We present a scheme for multi-hop cyclic joint remote state preparation by fusing the ideas of multi-hop teleportation and cyclic joint remote state preparation. To realize n −hop cyclic joint remote state preparation, we suppose that there are n + 2 subsystems. S1, S2 and S3 constitute a cycle in the first hop. Based on it, S3, S4 and S5 form another cycle as the second hop. Notably, S3 is an intermediate node used to connect these two hops. Then, we can obtain n cycles (hops) in the same way. Specially, if n + 2 is even, there is no way to constitute n cycles. To solve this problem, we propose two different schemes. Our schemes can realize the cyclic JRSP hop by hop via the intermediate node with n + 2 subsystems. Even without direct quantum channel to connect, these subsystems also can participate in the process of preparation through intermediate nodes. Furthermore, we consider the security of our scheme by analyzing inside attack and outside attack, and we found that the success of outside attack is not affected by the attacking time. Finally, we generalized a formula to calculate the efficiency of bidirectional JRSP, which is also suitable for cyclic JRSP.
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This work is supported by the National Natural Science Foundation of China (Grant No.11671284) and Sichuan Provincial Natural Science Foundation of China (Grant No.2015JY0002, 2017JY0197).
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Zhang, C., Bai, M. Multi-Hop Cyclic Joint Remote State Preparation. Int J Theor Phys (2020). https://doi.org/10.1007/s10773-020-04405-4
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