In this paper, a novel protocol for bidirectional controlled quantum teleportation (BCQT) using eight-qubit entangled state as a quantum channel is proposed by which the users can teleport an arbitrary entangled state and a pure two-qubit state to each other simultaneously under permission of a third party as a controller. This protocol is based on the controlled-not operation, appropriate single-qubit unitary operations and single-qubit measurements in the Z and X basis which are more efficient than two-qubit measurements. In addition, in this protocol, the probability of guessing Charlie's qubit by eavesdropper is reduced and supervisor can select the control of one of the users or both. Also, the proposed protocol is optimal in terms of used quantum resources, the efficiency and the number of measurements into previous ones. Then, we review the proposed protocol in typical noisy channels including the amplitude-damping and the phase-damping noises. We analytically derive the fidelities of the BCQT process and show that they only depend on the amplitude parameter of the initial state and the decoherence noisy rate.

中文翻译：

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在嘈杂环境中使用八量子位量子通道进行双向控制量子隐形传态

在本文中，提出了一种使用八量子位纠缠态作为量子通道的双向受控量子隐形传态（BCQT）的新协议，通过该协议，用户可以在许可的情况下同时将任意纠缠态和纯两量子位态相互传送。第三方作为控制者。该协议基于受控非操作、适当的单量子位单一操作和 Z 和 X 基础上的单量子位测量，它们比两个量子位测量更有效。此外，在该协议中，窃听者猜测查理量子比特的概率降低了，监督者可以选择控制其中一个用户或两者。此外，所提出的协议在使用的量子资源、效率和测量次数方面是最佳的。然后，我们在典型的噪声通道中审查了提议的协议，包括幅度阻尼和相位阻尼噪声。我们通过分析推导出 BCQT 过程的保真度，并表明它们仅取决于初始状态的幅度参数和退相干噪声率。