采用张量表示和广义三维贝尔基测量的方法, 提出了实现三能级单量子态控制双向量子隐形传态的协议.协议中, 控制者Carol的量子态为任意广义三维贝尔基.选择六粒子纠缠态作为量子通道, 并给出了判断任意六粒子纠缠态能否作为量子通道的必要条件.基于该条件, 借助SO(3)群元素的幺正性, 选择其任意两个元素作为幺正矩阵, 给出了构建量子通道的一般方法.列举了两个具体构建量子通道的例子, 其中Alice、Bob、Carol共同作用, 进行相应的广义三维贝尔基测量和对应的幺正变换, 最终实现了Alice和Bob之间量子态的交换, 从而验证了所提协议的可行性.

In order to realize the single-qutrit state controlled bidirectional quantum teleportation, a protocol was proposed by using the methods of tensor representation and generalized three-dimensional Bell basis measurement. In this protocol, the quantum state of the controller Carol is arbitrary generalized three-dimensional Bell basis. The six-qutrit entangled state was chosen as the initial quantum channel, and the necessary conditions to judge whether any six-qutrit entangled state could be used as quantum channel were given. Based on the necessary conditions, with the aid of the unitary property of the SO(3) group element, a general method for constructing quantum channels was given by selecting its arbitrary two elements as the unitary matrices. Two specific examples were given, in which Alice, Bob and Carol worked together by performing generalized three-demensional Bell basis measurement and corresponding unitary transformation. At last, the exchange of quantum state between Alice and Bob was achieved, which verified the feasibility of the proposed protocol.