measurements are also needed in this process. The total success probability and classical communication cost are calculated.
We present two schemes for preparing remotely a three-particle entangled state by two different quantum channels. In the first scheme, two partial three-particle entangled states are used as the quantum channels, while in the second scheme, three two-particle non-maximally entangled states are employed as the quantum channels. It is shown that the remote state preparation can be successfully realized with certain probability, for both two schemes, if a sender performs some projective measurements and a receiver adopts some appropriate unitary transformations. It is shown also that the successful probabilities of these two schemes are different.