Asymmetric Bidirectional Controlled Teleportation by Using Nine-Qubit Entangled State in Noisy Environment

In this paper, a novel protocol for asymmetric bidirectional controlled quantum teleportation (ABCQT) by using the nine-qubit entangled state as a quantum channel is proposed. Alice transmits an arbitrary three-qubit entangled state to Bob and at the same time, Bob transmits an arbitrary single-qubit entangled state to Alice under the permission of a third party as a controller. This protocol is based on the Hadamard (H) gates, controlled-not (CNOT) operations, appropriate unitary operations, and single-qubit Von Neumann measurements (SM) which are more efficient than multi-qubit joint measurements (JM). This scheme explicitly shows how the channel of nine-qubit entangled state prepares, and it is discussed in six types of noisy scenarios (amplitude-damping, phase-damping, bit-flip, phase-flip, bit-phase-flip, and depolarizing noisy scenarios). Then, we analytically derive the fidelities of the ABCQT process and show that they only depend on the amplitude parameter of the initial state and the decoherence noisy rate. Finally, compared with previous schemes, this scheme also shows remarkable advantages.