Abstract: A perfect protocol for bidirectional controlled teleportation (BCT) of three-dimensional single-particle states is put forward by using pre-shared two generalized maximally entangled GHZ states as the quantum channel. In the protocol, two distant parties can simultaneously and deterministically exchange their three-dimensional single-particle states under control of a third remote party in such a way that it cannot succeed without permission of the controller. In order to extend this protocol, two protocols for bidirectional controlled teleportation of three-dimensional single-particle states are proposed by using projective measurement and positive operator-valued measurement, respectively. In these two protocols, two generalized non-maximally entangled GHZ states are employed as the quantum channel linking three legitimate participants, and the quantum task can also be achieved with certain probability.

Key words: bidirectional controlled teleportation, three-dimensional quantum state, generalized GHZ state, projective measurement, positive operator-valued measurement

摘要： 以事先分享的两个广义最大纠缠GHZ态为量子信道，提出了一个三维单粒子态双向受控隐形传态协议。在该协议中，遥远的两方可以在第三个遥远方的控制下同时、确定性地交换他们的三维单粒子态，这种交换在没有控制者的许可下是不会成功的。为了推广这一协议，采用投影测量和正算子值测量，分别提出了两个双向受控的三维单粒子态隐形传输协议。在这两个协议中，两个广义非最大纠缠GHZ态被用作量子信道来连接三个合法参与者，量子任务总能以一定的概率来完成。

关键词: 双向受控隐形传态, 三维量子态, 广义GHZ态, 投影测量, 正算子值测量