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. S 1 , S 2 and S 3 constitute a cycle in the first hop. Based on it, S 3 , S 4 and S 5 form another cycle as the second hop. Notably, S 3 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.

中文翻译：

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多跳循环联合远程状态准备

我们融合了多跳隐形传态和循环联合远程状态准备的思想，提出了一种多跳循环联合远程状态准备的方案。为了实现n-hop循环联合远程状态准备，我们假设有n+2个子系统。S 1 、S 2 和S 3 在第一跳中构成一个循环。在此基础上，S 3 、S 4 和S 5 形成另一个循环作为第二跳。值得注意的是，S 3 是用于连接这两个跳的中间节点。然后，我们可以用同样的方式获得 n 个周期（跳）。特别地，如果n + 2 是偶数，则无法构成n 个循环。为了解决这个问题，我们提出了两种不同的方案。我们的方案可以通过具有 n + 2 个子系统的中间节点逐跳实现循环 JRSP。即使没有直接的量子通道连接，这些子系统也可以通过中间节点参与准备过程。此外，我们通过分析内部攻击和外部攻击来考虑我们方案的安全性，我们发现外部攻击的成功不受攻击时间的影响。最后，我们概括了一个公式来计算双向 JRSP 的效率，该公式也适用于循环 JRSP。