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The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.

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Bichen Che, Shuntian Zheng, Zhao Dou, Xiubo Chen, Lixiang Li, Jian Li, and Yixian Yang J. Opt. Commun. Netw. 16(3) 317-327 (2024)

Relationship between the Measurement Results of the Auxiliary Particles a 1 , a 2 , and a 3 , the Measurement Basis for Preparing the Amplitude Information and Phase Information, and the Recovery Operation of the Receiver

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The weight graph states (WGS) usually serve as the imperfect generation of the graph states due to the limitation in experiments. In this paper, we study the deterministic remote state preparation (RSP) protocol by leveraging multiple WGS. First, we introduce the quantum circuit of the entanglement concentration based on the theory of majorization, calculating the entanglement coefficients by applying the Schmidt decomposition onto the bipartite WGS. Then, we establish the positive operator-valued measurement (POVM) that helps to extract available entanglement for the RSP protocol. In three-particle 1D WGS, we demonstrate that the bipartite entanglement between the sender and the receiver depends on the measurement basis selected by the repeater node. Here we find a set of orthogonal bases that retains the entanglement unchanged, which guarantees the robustness of the RSP scheme. In the end, we discuss the performance of our protocol and extend the channel to the multi-particle 1D WGS, illustrating the relationship between the entanglements and the different weights of edges. Our scheme provides a viable method to reuse the imperfect graph states, hoping to contribute to the future study of graph states in quantum networks.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Relationship between the Final Results of the Particle B 1 and the Measurement Result of the Particles a 1 , a 2 , A 1 , A 2 , and B 2